{"title":"Robotics","prompt":"I want to understand robotics","summary":"A robot is a machine that senses, decides and acts in the physical world, in a loop. Its body may use rigid links and joints, continuously bending structures, or both, moved by actuators and watched by sensors. Software turns sensor data into an estimate of where the robot and the objects around it are, plans a motion, and a controller drives the actuators to follow that motion while sensors report the result. The same parts and loops sit under every form: an arm in a factory cell, a warehouse robot, a quadruped, a humanoid, a drone. Practitioners spend most of their time on the gaps between model and reality: calibration, noise, delay, contact and safety.","root":"robot","nodes":[{"term":"Robot","aka":["robot at work","mobile manipulator"],"kind":"product","plain":"A robot is a machine that senses, computes and acts on the physical world through actuators. 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In most robots the links are rigid; a continuum arm bends along a flexible backbone instead. Its geometry limits reach, dexterity, payload and stiffness before software begins.","does":"It defines the robot's possible configurations and motions.","ask":"Can the mechanism reach every required pose while carrying the load?","cues":["Connected links and joints","Rigid links or a flexible backbone","Reach, dexterity, payload and stiffness set by geometry"],"children":["robot-arm","links-and-joints","degrees-of-freedom","workspace","kinematics","end-effector","drive-base"],"at":[0.36,0.95,0.05],"variants":[{"label":"Body","items":[{"id":"body-rigid","name":"Rigid link chain","plain":"Rigid links joined by joints, each joint adding a known motion. Most arms, from industrial robots to hobby servo arms, are built this way.","sources":[{"label":"Kevin M. Lynch and Frank C. 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The simple constant-curvature model treats each segment as one arc and ignores the backbone's elasticity, loads and gravity.","sources":[{"label":"Jessica Burgner-Kahrs, Constant-Curvature Model of Tendon-driven Continuum Robots","url":"https://www.opencontinuumrobotics.com/101/2022/12/09/tdcr-cc-model.html","kind":"practitioner","page":"Planar Bending Segment","quote":"Pulling on one tendon requires releasing the other tendon in order to achieve bending.","work":"jessica-burgner-kahrs-constant-curvature-model-of"},{"label":"Jessica Burgner-Kahrs, Constant-Curvature Model of Tendon-driven Continuum Robots","url":"https://www.opencontinuumrobotics.com/101/2022/12/09/tdcr-cc-model.html","kind":"practitioner","page":"Remarks","quote":"The kinematic formulation cannot account for the elastic properties of the backbone. It cannot account for any external forces or moments or gravity","work":"jessica-burgner-kahrs-constant-curvature-model-of"},{"label":"Wikipedia, Snake-arm robot","url":"https://en.wikipedia.org/wiki/Snake-arm_robot","kind":"reference","page":"Definition","quote":"Snake-arm robots are also described as continuum robots and elephant's trunk robots","work":"wikipedia-snake-arm-robot"}],"look":{"parts":[{"shape":"cylinder","radiusTop":0.014,"radiusBottom":0.014,"height":0.089,"pos":[0.184,0.662,0.05],"rot":[0,0,-18.496],"color":"#9aa0aa","material":"metal","slot":"arm"},{"shape":"cylinder","radiusTop":0.014,"radiusBottom":0.014,"height":0.075,"pos":[0.214,0.738,0.05],"rot":[0,0,-25.408],"color":"#9aa0aa","material":"metal","slot":"arm"},{"shape":"cylinder","radiusTop":0.014,"radiusBottom":0.014,"height":0.064,"pos":[0.249,0.798,0.05],"rot":[0,0,-35.066],"color":"#9aa0aa","material":"metal","slot":"arm"},{"shape":"cylinder","radiusTop":0.014,"radiusBottom":0.014,"height":0.054,"pos":[0.287,0.842,0.05],"rot":[0,0,-48.507],"color":"#9aa0aa","material":"metal","slot":"arm"},{"shape":"cylinder","radiusTop":0.014,"radiusBottom":0.014,"height":0.049,"pos":[0.33,0.87,0.05],"rot":[0,0,-65.99],"color":"#9aa0aa","material":"metal","slot":"arm"},{"shape":"cylinder","radiusTop":0.014,"radiusBottom":0.014,"height":0.049,"pos":[0.377,0.882,0.05],"rot":[0,0,-85.343],"color":"#9aa0aa","material":"metal","slot":"arm"},{"shape":"cylinder","radiusTop":0.014,"radiusBottom":0.014,"height":0.055,"pos":[0.428,0.878,0.05],"rot":[0,0,-102.688],"color":"#9aa0aa","material":"metal","slot":"arm"},{"shape":"cylinder","radiusTop":0.014,"radiusBottom":0.014,"height":0.064,"pos":[0.484,0.858,0.05],"rot":[0,0,-115.964],"color":"#9aa0aa","material":"metal","slot":"arm"},{"shape":"cylinder","radiusTop":0.014,"radiusBottom":0.014,"height":0.076,"pos":[0.543,0.822,0.05],"rot":[0,0,-125.494],"color":"#9aa0aa","material":"metal","slot":"arm"},{"shape":"cylinder","radiusTop":0.014,"radiusBottom":0.014,"height":0.089,"pos":[0.607,0.77,0.05],"rot":[0,0,-132.317],"color":"#9aa0aa","material":"metal","slot":"arm"},{"shape":"cylinder","radiusTop":0.057,"radiusBottom":0.057,"height":0.02,"pos":[0.198,0.704,0.05],"rot":[0,0,-21.671],"color":"#d9dde3","material":"gloss","slot":"arm"},{"shape":"cylinder","radiusTop":0.055,"radiusBottom":0.055,"height":0.02,"pos":[0.23,0.772,0.05],"rot":[0,0,-29.827],"color":"#d9dde3","material":"gloss","slot":"arm"},{"shape":"cylinder","radiusTop":0.053,"radiusBottom":0.053,"height":0.02,"pos":[0.267,0.824,0.05],"rot":[0,0,-41.26],"color":"#d9dde3","material":"gloss","slot":"arm"},{"shape":"cylinder","radiusTop":0.05,"radiusBottom":0.05,"height":0.02,"pos":[0.308,0.86,0.05],"rot":[0,0,-56.807],"color":"#d9dde3","material":"gloss","slot":"arm"},{"shape":"cylinder","radiusTop":0.048,"radiusBottom":0.048,"height":0.02,"pos":[0.353,0.88,0.05],"rot":[0,0,-75.677],"color":"#d9dde3","material":"gloss","slot":"arm"},{"shape":"cylinder","radiusTop":0.045,"radiusBottom":0.045,"height":0.02,"pos":[0.402,0.884,0.05],"rot":[0,0,-94.467],"color":"#d9dde3","material":"gloss","slot":"arm"},{"shape":"cylinder","radiusTop":0.042,"radiusBottom":0.042,"height":0.02,"pos":[0.455,0.872,0.05],"rot":[0,0,-109.85],"color":"#d9dde3","material":"gloss","slot":"arm"},{"shape":"cylinder","radiusTop":0.04,"radiusBottom":0.04,"height":0.02,"pos":[0.512,0.844,0.05],"rot":[0,0,-121.133],"color":"#d9dde3","material":"gloss","slot":"arm"},{"shape":"cylinder","radiusTop":0.037,"radiusBottom":0.037,"height":0.02,"pos":[0.574,0.8,0.05],"rot":[0,0,-129.182],"color":"#d9dde3","material":"gloss","slot":"arm"},{"shape":"cylinder","radiusTop":0.035,"radiusBottom":0.035,"height":0.02,"pos":[0.64,0.74,0.05],"rot":[0,0,-135],"color":"#d9dde3","material":"gloss","slot":"arm"}]}}]}],"sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 2 §§2.1–2.5; Ch. 4","quote":"Basically, a mechanism is constructed by connecting rigid bodies, called links, together by means of joints, so that relative motion between adjacent links becomes possible.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"},{"label":"Jessica Burgner-Kahrs, Continuum Robotics 101","url":"https://www.opencontinuumrobotics.com/101/2022/10/21/cr-intro.html","kind":"practitioner","page":"Definition","quote":"Continuum robots do not contain rigid links and identifiable rotational joints. Instead the structures bend continuously along their length via elastic deformation and produce motion through the generation of smooth curves, similar to tentacles or tongues of the animal kingdom.","work":"morphology-cr-intro"}],"id":"mechanism","look":{"parts":[{"shape":"box","size":[0.62,0.26,0.5],"pos":[0,0.22,0],"color":"#3a3f47","material":"matte","radius":0.04},{"shape":"box","size":[0.64,0.035,0.52],"pos":[0,0.1,0],"color":"#e8b82e","material":"matte"},{"shape":"cylinder","radiusTop":0.1,"radiusBottom":0.1,"height":0.06,"pos":[-0.34,0.1,0.04],"color":"#16181c","rot":[0,0,90],"material":"matte"},{"shape":"cylinder","radiusTop":0.1,"radiusBottom":0.1,"height":0.06,"pos":[0.34,0.1,0.04],"color":"#16181c","rot":[0,0,90],"material":"matte"},{"shape":"cylinder","radiusTop":0.04,"radiusBottom":0.04,"height":0.07,"pos":[-0.34,0.1,0.04],"color":"#9aa0aa","rot":[0,0,90],"material":"metal"},{"shape":"cylinder","radiusTop":0.04,"radiusBottom":0.04,"height":0.07,"pos":[0.34,0.1,0.04],"color":"#9aa0aa","rot":[0,0,90],"material":"metal"},{"shape":"cylinder","radiusTop":0.06,"radiusBottom":0.06,"height":0.2,"pos":[0.17,0.445,0.05],"color":"#d9dde3","material":"gloss"},{"shape":"cylinder","radiusTop":0.075,"radiusBottom":0.075,"height":0.09,"pos":[0.17,0.505,0.05],"color":"#d9dde3","material":"gloss"},{"shape":"cylinder","radiusTop":0.062,"radiusBottom":0.062,"height":0.14,"pos":[0.17,0.58,0.05],"color":"#2f6fd6","rot":[90,0,0],"material":"gloss"},{"shape":"cylinder","radiusTop":0.042,"radiusBottom":0.042,"height":0.4159,"pos":[0.265,0.765,0.05],"rot":[0,0,-27.18],"color":"#d9dde3","material":"gloss","slot":"arm"},{"shape":"cylinder","radiusTop":0.052,"radiusBottom":0.052,"height":0.12,"pos":[0.36,0.95,0.05],"color":"#2f6fd6","rot":[90,0,0],"material":"gloss","slot":"arm"},{"shape":"cylinder","radiusTop":0.036,"radiusBottom":0.036,"height":0.2907,"pos":[0.49,0.885,0.05],"rot":[0,0,-116.57],"color":"#d9dde3","material":"gloss","slot":"arm"},{"shape":"cylinder","radiusTop":0.042,"radiusBottom":0.042,"height":0.1,"pos":[0.62,0.82,0.05],"color":"#2f6fd6","rot":[90,0,0],"material":"gloss","slot":"arm"},{"shape":"cylinder","radiusTop":0.03,"radiusBottom":0.03,"height":0.1077,"pos":[0.64,0.77,0.05],"rot":[0,0,-158.2],"color":"#d9dde3","material":"gloss","slot":"arm"},{"shape":"box","size":[0.12,0.035,0.06],"pos":[0.66,0.68,0.05],"color":"#2b3038","material":"matte"},{"shape":"box","size":[0.016,0.085,0.034],"pos":[0.62,0.622,0.05],"color":"#5b616b","material":"metal"},{"shape":"box","size":[0.016,0.085,0.034],"pos":[0.7000000000000001,0.622,0.05],"color":"#5b616b","material":"metal"}]}},{"term":"Robot arm (manipulator)","aka":["robot arms","robotic arm","manipulator arm","articulated arm","snake-like arm"],"kind":"part","plain":"A robot arm positions a tool or hand through a moving structure. 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Choose the movement and load requirements before copying the outer shape.","children":["arm-architecture","tendon-drive","arm-shell","arm-prototyping"],"at":[0.36,0.95,0.05],"links":[{"to":"end-effector","rel":"see also"},{"to":"workspace","rel":"see also"},{"to":"degrees-of-freedom","rel":"see also"},{"to":"kinematics","rel":"see also"},{"to":"actuation","rel":"see also"},{"to":"safety","rel":"see also"}],"sources":[{"label":"Jessica Burgner-Kahrs, Continuum Robotics 101","url":"https://www.opencontinuumrobotics.com/101/2022/10/21/cr-intro.html","kind":"practitioner","page":"Introduction; Definition","quote":"The boundary that separates continuum robots from other snake-like or hyper-redundant manipulators is sometimes obscured by manipulator designs that use continuously bending elastic elements along with conventional discrete joints in the same structure.","work":"morphology-cr-intro"},{"label":"Kevin M. Lynch and Frank C. 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Count independently actuated coordinates rather than counting ribs or cosmetic rings.","trouble":"Calling a ribbed exterior continuum, or calling a long segmented arm soft, can hide the load path and the model you actually need.","at":[0,0.33,0],"links":[{"to":"links-and-joints","rel":"see also"},{"to":"degrees-of-freedom","rel":"see also"},{"to":"tendon-drive","rel":"see also"}],"variants":[{"label":"Architecture","items":[{"id":"architecture-serial","name":"Serial articulated","plain":"A finite chain of rigid links and identifiable revolute or prismatic joints; this is the baseline arm topology taught in conventional manipulator kinematics.","sources":[{"label":"Jessica Burgner-Kahrs, Continuum Robotics 101","url":"https://www.opencontinuumrobotics.com/101/2022/10/21/cr-intro.html","kind":"practitioner","page":"Continuum Robotics 101: serial and rigid-link robots","quote":"Those robots are inspired by the human anatomy as they resemble a similar structure in terms of rigid-links and joints.","work":"morphology-cr-intro"}]},{"id":"architecture-hyperredundant","name":"Hyper-redundant / snake-like","plain":"A serial arm with many short links and joints can approximate a smooth snake or tentacle silhouette; it remains a finite-joint mechanism rather than a strict continuum.","sources":[{"label":"Jessica Burgner-Kahrs, Continuum Robotics 101","url":"https://www.opencontinuumrobotics.com/101/2022/10/21/cr-intro.html","kind":"practitioner","page":"Continuum Robotics 101: hyper-redundant robots","quote":"The more joints one adds and the shorter the link length in between these joints becomes, the robot structure becomes hyperredundant","work":"morphology-cr-intro"},{"label":"Ian D. 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It overlaps with continuum robotics when the body bends continuously; the labels describe different properties of the construction.","sources":[{"label":"Matthew Borgatti, Adafruit Silicone Robo-Tentacle","url":"https://learn.adafruit.com/silicone-robo-tentacle/a-little-background","kind":"maker","page":"A little background","quote":"Soft robots can potentially do a lot of jobs a hard robot made of steel and servos just can't do. 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A finite number of spacer disks is equally distributed along the whole length of the TDCR. 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Loc-Line comparison","quote":"No spring back - unlike the metal coil goosenecks, the ball and socket joints have no spring back.","work":"morphology-hackaday-gooseneck"}],"unverified":"No opened maker or lab source in this pass establishes a universal home-built sleeve material, thickness or load rating. Treat a cosmetic shell as non-load-bearing until the specific build proves its clearance, wear and load path.","deeper":"Next level: make a removable collar, choose sleeve versus bellows from the joint travel, leave a separate tendon/wire service path, and cycle the bare mechanism before fitting the cover.","id":"arm-shell","look":{"parts":[{"shape":"box","size":[0.46,0.06,0.38],"pos":[0,0.03,0],"radius":0.02,"color":"#aeb6c2","material":"metal","slot":"mechanism"},{"shape":"cylinder","radiusTop":0.1,"radiusBottom":0.1,"height":0.06,"pos":[0,0.09,0],"color":"#343a43","material":"matte","slot":"mechanism"},{"shape":"box","size":[0.07,0.547,0.06],"pos":[0.033,0.442,0],"rot":[0,0,-6.88],"color":"#c3cad2","material":"metal","slot":"mechanism"},{"shape":"box","size":[0.06,0.527,0.055],"pos":[0.308,0.816,0],"rot":[0,0,-67.04],"color":"#c3cad2","material":"metal","slot":"mechanism"},{"shape":"cylinder","radiusTop":0.07,"radiusBottom":0.07,"height":0.2,"pos":[0,0.17,0],"rot":[90,0,0],"color":"#d58b31","material":"gloss","slot":"mechanism"},{"shape":"cylinder","radiusTop":0.06,"radiusBottom":0.06,"height":0.18,"pos":[0.066,0.713,0],"rot":[90,0,0],"color":"#d58b31","material":"gloss","slot":"mechanism"},{"shape":"box","size":[0.035,0.185,0.07],"pos":[0.551,0.919,0],"rot":[0,0,-157.04],"color":"#343a43","material":"metal","slot":"mechanism"},{"shape":"box","size":[0.035,0.083,0.06],"pos":[0.635,0.873,0],"rot":[0,0,-67.04],"color":"#343a43","material":"metal","slot":"mechanism"},{"shape":"box","size":[0.035,0.082,0.06],"pos":[0.576,1.011,0],"rot":[0,0,-67.04],"color":"#343a43","material":"metal","slot":"mechanism"},{"shape":"cylinder","radiusTop":0.125,"radiusBottom":0.125,"height":0.32,"pos":[0.029,0.408,0],"rot":[0,0,-6.88],"color":"#3a414b","material":"gloss","cut":110,"slot":"outer"},{"shape":"cylinder","radiusTop":0.115,"radiusBottom":0.115,"height":0.35,"pos":[0.362,0.839,0],"rot":[0,0,-67.04],"color":"#3a414b","material":"gloss","cut":110,"slot":"outer"},{"shape":"torus","radius":0.125,"tube":0.024,"pos":[0.048,0.567,0],"rot":[-90,6.88,6.88],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"torus","radius":0.125,"tube":0.024,"pos":[0.052,0.597,0],"rot":[-90,9.51,9.51],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"torus","radius":0.125,"tube":0.024,"pos":[0.059,0.626,0],"rot":[-90,17.35,17.35],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"torus","radius":0.125,"tube":0.024,"pos":[0.07,0.654,0],"rot":[-90,25.19,25.19],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"torus","radius":0.125,"tube":0.024,"pos":[0.084,0.681,0],"rot":[-90,33.03,33.03],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"torus","radius":0.125,"tube":0.024,"pos":[0.102,0.705,0],"rot":[-90,40.88,40.88],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"torus","radius":0.125,"tube":0.024,"pos":[0.124,0.726,0],"rot":[-90,48.72,48.72],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"torus","radius":0.125,"tube":0.024,"pos":[0.147,0.744,0],"rot":[-90,56.56,56.56],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"torus","radius":0.125,"tube":0.024,"pos":[0.174,0.759,0],"rot":[-90,64.4,64.4],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"torus","radius":0.125,"tube":0.024,"pos":[0.201,0.771,0],"rot":[-90,67.04,67.04],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"cylinder","radiusTop":0.112,"radiusBottom":0.112,"height":0.03,"pos":[0.05,0.582,0],"rot":[0,0,-7.32],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"cylinder","radiusTop":0.112,"radiusBottom":0.112,"height":0.03,"pos":[0.055,0.612,0],"rot":[0,0,-13.44],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"cylinder","radiusTop":0.112,"radiusBottom":0.112,"height":0.03,"pos":[0.064,0.64,0],"rot":[0,0,-21.28],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"cylinder","radiusTop":0.112,"radiusBottom":0.112,"height":0.03,"pos":[0.077,0.667,0],"rot":[0,0,-29.12],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"cylinder","radiusTop":0.112,"radiusBottom":0.112,"height":0.03,"pos":[0.093,0.693,0],"rot":[0,0,-36.96],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"cylinder","radiusTop":0.112,"radiusBottom":0.112,"height":0.03,"pos":[0.113,0.715,0],"rot":[0,0,-44.79],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"cylinder","radiusTop":0.112,"radiusBottom":0.112,"height":0.03,"pos":[0.136,0.735,0],"rot":[0,0,-52.63],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"cylinder","radiusTop":0.112,"radiusBottom":0.112,"height":0.03,"pos":[0.161,0.752,0],"rot":[0,0,-60.47],"color":"#262c34","material":"matte","slot":"outer"},{"shape":"cylinder","radiusTop":0.112,"radiusBottom":0.112,"height":0.03,"pos":[0.187,0.765,0],"rot":[0,0,-66.59],"color":"#262c34","material":"matte","slot":"outer"}]}},{"term":"Arm prototyping","aka":["prototype arm","bench arm","proof-of-motion build"],"kind":"process","plain":"Arm prototyping turns a desired gesture, payload and reach into a sequence of mockups and guarded hardware tests. Start with an unpowered geometry model; add power only after checking masses, lever arms, stops, wiring and hazards.","does":"It replaces guesses about reach, downstream link mass, torque and power with a measured build that can be changed before a full arm is assembled.","ask":"What is the smallest guarded experiment that can prove the gesture, payload, reach and joint load?","range":"Route: write the gesture and tool/payload requirement; place shoulder, elbow and wrist points in a scale drawing; weigh every proposed downstream part; make a freely movable cardboard, dowel or printed mockup with no power; build one joint with its chosen bracket, bearing, horn and actuator; restrain travel and measure force, voltage, current, temperature and supply sag at known poses; then add one link at a time until the complete small arm repeats the requirement. Keep pinch points guarded, provide a catch or support for an arm that could fall or backdrive on power removal, and keep children and bystanders outside the powered-test envelope.","trouble":"The mockup cannot reach the gesture, the shoulder sags when the elbow or payload is added, the joint binds or twists, the actuator overheats or browns out, the arm falls when torque is removed, cables enter a pinch point, or the measured envelope differs from the drawing.","at":[-0.45,0.05,0.22],"children":["joint-torque-budget","servo-joint","arm-bring-up"],"links":[{"to":"workspace","rel":"see also"},{"to":"actuation","rel":"see also"},{"to":"robot-dynamics","rel":"see also"},{"to":"safety","rel":"see also"},{"to":"risk-assessment","rel":"see also"},{"to":"emergency-stop","rel":"see also"},{"to":"field-testing","rel":"see also"}],"variants":[{"label":"Build route","items":[{"id":"route-bench-joint","name":"Bench joint first","plain":"Make a cardboard or dowel geometry mockup, then test one conventional hobby servo in a bracketed, bearing-supported joint before building the rest of the arm.","sources":[{"label":"Jan, Pololu Servo Control Interface in Detail","url":"https://www.pololu.com/blog/17/servo-control-interface-in-detail","kind":"practitioner","page":"Pulse width and calibration","quote":"There is no standard correspondence between the pulse width and the servo position.","work":"arm-build-pololu-servo-control"},{"label":"Interactive Machines, Shutter robot arm assembly","url":"https://shutter.interactive-machines.com/build/arm/","kind":"maker","page":"Steps 4–5, bearing mounts and pan plate","quote":"Attach both Bearing Mounts to the horn and idler of Servo 2 using 2 Servo Washers and 16 M2.5 x 5mm screws","work":"arm-build-shutter-arm"}]},{"id":"route-so100","name":"SO-100 / SO-101-style open build","plain":"An open SO-100 / SO-101-style arm route documented by TheRobotStudio and Hugging Face, with parts, 3D-printing and bus-motor configuration instructions. Treat its files and motor versions as version-specific; it is not a child-safety endorsement.","sources":[{"label":"TheRobotStudio and Hugging Face, SO-100 Arm sourcing and printing guide","url":"https://raw.githubusercontent.com/TheRobotStudio/SO-ARM100/main/SO100.md","kind":"maker","page":"Opening and sourcing parts","quote":"The SO-100 arm is the original robot arm designed by the [RobotStudio](https://www.therobotstudio.com) in collaboration with [Hugging Face](https://huggingface.co/lerobot).","work":"arm-build-so-arm100"},{"label":"Hugging Face LeRobot, SO-100 assembly and motor configuration","url":"https://raw.githubusercontent.com/huggingface/lerobot/main/docs/source/so100.mdx","kind":"maker","page":"Source the parts","quote":"It contains the bill of materials, with a link to source the parts, as well as the instructions to 3D print the parts.","work":"arm-build-lerobot-so100"},{"label":"Hugging Face LeRobot, SO-100 assembly and motor configuration","url":"https://raw.githubusercontent.com/huggingface/lerobot/main/docs/source/so100.mdx","kind":"maker","page":"Set the motors IDs and baudrates","quote":"Each motor is identified by a unique id on the bus.","work":"arm-build-lerobot-so100"}],"look":{"parts":[{"shape":"box","size":[0.26,0.06,0.24],"pos":[0.6,0.08,0],"color":"#eceae4","material":"matte","slot":"arm"},{"shape":"box","size":[0.12,0.08,0.16],"pos":[0.6,0.15,0],"color":"#1f2329","material":"matte","slot":"arm"},{"shape":"box","size":[0.14,0.1,0.12],"pos":[0.6,0.24,0],"color":"#1f2329","material":"matte","slot":"arm"},{"shape":"box","size":[0.07,0.354,0.07],"pos":[0.65,0.41,0],"rot":[0,0,-16.39],"color":"#eceae4","material":"matte","slot":"arm"},{"shape":"box","size":[0.13,0.09,0.11],"pos":[0.7,0.58,0],"color":"#1f2329","material":"matte","slot":"arm"},{"shape":"box","size":[0.06,0.234,0.06],"pos":[0.81,0.54,0],"rot":[0,0,-109.98],"color":"#eceae4","material":"matte","slot":"arm"},{"shape":"box","size":[0.1,0.09,0.1],"pos":[0.92,0.5,0],"color":"#1f2329","material":"matte","slot":"arm"},{"shape":"box","size":[0.08,0.08,0.1],"pos":[0.95,0.42,0],"color":"#1f2329","material":"matte","slot":"arm"},{"shape":"box","size":[0.07,0.1,0.08],"pos":[0.98,0.33,0],"color":"#1f2329","material":"matte","slot":"arm"},{"shape":"box","size":[0.03,0.122,0.05],"pos":[0.94,0.24,0],"rot":[0,0,170.54],"color":"#eceae4","material":"matte","slot":"arm"},{"shape":"box","size":[0.025,0.114,0.05],"pos":[1.015,0.245,0],"rot":[0,0,-164.74],"color":"#eceae4","material":"matte","slot":"arm"}]}},{"id":"route-openmanipulator-x","name":"ROBOTIS OpenMANIPULATOR-X route","plain":"A documented OpenMANIPULATOR-X reference route: the official instructions distinguish the official package from a home-made one and require each DYNAMIXEL to be configured before operation. Use it as a reference build, not a universal payload or safety guarantee.","sources":[{"label":"ROBOTIS, OpenMANIPULATOR-X Basic Operation","url":"https://emanual.robotis.com/docs/en/platform/openmanipulator_x/quick_start_guide_basic_operation/","kind":"maker","page":"Opening and configuration","quote":"Please note that this instruction is written for the **ROBOTIS official OpenMANIPULATOR-X package**. If you are operating a home made OpenMANIPULATOR-X, make sure to configure each DYNAMIXEL as below before operating.","work":"arm-build-openmanipulator-basic"}],"look":{"parts":[{"shape":"box","size":[0.3,0.05,0.26],"pos":[0.6,0.075,0],"radius":0.02,"color":"#c9ced4","material":"matte","slot":"arm"},{"shape":"box","size":[0.1,0.1,0.12],"pos":[0.6,0.15,0],"color":"#2a2e35","material":"gloss","slot":"arm"},{"shape":"box","size":[0.07,0.1,0.07],"pos":[0.6,0.25,0],"color":"#c9ced4","material":"matte","slot":"arm"},{"shape":"box","size":[0.1,0.1,0.12],"pos":[0.6,0.32,0],"color":"#2a2e35","material":"gloss","slot":"arm"},{"shape":"box","size":[0.055,0.283,0.06],"pos":[0.62,0.46,0],"rot":[0,0,-8.13],"color":"#c9ced4","material":"matte","slot":"arm"},{"shape":"box","size":[0.055,0.06,0.06],"pos":[0.67,0.6,0],"rot":[0,0,-90],"color":"#c9ced4","material":"matte","slot":"arm"},{"shape":"box","size":[0.1,0.1,0.12],"pos":[0.7,0.6,0],"color":"#2a2e35","material":"gloss","slot":"arm"},{"shape":"box","size":[0.055,0.204,0.06],"pos":[0.8,0.58,0],"rot":[0,0,-101.31],"color":"#c9ced4","material":"matte","slot":"arm"},{"shape":"box","size":[0.1,0.1,0.12],"pos":[0.92,0.55,0],"color":"#2a2e35","material":"gloss","slot":"arm"},{"shape":"box","size":[0.1,0.08,0.1],"pos":[0.98,0.47,0],"color":"#2a2e35","material":"gloss","slot":"arm"},{"shape":"box","size":[0.03,0.1,0.06],"pos":[0.95,0.37,0],"rot":[0,0,-180],"color":"#c9ced4","material":"matte","slot":"arm"},{"shape":"box","size":[0.03,0.1,0.06],"pos":[1.02,0.37,0],"rot":[0,0,-180],"color":"#c9ced4","material":"matte","slot":"arm"}]}}]}],"sources":[{"label":"Bruno Siciliano and Oussama Khatib (eds.), Springer Handbook of Robotics (1st ed.)","url":"https://link.springer.com/rwe/10.1007/978-3-540-30301-5_4","kind":"book","isbn":"9783540303015","page":"Chapter 4, pp. 67–86, abstract","quote":"The tasks a robot is to perform and the associated precision of its movement determine detailed features such as mechanical structure, transmission, and actuator selection.","work":"arm-build-springer-mechanisms-actuation"},{"label":"Manoel Carlos Ramon, Intel Galileo and Intel Galileo Gen 2","url":"https://link.springer.com/chapter/10.1007/978-1-4302-6838-3_11","kind":"book","isbn":"9781430268383","page":"Chapter 11, pp. 509–577, introduction","quote":"There are several factors you must consider when constructing a robot arm, including the maximum load weight, the stall torques of each one of the servos, how much weight each servo must support related to its position in the arm, and the weight each frame that constitutes the arm.","work":"arm-build-springer-robot-arm"},{"label":"ROBOTIS, XL430-W250-T technical manual and safety warnings","url":"https://emanual.robotis.com/docs/en/dxl/x/xl430-w250/","kind":"maker","page":"Safety warnings","quote":"Never place fingers, arms, toes, and other body parts near product during operation.","work":"arm-build-robotis-xl430"}],"unverified":"The staged mockup-to-joint-to-arm recipe, exact guards, current limits and test durations are conservative procedural advice rather than a certification or universal safe-force rule; adapt them through the risk assessment and each component manual.","id":"arm-prototyping","look":{"parts":[{"shape":"box","size":[1.8,0.05,0.9],"pos":[0,0.025,0],"radius":0.02,"color":"#a77b52","material":"matte","slot":"bench"},{"shape":"plane","size":[0.42,0.3],"pos":[-0.62,0.3,-0.18],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 280 200\"><rect x=\"1\" y=\"1\" width=\"278\" height=\"198\" rx=\"8\" fill=\"#f5f0e6\" stroke=\"#c7bda9\" stroke-width=\"2\"/><text x=\"16\" y=\"34\" font-family=\"Liberation Sans,Arial,sans-serif\" font-size=\"20\" font-weight=\"700\" fill=\"#2d3139\">Torque budget</text><text x=\"16\" y=\"70\" font-family=\"Liberation Mono,monospace\" font-size=\"19\" fill=\"#2d3139\">τ = Σ m·g·r</text><circle cx=\"40\" cy=\"140\" r=\"10\" fill=\"#2d3139\"/><path d=\"M40 140 H220\" stroke=\"#2d3139\" stroke-width=\"7\"/><path d=\"M220 140 V168\" stroke=\"#59616a\" stroke-width=\"2\"/><rect x=\"206\" y=\"168\" width=\"28\" height=\"22\" fill=\"#59616a\"/><path d=\"M40 112 H220\" stroke=\"#d9a84e\" stroke-width=\"2\"/><text x=\"124\" y=\"106\" font-family=\"Liberation Mono,monospace\" font-size=\"16\" fill=\"#9a6b1f\">r</text></svg>","slot":"card"},{"shape":"box","size":[0.08,0.24,0.03],"pos":[-0.62,0.17,-0.2],"color":"#aeb6c2","material":"metal","slot":"card"},{"shape":"box","size":[0.2,0.02,0.12],"pos":[-0.62,0.06,-0.2],"color":"#aeb6c2","material":"metal","slot":"card"},{"shape":"box","size":[0.16,0.03,0.12],"pos":[-0.42,0.065,0.26],"color":"#c9a26b","material":"matte","slot":"mockup"},{"shape":"box","size":[0.06,0.267,0.012],"pos":[-0.39,0.19,0.26],"rot":[0,0,-12.99],"color":"#d2ad78","material":"matte","slot":"mockup"},{"shape":"box","size":[0.05,0.161,0.012],"pos":[-0.29,0.36,0.26],"rot":[0,0,-60.26],"color":"#d2ad78","material":"matte","slot":"mockup"},{"shape":"cylinder","radiusTop":0.016,"radiusBottom":0.016,"height":0.02,"pos":[-0.36,0.32,0.272],"rot":[90,0,0],"color":"#d4af37","material":"metal","slot":"mockup"},{"shape":"cylinder","radiusTop":0.016,"radiusBottom":0.016,"height":0.02,"pos":[-0.42,0.08,0.272],"rot":[90,0,0],"color":"#d4af37","material":"metal","slot":"mockup"},{"shape":"box","size":[0.2,0.28,0.16],"pos":[-0.03,0.19,0],"color":"#aeb6c2","material":"metal","slot":"joint"},{"shape":"box","size":[0.21,0.11,0.2],"pos":[-0.03,0.38,0],"color":"#1f2329","material":"matte","slot":"joint"},{"shape":"cylinder","radiusTop":0.055,"radiusBottom":0.055,"height":0.02,"pos":[0.02,0.36,0.11],"rot":[90,0,0],"color":"#ece9e2","material":"matte","slot":"joint"},{"shape":"box","size":[0.045,0.383,0.02],"pos":[0.107,0.518,0.065],"rot":[-19.93,4.84,-27.06],"color":"#c3cad2","material":"metal","slot":"joint"},{"shape":"box","size":[0.26,0.05,0.22],"pos":[0.58,0.075,0],"color":"#343a43","material":"matte","slot":"arm"},{"shape":"box","size":[0.2,0.1,0.12],"pos":[0.58,0.22,0],"color":"#1f2329","material":"matte","slot":"arm"},{"shape":"cylinder","radiusTop":0.025,"radiusBottom":0.025,"height":0.349,"pos":[0.62,0.39,0],"rot":[0,0,-13.24],"color":"#d8b98a","material":"matte","slot":"arm"},{"shape":"box","size":[0.18,0.09,0.11],"pos":[0.66,0.56,0],"color":"#1f2329","material":"matte","slot":"arm"},{"shape":"cylinder","radiusTop":0.022,"radiusBottom":0.022,"height":0.228,"pos":[0.77,0.59,0],"rot":[0,0,-74.74],"color":"#d8b98a","material":"matte","slot":"arm"},{"shape":"box","size":[0.12,0.08,0.12],"pos":[0.3,0.09,0.32],"radius":0.02,"color":"#e5b82c","material":"gloss","slot":"stop"},{"shape":"cylinder","radiusTop":0.045,"radiusBottom":0.05,"height":0.03,"pos":[0.3,0.145,0.32],"color":"#c8463d","material":"gloss","slot":"stop"}]}},{"term":"Joint torque budget","aka":["load table","moment budget","torque sizing"],"kind":"measure","plain":"A joint torque budget lists every force that one axis must resist or create at each important configuration. It includes downstream links, servos, gearboxes, brackets, cables, tool and payload, not only the payload at the tip.","does":"It turns gesture, reach and mass measurements into a torque and power requirement that can be compared with an actuator's applicable torque-speed and thermal data.","ask":"At the worst pose, what are each mass, centre of mass, perpendicular lever arm, acceleration, friction assumption, supply voltage, current and duty cycle?","range":"Start with a free-body sketch for each joint and its unit axis a_j at each pose. For gravity, the signed scalar torque about that axis is τg,j(q) = a_j · Σ_i ((r_i − r_j) × m_i g), where r_i is each mass centre, r_j is the joint position, and g is the gravity-acceleration vector; include the end effector, payload, downstream actuators and links. In a planar arm with a horizontal joint axis, the signed gravity torque is Σ_i m_i g ℓ_i with signed horizontal lever arms ℓ_i, and its magnitude is |Σ_i m_i g ℓ_i|; opposite-sign terms reduce the net magnitude, while a vertical yaw axis gets zero gravity torque. At static hold, the commanded motor torque must oppose the applied gravity and external torque, with sign set by the chosen axis. A force at angle θ uses |τ| = rF sin θ = r⊥F only in the chosen axis/plane, so an arm's length alone is not enough. For an end-effector wrench F expressed in the frame used by J, use the Jacobian-transpose map τ_F = J(q)ᵀF; if F is a disturbance applied to the robot, the holding motor command has the opposite sign. Add acceleration/inertia, friction and transmission losses only when they are modelled or measured and record the assumptions.\n\nFor each candidate actuator record the manufacturer's stall/maximum figure, rated or continuous figure or torque-speed curve, voltage, current, speed, mass, output spline/horn, thermal limits and bus or PWM interface. Do not treat stall torque as continuous capacity. Measure a restrained joint with a known perpendicular force or load cell and log angle, supply V, current I, input P = V I, temperature, duration and supply sag; stop on unexpected motion, pinch, smoke, odour or rapid heating.","trouble":"The shoulder passes a payload-only calculation but stalls after the elbow servo is installed; torque changes sharply with pose; the quoted stall number has no duty-cycle meaning; current spikes collapse the supply; temperature rises while holding; or the physical joint flexes before the actuator reaches its quoted limit.","at":[-0.62,0.3,-0.18],"links":[{"to":"workspace","rel":"see also"},{"to":"robot-dynamics","rel":"see also"},{"to":"actuation","rel":"see also"},{"to":"electric-motor","rel":"see also"},{"to":"motor-driver","rel":"see also"},{"to":"safety","rel":"see also"},{"to":"risk-assessment","rel":"see also"}],"sources":[{"label":"OpenStax, University Physics Volume 1, §10.6 Torque","url":"https://openstax.org/books/university-physics-volume-1/pages/10-6-torque","kind":"reference","page":"§10.6, Torque","quote":"The SI unit of torque is newtons times meters, usually written as N·m.","work":"arm-build-openstax-torque"},{"label":"OpenStax, University Physics Volume 1, §10.6 Torque","url":"https://openstax.org/books/university-physics-volume-1/pages/10-6-torque","kind":"reference","page":"§10.6, Torque","quote":"The first point implies that the farther the force is applied from the axis of rotation, the greater the angular acceleration; the second implies that the effectiveness depends on the angle at which the force is applied.","work":"arm-build-openstax-torque"},{"label":"Manoel Carlos Ramon, Intel Galileo and Intel Galileo Gen 2","url":"https://link.springer.com/chapter/10.1007/978-1-4302-6838-3_11","kind":"book","isbn":"9781430268383","page":"Chapter 11, pp. 509–577, torque sizing discussion","quote":"The formula that defines torque can be expressed as follows: T = F × L","work":"arm-build-springer-robot-arm"},{"label":"Manoel Carlos Ramon, Intel Galileo and Intel Galileo Gen 2","url":"https://link.springer.com/chapter/10.1007/978-1-4302-6838-3_11","kind":"book","isbn":"9781430268383","page":"Chapter 11, pp. 509–577, several actuators","quote":"each servo will have a different torque due to its location along the arm.","work":"arm-build-springer-robot-arm"},{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics §5.2 Statics of Open Chains","url":"https://modernrobotics.northwestern.edu/nu-gm-book-resource/5-2-statics-of-open-chains/","kind":"reference","page":"§5.2, Statics of Open Chains","quote":"To resist a wrench minus F applied to the end-effector at a configuration theta, the joint torques and forces tau must be J of theta transposed times F.","work":"arm-build-modern-robotics-statics"},{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics §5.2 Statics of Open Chains","url":"https://modernrobotics.northwestern.edu/nu-gm-book-resource/5-2-statics-of-open-chains/","kind":"reference","page":"§5.2, Statics of Open Chains","quote":"This result holds no matter what frame the Jacobian and wrench are expressed in.","work":"arm-build-modern-robotics-statics"},{"label":"ROBOTIS, XL430-W250-T technical manual and safety warnings","url":"https://emanual.robotis.com/docs/en/dxl/x/xl430-w250/","kind":"maker","page":"Torque specification note","quote":"The given Stall torque rating for a servo is different from it’s continuous output rating, and may also differ from it’s expected real world performance.","work":"arm-build-robotis-xl430"},{"label":"Jan, Pololu Servo Control Interface in Detail","url":"https://www.pololu.com/blog/17/servo-control-interface-in-detail","kind":"practitioner","page":"Power and current observations","quote":"multiple servos can quickly become a very demanding load for a power supply.","work":"arm-build-pololu-servo-control"}],"unverified":"The measurement recipe and the choice of any design margin, test duration or current limit are procedural advice; no universal safe-force, safety-factor or continuous-torque value is asserted here.","deeper":"The next level would hold free-body diagrams, centre-of-mass measurements, configuration sweeps, torque-speed curves, RMS/thermal duty cycles, bearing loads, structural deflection and recorded V/I/temperature traces.","id":"joint-torque-budget","look":{"parts":[{"shape":"plane","size":[0.92,0.44],"pos":[-0.04,0.74,-0.04],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 210\"><rect x=\"1\" y=\"1\" width=\"438\" height=\"208\" rx=\"10\" fill=\"#f5f0e6\" stroke=\"#c7bda9\" stroke-width=\"2\"/><text x=\"22\" y=\"36\" font-family=\"Liberation Sans,Arial,sans-serif\" font-size=\"21\" font-weight=\"700\" fill=\"#2d3139\">Torque budget, one joint</text><text x=\"22\" y=\"72\" font-family=\"Liberation Mono,monospace\" font-size=\"19\" fill=\"#2d3139\">τ = Σ m · g · r</text><text x=\"236\" y=\"71\" font-family=\"Liberation Sans,Arial,sans-serif\" font-size=\"14\" fill=\"#59616a\">r: horizontal distance</text><path d=\"M22 88 H418\" stroke=\"#c7bda9\"/><g font-family=\"Liberation Mono,monospace\" font-size=\"16\" fill=\"#59616a\"><text x=\"22\" y=\"114\">payload + tool</text><text x=\"22\" y=\"138\">links beyond the joint</text><text x=\"22\" y=\"162\">servos beyond the joint</text></g><path d=\"M22 176 H418\" stroke=\"#c7bda9\"/><text x=\"22\" y=\"199\" font-family=\"Liberation Sans,Arial,sans-serif\" font-size=\"15\" fill=\"#9a4e3f\">worst pose, then compare with rated torque at your voltage</text></svg>"},{"shape":"box","size":[0.24,0.14,0.24],"pos":[-0.42,0.07,0],"radius":0.02,"color":"#aeb6c2","material":"metal"},{"shape":"box","size":[0.3,0.16,0.18],"pos":[-0.37,0.24,0],"color":"#1f2329","material":"matte"},{"shape":"cylinder","radiusTop":0.06,"radiusBottom":0.06,"height":0.025,"pos":[-0.42,0.24,0.1],"rot":[90,0,0],"color":"#ece9e2","material":"matte"},{"shape":"box","size":[0.045,0.74,0.025],"pos":[-0.05,0.24,0.12],"rot":[0,0,-90],"color":"#c3cad2","material":"metal"},{"shape":"cylinder","radiusTop":0.005,"radiusBottom":0.005,"height":0.11,"pos":[0.32,0.175,0.12],"rot":[0,0,-180],"color":"#d9d4c7","material":"matte"},{"shape":"lathe","profile":[[0,0],[0.07,0],[0.075,0.01],[0.075,0.1],[0.065,0.11],[0.03,0.115],[0.02,0.14],[0,0.145]],"pos":[0.32,-0.03,0.12],"color":"#5d646d","material":"metal"},{"shape":"cylinder","radiusTop":0.012,"radiusBottom":0.012,"height":0.14,"pos":[0.45,0.17,0.12],"rot":[0,0,-180],"color":"#c8463d","material":"gloss"},{"shape":"cone","radius":0.032,"height":0.065,"pos":[0.45,0.07,0.12],"rot":[0,0,-180],"color":"#c8463d","material":"gloss"},{"shape":"cylinder","radiusTop":0.006,"radiusBottom":0.006,"height":0.74,"pos":[-0.05,0.4,0.12],"rot":[0,0,-90],"color":"#d9a84e","material":"matte"},{"shape":"cylinder","radiusTop":0.006,"radiusBottom":0.006,"height":0.06,"pos":[-0.42,0.4,0.12],"color":"#d9a84e","material":"matte"},{"shape":"cylinder","radiusTop":0.006,"radiusBottom":0.006,"height":0.06,"pos":[0.32,0.4,0.12],"color":"#d9a84e","material":"matte"}]}},{"term":"Servo joint","aka":["actuated hinge","servo axis","motorized joint","hobby servo","smart servo","bus servo"],"kind":"part","plain":"A servo joint combines an actuator with a horn or hub, link bracket, supported pivot and fasteners so a commanded axis can hold a known angle. The servo output transmits torque; a bearing or through-axle should carry the link's radial and overturning loads when the design needs that support.","does":"It converts an actuator choice into a repeatable, serviceable joint while exposing the interfaces that usually cause wobble, binding, overload or wrong zero.","ask":"Is this axis best served by a simple hobby servo and pulse command, or by a smart serial/bus servo with address, feedback and limits; are the horn, bracket, bearing, voltage and controller compatible?","range":"Conventional hobby servo: start from the maker's pulse interface and calibrated neutral/limits; select torque at the actual supply voltage and leave room for the link and downstream mass. Smart serial/bus servo: match bus type, voltage, unique IDs, controller/interface and the documented position, load, voltage and temperature feedback; configure the chosen limits before motion. Neither label makes a joint safe by itself.\n\nWith power removed, fit the servo in a bracket, support the opposite pivot with a compatible bearing or through-axle when needed, centre the actuator at its documented neutral, install the matching horn/hub and attach the link without side-loading the output. Check full unpowered travel, screw clearance, horn orientation, cable strain relief and pinch points. On first power, command a tiny range on a restrained, guarded joint; compare measured angle and current with the budget before adding a link. Treat quoted stall torque as a momentary specification, not a continuous holding promise.","trouble":"The horn slips or is the wrong spline, the bearing is missing or clamped incorrectly, the bracket twists, the joint has backlash or binds, a hobby servo buzzes at its endpoint, a bus servo has duplicate IDs or wrong voltage, the output heats while holding, or power removal lets the link fall/backdrive.","at":[0.02,0.36,0.11],"links":[{"to":"links-and-joints","rel":"see also"},{"to":"actuation","rel":"see also"},{"to":"electric-motor","rel":"see also"},{"to":"gearbox","rel":"see also"},{"to":"motor-driver","rel":"see also"},{"to":"emergency-stop","rel":"see also"},{"to":"safety","rel":"see also"}],"variants":[{"label":"Servo interface","items":[{"id":"pulse-command-hobby","name":"Pulse-command hobby servo","plain":"A conventional hobby/PWM servo receives timed pulses; the REV SRS V2 is an example of a configurable pulse servo, not an addressed bus device. Its neutral and pulse-to-angle mapping are component-specific, so calibrate neutral and limits before relying on a joint angle.","sources":[{"label":"Jan, Pololu Servo Control Interface in Detail","url":"https://www.pololu.com/blog/17/servo-control-interface-in-detail","kind":"practitioner","page":"Pulse width and calibration","quote":"The pulse width is generally the most important part of the interface, and that is what we intentionally vary to change the command to the servo.","work":"arm-build-pololu-servo-control"},{"label":"Jan, Pololu Servo Control Interface in Detail","url":"https://www.pololu.com/blog/17/servo-control-interface-in-detail","kind":"practitioner","page":"Pulse width and calibration","quote":"There is no standard correspondence between the pulse width and the servo position.","work":"arm-build-pololu-servo-control"},{"label":"REV Robotics, Smart Robot Servo V2 documentation","url":"https://docs.revrobotics.com/rev-crossover-products/servo/smart-robot-servo-v2","kind":"maker","page":"Default operation","quote":"The default range for the SRS V2 is 270°. This range is mapped to an input pulse range of 500μs to 2500μs with 1500μs as the center point.","work":"arm-build-rev-smart-servo"}]},{"id":"addressed-serial-bus","name":"Addressed serial bus servo","plain":"An addressed serial/bus servo uses a compatible interface and per-motor identity; read the chosen actuator's documented feedback and operating limits before motion.","sources":[{"label":"ROBOTIS, DYNAMIXEL Selection Guide","url":"https://emanual.robotis.com/docs/en/reference/dxl-selection-guide/","kind":"maker","page":"Communication","quote":"To communicate with DYNAMIXELs using a controller, the same communication interface(TTL or RS-485) must be used.","work":"arm-build-robotis-selection"},{"label":"Hugging Face LeRobot, SO-100 assembly and motor configuration","url":"https://raw.githubusercontent.com/huggingface/lerobot/main/docs/source/so100.mdx","kind":"maker","page":"Set the motors IDs and baudrates","quote":"Each motor is identified by a unique id on the bus.","work":"arm-build-lerobot-so100"},{"label":"ROBOTIS America, DYNAMIXEL XM430-W350-T product documentation","url":"https://robotis.us/products/dynamixel-xm430-w350-t","kind":"maker","page":"Supported feedback","quote":"real-time data on position, speed, load, voltage, and temperature","work":"arm-build-robotis-xm430"}],"look":{"parts":[{"shape":"cylinder","radiusTop":0.016,"radiusBottom":0.016,"height":0.122,"pos":[-0.38,0.46,0.08],"rot":[0,0,99.46],"color":"#30353c","material":"gloss","slot":"cable"},{"shape":"cylinder","radiusTop":0.016,"radiusBottom":0.016,"height":0.17,"pos":[-0.48,0.375,0.08],"rot":[0,0,151.93],"color":"#30353c","material":"gloss","slot":"cable"},{"shape":"cylinder","radiusTop":0.016,"radiusBottom":0.016,"height":0.181,"pos":[-0.53,0.21,0.08],"rot":[0,0,173.66],"color":"#30353c","material":"gloss","slot":"cable"},{"shape":"cylinder","radiusTop":0.016,"radiusBottom":0.016,"height":0.139,"pos":[-0.38,0.565,-0.08],"rot":[0,0,59.74],"color":"#30353c","material":"gloss","slot":"cable"},{"shape":"cylinder","radiusTop":0.016,"radiusBottom":0.016,"height":0.19,"pos":[-0.47,0.69,-0.08],"rot":[0,0,18.43],"color":"#30353c","material":"gloss","slot":"cable"},{"shape":"cylinder","radiusTop":0.016,"radiusBottom":0.016,"height":0.146,"pos":[-0.48,0.85,-0.08],"rot":[0,0,-15.95],"color":"#30353c","material":"gloss","slot":"cable"},{"shape":"box","size":[0.03,0.045,0.07],"pos":[-0.31,0.47,0.08],"color":"#f1efe8","material":"matte","slot":"connector"},{"shape":"box","size":[0.03,0.045,0.07],"pos":[-0.31,0.53,-0.08],"color":"#f1efe8","material":"matte","slot":"connector"},{"shape":"box","size":[0.08,0.05,0.09],"pos":[-0.54,0.09,0.08],"color":"#f1efe8","material":"matte","slot":"connector"},{"shape":"box","size":[0.08,0.05,0.09],"pos":[-0.45,0.95,-0.08],"rot":[0,0,-16.7],"color":"#f1efe8","material":"matte","slot":"connector"}]}}]}],"sources":[{"label":"Jan, Pololu Servo Control Interface in Detail","url":"https://www.pololu.com/blog/17/servo-control-interface-in-detail","kind":"practitioner","page":"Pulse width and calibration","quote":"The pulse width is generally the most important part of the interface, and that is what we intentionally vary to change the command to the servo.","work":"arm-build-pololu-servo-control"},{"label":"Jan, Pololu Servo Control Interface in Detail","url":"https://www.pololu.com/blog/17/servo-control-interface-in-detail","kind":"practitioner","page":"Pulse width and calibration","quote":"There is no standard correspondence between the pulse width and the servo position.","work":"arm-build-pololu-servo-control"},{"label":"REV Robotics, Smart Robot Servo V2 documentation","url":"https://docs.revrobotics.com/rev-crossover-products/servo/smart-robot-servo-v2","kind":"maker","page":"Smart Robot Servo V2 overview","quote":"One SRS V2 can be used as a standard angular servo, a custom angular servo, and a continuous rotation servo by simply changing its settings with the SRS Programmer.","work":"arm-build-rev-smart-servo"},{"label":"REV Robotics, Smart Robot Servo V2 documentation","url":"https://docs.revrobotics.com/rev-crossover-products/servo/smart-robot-servo-v2","kind":"maker","page":"Angular limits","quote":"The SRS V2 can be easily configured with the SRS Programmer to limit right and left motion at two user-defined angles.","work":"arm-build-rev-smart-servo"},{"label":"REV Robotics, Smart Robot Servo V2 documentation","url":"https://docs.revrobotics.com/rev-crossover-products/servo/smart-robot-servo-v2","kind":"maker","page":"Smart Robot Servo V2 Basics","quote":"Splines are like keys, so only matched types will fit together.","work":"arm-build-rev-smart-servo"},{"label":"Interactive Machines, Shutter robot arm assembly","url":"https://shutter.interactive-machines.com/build/arm/","kind":"maker","page":"Steps 4–5, bearing mounts and pan plate","quote":"Attach both Bearing Mounts to the horn and idler of Servo 2 using 2 Servo Washers and 16 M2.5 x 5mm screws","work":"arm-build-shutter-arm"},{"label":"ROBOTIS, DYNAMIXEL Selection Guide","url":"https://emanual.robotis.com/docs/en/reference/dxl-selection-guide/","kind":"maker","page":"Communication","quote":"To communicate with DYNAMIXELs using a controller, the same communication interface(TTL or RS-485) must be used.","work":"arm-build-robotis-selection"},{"label":"Hugging Face LeRobot, SO-100 assembly and motor configuration","url":"https://raw.githubusercontent.com/huggingface/lerobot/main/docs/source/so100.mdx","kind":"maker","page":"Set the motors IDs and baudrates","quote":"Each motor is identified by a unique id on the bus.","work":"arm-build-lerobot-so100"},{"label":"ROBOTIS America, DYNAMIXEL XM430-W350-T product documentation","url":"https://robotis.us/products/dynamixel-xm430-w350-t","kind":"maker","page":"Supported feedback","quote":"real-time data on position, speed, load, voltage, and temperature","work":"arm-build-robotis-xm430"},{"label":"ROBOTIS America, DYNAMIXEL XM430-W350-T product documentation","url":"https://robotis.us/products/dynamixel-xm430-w350-t","kind":"maker","page":"Torque and feedback specifications","quote":"Estimated rated torque disclosure : This is an estimated value for continuous torque, calculated at 20% of stall torque.","work":"arm-build-robotis-xm430"}],"unverified":"Exact bracket thickness, bearing life, fastener preload, horn spline fit, allowable duty cycle and the safe restrained-test force depend on the chosen components; use their manuals and the risk assessment.","deeper":"The next level would hold joint drawings, bearing/shaft fits, horn standards, cable routing, hard stops, compliance, backlash, calibration, bus topology and service procedures.","id":"servo-joint","look":{"parts":[{"shape":"box","size":[1.1,0.05,0.62],"pos":[0,0.025,0],"radius":0.02,"color":"#a77b52","material":"matte","slot":"body"},{"shape":"box","size":[0.36,0.35,0.3],"pos":[-0.1,0.225,0],"color":"#aeb6c2","material":"metal","slot":"body"},{"shape":"box","size":[0.4,0.2,0.38],"pos":[-0.1,0.5,0],"color":"#1f2329","material":"matte","slot":"body"},{"shape":"box","size":[0.54,0.2,0.025],"pos":[-0.1,0.5,0.07],"color":"#1f2329","material":"matte","slot":"body"},{"shape":"cylinder","radiusTop":0.05,"radiusBottom":0.05,"height":0.03,"pos":[0,0.5,0.2],"rot":[90,0,0],"color":"#1f2329","material":"matte","slot":"body"},{"shape":"cylinder","radiusTop":0.1,"radiusBottom":0.1,"height":0.022,"pos":[0,0.5,0.225],"rot":[90,0,0],"color":"#ece9e2","material":"matte","slot":"output"},{"shape":"cylinder","radiusTop":0.065,"radiusBottom":0.065,"height":0.03,"pos":[0,0.5,-0.205],"rot":[90,0,0],"color":"#8b939c","material":"metal","slot":"pivot"},{"shape":"box","size":[0.09,0.42,0.018],"pos":[0.101,0.684,0.245],"rot":[0,0,-28.65],"color":"#c3cad2","material":"metal","slot":"link"},{"shape":"box","size":[0.09,0.42,0.018],"pos":[0.101,0.684,-0.235],"rot":[0,0,-28.65],"color":"#c3cad2","material":"metal","slot":"link"},{"shape":"box","size":[0.09,0.022,0.5],"pos":[0.201,0.869,0],"rot":[0,0,-28.65],"color":"#c3cad2","material":"metal","slot":"link"},{"shape":"cylinder","radiusTop":0.032,"radiusBottom":0.032,"height":0.58,"pos":[0.34,1.123,0],"rot":[0,0,-28.65],"color":"#c3cad2","material":"metal","slot":"link"},{"shape":"cylinder","radiusTop":0.02,"radiusBottom":0.02,"height":0.02,"pos":[0,0.5,0.26],"rot":[90,0,0],"color":"#aeb6c2","material":"metal","slot":"link"},{"shape":"cylinder","radiusTop":0.009,"radiusBottom":0.009,"height":0.122,"pos":[-0.36,0.46,-0.018],"rot":[0,0,99.46],"color":"#5a3a22","material":"gloss","slot":"cable"},{"shape":"cylinder","radiusTop":0.009,"radiusBottom":0.009,"height":0.153,"pos":[-0.46,0.385,-0.018],"rot":[0,0,148.39],"color":"#5a3a22","material":"gloss","slot":"cable"},{"shape":"cylinder","radiusTop":0.009,"radiusBottom":0.009,"height":0.201,"pos":[-0.51,0.22,-0.018],"rot":[0,0,174.29],"color":"#5a3a22","material":"gloss","slot":"cable"},{"shape":"cylinder","radiusTop":0.009,"radiusBottom":0.009,"height":0.122,"pos":[-0.36,0.46,0],"rot":[0,0,99.46],"color":"#c0392b","material":"gloss","slot":"cable"},{"shape":"cylinder","radiusTop":0.009,"radiusBottom":0.009,"height":0.153,"pos":[-0.46,0.385,0],"rot":[0,0,148.39],"color":"#c0392b","material":"gloss","slot":"cable"},{"shape":"cylinder","radiusTop":0.009,"radiusBottom":0.009,"height":0.201,"pos":[-0.51,0.22,0],"rot":[0,0,174.29],"color":"#c0392b","material":"gloss","slot":"cable"},{"shape":"cylinder","radiusTop":0.009,"radiusBottom":0.009,"height":0.122,"pos":[-0.36,0.46,0.018],"rot":[0,0,99.46],"color":"#e08a2e","material":"gloss","slot":"cable"},{"shape":"cylinder","radiusTop":0.009,"radiusBottom":0.009,"height":0.153,"pos":[-0.46,0.385,0.018],"rot":[0,0,148.39],"color":"#e08a2e","material":"gloss","slot":"cable"},{"shape":"cylinder","radiusTop":0.009,"radiusBottom":0.009,"height":0.201,"pos":[-0.51,0.22,0.018],"rot":[0,0,174.29],"color":"#e08a2e","material":"gloss","slot":"cable"},{"shape":"box","size":[0.07,0.06,0.08],"pos":[-0.52,0.085,0],"color":"#17191d","material":"matte","slot":"connector"}]}},{"term":"Arm bring-up","aka":["commissioning sequence","first power-up","bench checkout"],"kind":"process","plain":"Arm bring-up progresses from an unpowered mockup to one restrained axis and then a small complete arm. Check geometry first, enable one actuator, add one link at a time, then test slow unloaded motion before applying the intended payload.","does":"It catches wrong zero, wiring, polarity, limits, brownout, thermal, binding, pinch and fall/backdrive problems before a complete arm can amplify them.","ask":"What is the next smallest powered test, what can move or fall if power disappears, who is outside the envelope, and what observation makes us stop?","range":"1. Record the gesture, reach, payload, joint limits and torque budget. Complete the risk assessment; mark pinch points and a no-entry powered-test envelope. Fit mechanical travel limits, a fixed base, guards and a catch/support for links that could sag, fall or backdrive when torque is disabled. Keep children and bystanders outside the powered-test envelope.\n2. With power removed, move the mockup through the intended range. Check horn zero marks, bracket/bearing alignment, screw clearance, cable strain relief and that the end effector cannot trap fingers.\n3. Connect one joint only, at the maker's documented voltage and interface, with a restrained low-energy setup and a normal shutdown plus the appropriate emergency-stop path. Command a tiny motion. Record commanded/measured angle, supply voltage, current, input power, temperature, duration, noise, vibration and supply sag.\n4. Remove power using the planned shutdown and observe only from outside the guarded envelope whether the link sags or backdrives; on an analog hobby servo, lost control pulses may remove holding effort, while some digital servos keep holding and others turn off, so the catch must prevent a strike. Stop for unexpected motion, loss of communication, pinch, rapid heating, smoke, odour or a current spike.\n5. Add one downstream link or actuator at a time. Recheck the torque budget and repeat the single-step observation before increasing range, speed, acceleration or payload. Finish with a small complete arm, slow and unloaded first, then known loads that remain inside the documented design envelope. Log every failure and change before field testing.","trouble":"The arm moves at boot, starts from an unsafe pose, runs in the wrong direction, loses a bus device, browns out, heats while holding, oscillates, pinches a cable or finger, drops a link at power-off, or reaches a pose that the unpowered mockup did not predict.","at":[0.66,0.45,0],"links":[{"to":"field-testing","rel":"see also"},{"to":"safety","rel":"see also"},{"to":"risk-assessment","rel":"see also"},{"to":"emergency-stop","rel":"see also"},{"to":"workspace","rel":"see also"},{"to":"actuation","rel":"see also"}],"sources":[{"label":"ROBOTIS, OpenMANIPULATOR-X Basic Operation","url":"https://emanual.robotis.com/docs/en/platform/openmanipulator_x/quick_start_guide_basic_operation/","kind":"maker","page":"Launch Controller warning","quote":"Please check each joint position before running OpenMANIPULATOR-X. If joints are set inappropriately, OpenMANIPULATOR-X might not start operating.","work":"arm-build-openmanipulator-basic"},{"label":"Hugging Face LeRobot, SO-100 assembly and motor configuration","url":"https://raw.githubusercontent.com/huggingface/lerobot/main/docs/source/so100.mdx","kind":"maker","page":"Set the motors IDs and baudrates","quote":"Each motor is identified by a unique id on the bus.","work":"arm-build-lerobot-so100"},{"label":"Hugging Face LeRobot, SO-100 assembly and motor configuration","url":"https://raw.githubusercontent.com/huggingface/lerobot/main/docs/source/so100.mdx","kind":"maker","page":"Motor configuration tip","quote":"Check your cabling at each step before pressing Enter.","work":"arm-build-lerobot-so100"},{"label":"ROBOTIS, XL430-W250-T technical manual and safety warnings","url":"https://emanual.robotis.com/docs/en/dxl/x/xl430-w250/","kind":"maker","page":"Safety warnings","quote":"Keep product out of reach of children.","work":"arm-build-robotis-xl430"},{"label":"ROBOTIS, XL430-W250-T technical manual and safety warnings","url":"https://emanual.robotis.com/docs/en/dxl/x/xl430-w250/","kind":"maker","page":"Safety warnings","quote":"Check input polarity before installing or energizing wiring or cables.","work":"arm-build-robotis-xl430"},{"label":"Jan, Pololu Servo Control Interface in Detail","url":"https://www.pololu.com/blog/17/servo-control-interface-in-detail","kind":"practitioner","page":"Analog servo behavior","quote":"if you stop sending pulses, the servos will stop trying to hold a position and effectively turn off","work":"arm-build-pololu-servo-control"},{"label":"Jan, Pololu Servo Control Interface in Detail","url":"https://www.pololu.com/blog/17/servo-control-interface-in-detail","kind":"practitioner","page":"Digital servo behavior","quote":"some digital servos continue holding the most recent position even if the control signal goes away, and other digital servos turn off.","work":"arm-build-pololu-servo-control"}],"unverified":"The exact guarding, catch design, current limit, shutdown sequence and test envelope are procedural advice, not certification; set them through the risk assessment, emergency-stop design and component manuals. No universal safe force or safe distance is claimed.","deeper":"The next level would hold commissioning checklists, firmware and bus-ID records, limit/zero calibration, test logs, stop criteria, fault injection, rollback and field-test acceptance evidence.","id":"arm-bring-up","look":{"parts":[{"shape":"box","size":[1.5,0.05,0.8],"pos":[0.12,0.025,0],"radius":0.02,"color":"#a77b52","material":"matte"},{"shape":"torus","radius":0.5,"tube":0.012,"pos":[0.14,0.052,0],"rot":[-90,0,0],"color":"#e5b82c","material":"gloss"},{"shape":"box","size":[0.28,0.07,0.26],"pos":[0,0.085,0],"radius":0.02,"color":"#343a43","material":"matte"},{"shape":"cylinder","radiusTop":0.08,"radiusBottom":0.08,"height":0.08,"pos":[0,0.16,0],"color":"#aeb6c2","material":"metal"},{"shape":"box","size":[0.07,0.42,0.06],"pos":[0.09,0.45,0],"rot":[0,0,-25.35],"color":"#5d88b8","material":"matte"},{"shape":"box","size":[0.06,0.368,0.055],"pos":[0.35,0.57,0],"rot":[0,0,-112.38],"color":"#5d88b8","material":"matte"},{"shape":"cylinder","radiusTop":0.075,"radiusBottom":0.075,"height":0.18,"pos":[0,0.26,0],"rot":[90,0,0],"color":"#1f2329","material":"matte"},{"shape":"cylinder","radiusTop":0.065,"radiusBottom":0.065,"height":0.16,"pos":[0.18,0.64,0],"rot":[90,0,0],"color":"#1f2329","material":"matte"},{"shape":"box","size":[0.028,0.148,0.07],"pos":[0.52,0.5,0],"rot":[0,0,157.62],"color":"#3a3f47","material":"metal"},{"shape":"box","size":[0.028,0.066,0.06],"pos":[0.541,0.427,0],"rot":[0,0,-112.38],"color":"#3a3f47","material":"metal"},{"shape":"box","size":[0.028,0.066,0.06],"pos":[0.586,0.538,0],"rot":[0,0,-112.38],"color":"#3a3f47","material":"metal"},{"shape":"cylinder","radiusTop":0.018,"radiusBottom":0.018,"height":0.39,"pos":[0.4,0.245,0],"color":"#aeb6c2","material":"metal"},{"shape":"box","size":[0.13,0.04,0.12],"pos":[0.4,0.46,0],"color":"#e0a33a","material":"foam"},{"shape":"box","size":[0.16,0.1,0.16],"pos":[-0.48,0.1,0.25],"radius":0.02,"color":"#e5b82c","material":"gloss"},{"shape":"cylinder","radiusTop":0.03,"radiusBottom":0.03,"height":0.03,"pos":[-0.48,0.165,0.25],"color":"#343a43","material":"matte"},{"shape":"cylinder","radiusTop":0.06,"radiusBottom":0.065,"height":0.04,"pos":[-0.48,0.2,0.25],"color":"#c8463d","material":"gloss"},{"shape":"box","size":[0.34,0.2,0.2],"pos":[0.66,0.15,-0.22],"radius":0.02,"color":"#5b626b","material":"matte"},{"shape":"plane","size":[0.26,0.095],"pos":[0.66,0.17,-0.119],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 220 80\"><rect width=\"220\" height=\"80\" rx=\"6\" fill=\"#0d1a14\"/><text x=\"14\" y=\"50\" font-family=\"Liberation Mono,monospace\" font-size=\"30\" fill=\"#7dff9b\">--.-V</text><text x=\"118\" y=\"50\" font-family=\"Liberation Mono,monospace\" font-size=\"30\" fill=\"#ffb45c\">-.--A</text><text x=\"14\" y=\"72\" font-family=\"Liberation Sans,Arial,sans-serif\" font-size=\"11\" fill=\"#7f9c8b\">CURRENT LIMIT SET</text></svg>"},{"shape":"cylinder","radiusTop":0.01,"radiusBottom":0.01,"height":0.206,"pos":[-0.3,0.065,0.225],"rot":[-14.48,14.28,-89.22],"color":"#17191d","material":"matte"},{"shape":"cylinder","radiusTop":0.01,"radiusBottom":0.01,"height":0.142,"pos":[-0.15,0.065,0.15],"rot":[-52.81,27.69,-52.81],"color":"#17191d","material":"matte"}]}},{"term":"Links and joints","aka":["arm segments","hinges"],"kind":"part","plain":"Links are rigid bodies. A joint constrains the relative motion between neighbouring links; a serial chain is one path of links and joints from base to tool.","does":"Each joint contributes a known number of independent motions.","ask":"Which joint type is needed, and where are its axes?","cues":["Rigid bodies joined by constrained joints","Hinges or sliders between neighbouring links","One serial path from base to tool"],"at":[0.36,0.95,0.05],"variants":[{"label":"Joint","items":[{"id":"joint-revolute","name":"Revolute (R)","plain":"A revolute joint is a hinge: one angle describes rotation about one axis.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://modernrobotics.northwestern.edu/nu-gm-book-resource/2-2-degrees-of-freedom-of-a-robot/","kind":"book","isbn":"9781107156302","page":"§2.2 Degrees of Freedom of a Robot: Revolute joint","quote":"The most common type of joint is the revolute joint. It places 5 constraints on the motion of the second spatial rigid body relative to the first, and therefore the second body has only one degree of freedom relative to the first body, given by the angle of the revolute joint.","flag":"book resource page","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"look":{"parts":[{"shape":"cylinder","radiusTop":0.07,"radiusBottom":0.07,"height":0.6,"pos":[0,-0.3,0],"rot":[0,0,0],"color":"#d9dde3","material":"gloss","slot":"joint"},{"shape":"cylinder","radiusTop":0.12,"radiusBottom":0.12,"height":0.2,"pos":[0,0,0],"color":"#2f6fd6","rot":[90,0,0],"material":"gloss","slot":"joint"},{"shape":"cylinder","radiusTop":0.02,"radiusBottom":0.02,"height":0.32,"pos":[0,0,0],"color":"#c8463d","rot":[90,0,0],"material":"gloss","slot":"joint"},{"shape":"cylinder","radiusTop":0.07,"radiusBottom":0.07,"height":0.6021,"pos":[0.225,0.2,0],"rot":[0,0,-48.37],"color":"#d9dde3","material":"gloss","slot":"joint"},{"shape":"torus","radius":0.2,"tube":0.008,"pos":[0,0,0.12],"color":"#c8463d","slot":"joint"}]}},{"id":"joint-prismatic","name":"Prismatic (P)","plain":"A prismatic joint is a slider: one displacement describes translation along one axis.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://modernrobotics.northwestern.edu/nu-gm-book-resource/2-2-degrees-of-freedom-of-a-robot/","kind":"book","isbn":"9781107156302","page":"§2.2 Degrees of Freedom of a Robot: Prismatic joint","quote":"Another common joint with one degree of freedom is the prismatic joint, also called a linear joint.","flag":"book resource page","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"look":{"parts":[{"shape":"box","size":[0.18,0.7,0.18],"pos":[0,-0.25,0],"color":"#d9dde3","material":"gloss","slot":"joint"},{"shape":"box","size":[0.12,0.7,0.12],"pos":[0,0.35,0],"color":"#2f6fd6","material":"gloss","slot":"joint"},{"shape":"cylinder","radiusTop":0.015,"radiusBottom":0.015,"height":0.5,"pos":[0.2,0.35,0],"rot":[0,0,0],"color":"#c8463d","slot":"joint"},{"shape":"cone","radius":0.04,"height":0.08,"pos":[0.2,0.64,0],"color":"#c8463d","slot":"joint"}]}},{"id":"joint-spherical","name":"Spherical (S)","plain":"A spherical joint is a ball-and-socket joint with three rotational DoF; robot wrists often build it from three revolute joints.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://modernrobotics.northwestern.edu/nu-gm-book-resource/2-2-degrees-of-freedom-of-a-robot/","kind":"book","isbn":"9781107156302","page":"§2.2 Degrees of Freedom of a Robot: Spherical joint","quote":"The spherical joint, also called a ball-and-socket joint, has three degrees of freedom.","flag":"book resource page","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"look":{"parts":[{"shape":"cylinder","radiusTop":0.07,"radiusBottom":0.07,"height":0.5,"pos":[0,-0.35,0],"rot":[0,0,0],"color":"#d9dde3","material":"gloss","slot":"joint"},{"shape":"lathe","profile":[[0,-0.14],[0.1,-0.13],[0.15,-0.06],[0.16,0.02]],"pos":[0,0,0],"color":"#d9dde3","material":"gloss","slot":"joint"},{"shape":"sphere","radius":0.13,"pos":[0,0,0],"color":"#2f6fd6","material":"gloss","slot":"joint"},{"shape":"cylinder","radiusTop":0.07,"radiusBottom":0.07,"height":0.5991,"pos":[0.2,0.21,0.075],"rot":[14.57,-5.64,-42.14],"color":"#d9dde3","material":"gloss","slot":"joint"}]}}]}],"sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 2 §§2.1–2.2","quote":"Basically, a mechanism is constructed by connecting rigid bodies, called links, together by means of joints, so that relative motion between adjacent links becomes possible.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"deeper":"Next level: link dimensions, joint axes, limits, friction, compliance and collision shapes.","id":"links-and-joints","look":{"parts":[{"shape":"cylinder","radiusTop":0.07,"radiusBottom":0.07,"height":0.6,"pos":[0,-0.3,0],"rot":[0,0,0],"color":"#d9dde3","material":"gloss","slot":"joint"},{"shape":"cylinder","radiusTop":0.12,"radiusBottom":0.12,"height":0.2,"pos":[0,0,0],"color":"#2f6fd6","rot":[90,0,0],"material":"gloss","slot":"joint"},{"shape":"cylinder","radiusTop":0.02,"radiusBottom":0.02,"height":0.32,"pos":[0,0,0],"color":"#c8463d","rot":[90,0,0],"material":"gloss","slot":"joint"},{"shape":"cylinder","radiusTop":0.07,"radiusBottom":0.07,"height":0.6021,"pos":[0.225,0.2,0],"rot":[0,0,-48.37],"color":"#d9dde3","material":"gloss","slot":"joint"},{"shape":"torus","radius":0.2,"tube":0.008,"pos":[0,0,0.12],"color":"#c8463d","slot":"joint"}]}},{"term":"Degrees of freedom","aka":["DoF","axes"],"kind":"measure","plain":"Degrees of freedom (DoF) are the independent coordinates needed to describe a configuration.","does":"DoF tells whether the robot can command the task variables and whether redundant motion is available.","ask":"Does the task need six pose DoF, or is extra redundancy useful?","range":"A free spatial rigid body has 6 DoF. Revolute and prismatic joints each have 1; a spherical joint has 3. A planar mobile base has x, y and heading, and Grübler's formula counts mechanism mobility when constraints are independent.","trouble":"Too few DoF makes a pose impossible; extra DoF creates choices that still need limits, collision checks and a selection rule.","at":[0.17,0.58,0.05],"sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 2 §§2.1–2.3","quote":"Degrees of freedom = (number of variables) − (number of independent equations).","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"},{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://modernrobotics.northwestern.edu/nu-gm-book-resource/2-2-degrees-of-freedom-of-a-robot/","kind":"book","isbn":"9781107156302","page":"§2.2 Degrees of Freedom of a Robot: Joint types","quote":"The spherical joint, also called a ball-and-socket joint, has three degrees of freedom.","flag":"book resource page","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"deeper":"Next level: configuration space, independent constraints, redundancy and mobility formulas.","id":"degrees-of-freedom","look":{"parts":[{"shape":"box","size":[0.4,0.06,0.4],"pos":[0,-0.03,0],"color":"#5b616b","material":"metal"},{"shape":"cylinder","radiusTop":0.035,"radiusBottom":0.035,"height":0.3,"pos":[0,0.15,0],"rot":[0,0,0],"color":"#d9dde3","material":"gloss"},{"shape":"sphere","radius":0.06,"pos":[0,0,0],"color":"#2f6fd6","material":"gloss"},{"shape":"torus","radius":0.1,"tube":0.008,"pos":[0,0,0],"rot":[90,0,0],"color":"#2f6fd6"},{"shape":"cylinder","radiusTop":0.035,"radiusBottom":0.035,"height":0.4301,"pos":[0.125,0.475,0],"rot":[0,0,-35.54],"color":"#d9dde3","material":"gloss"},{"shape":"sphere","radius":0.06,"pos":[0,0.3,0],"color":"#3f9a5b","material":"gloss"},{"shape":"torus","radius":0.1,"tube":0.008,"pos":[0,0.3,0],"rot":[0,0,0],"color":"#3f9a5b"},{"shape":"cylinder","radiusTop":0.035,"radiusBottom":0.035,"height":0.4031,"pos":[0.425,0.75,0],"rot":[0,0,-60.26],"color":"#d9dde3","material":"gloss"},{"shape":"sphere","radius":0.06,"pos":[0.25,0.65,0],"color":"#e07a2d","material":"gloss"},{"shape":"torus","radius":0.1,"tube":0.008,"pos":[0.25,0.65,0],"rot":[90,0,0],"color":"#e07a2d"},{"shape":"cylinder","radiusTop":0.035,"radiusBottom":0.035,"height":0.2693,"pos":[0.725,0.8,0],"rot":[0,0,-111.8],"color":"#d9dde3","material":"gloss"},{"shape":"sphere","radius":0.06,"pos":[0.6,0.85,0],"color":"#c8463d","material":"gloss"},{"shape":"torus","radius":0.1,"tube":0.008,"pos":[0.6,0.85,0],"rot":[0,0,0],"color":"#c8463d"},{"shape":"cylinder","radiusTop":0.035,"radiusBottom":0.035,"height":0.25,"pos":[0.925,0.65,0],"rot":[0,0,-143.13],"color":"#d9dde3","material":"gloss"},{"shape":"sphere","radius":0.06,"pos":[0.85,0.75,0],"color":"#8a5cc2","material":"gloss"},{"shape":"torus","radius":0.1,"tube":0.008,"pos":[0.85,0.75,0],"rot":[90,0,0],"color":"#8a5cc2"},{"shape":"cylinder","radiusTop":0.035,"radiusBottom":0.035,"height":0.1581,"pos":[1.025,0.475,0],"rot":[0,0,-161.57],"color":"#d9dde3","material":"gloss"},{"shape":"sphere","radius":0.06,"pos":[1,0.55,0],"color":"#e8b82e","material":"gloss"},{"shape":"torus","radius":0.1,"tube":0.008,"pos":[1,0.55,0],"rot":[0,0,0],"color":"#e8b82e"}]}},{"term":"Workspace and payload","aka":["reach","how much it can lift"],"kind":"measure","plain":"Workspace is the set of tool poses the mechanism can reach. Payload is the load it can carry at a specified pose and speed.","does":"It decides whether the task fits the robot's geometry and load envelope.","ask":"Are all target poses reachable and dexterous with the required payload?","cues":["Tool poses inside the reachable set","Payload at a specified pose and speed","Position-reachable but orientation-infeasible targets","Load beyond the usable envelope"],"range":"Universal Robots lists the UR10e at 1,300 mm reach and 10 kg or 12.5 kg maximum payload. The exact usable payload depends on pose, speed and tool configuration.","trouble":"A target can be position-reachable but orientation-infeasible, outside the dexterous workspace, or too heavy at that pose.","at":[0.64,0.75,0.05],"sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 2 §2.5","quote":"The workspace is defined to be the subset of the task space that the end-effector frame can reach.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"},{"label":"Universal Robots, Technical Specifications UR10e","url":"https://www.universal-robots.com/media/1807466/ur10e_e-series_datasheets_web.pdf","kind":"maker","page":"Technical specification","quote":"Our most versatile robot, the UR10e delivers an impressive payload of 12.5 kg and 1300 mm reach, making it ideal for a wide range of applications.","work":"universal-robots-technical-specifications-ur10e"},{"label":"Mark W. Spong, Seth Hutchinson and M. 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Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Appendix C, Denavit–Hartenberg parameters","quote":"One widely used representation for the forward kinematics of open chains relies on the Denavit–Hartenberg parameters.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"svg":{"card":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect width=\"440\" height=\"300\" rx=\"10\" fill=\"#f6f4ef\"/><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#1f2430\" font-weight=\"700\">Forward kinematics</text><text x=\"20\" y=\"54\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#7a7f8c\">Denavit–Hartenberg table, one row per link</text><rect x=\"20\" y=\"70\" width=\"400\" height=\"30\" rx=\"3\" fill=\"#e9e6dd\" stroke=\"none\" stroke-width=\"0\"/><text x=\"50\" y=\"91\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"15\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">i</text><text x=\"130\" y=\"91\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"15\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">aᵢ₋₁</text><text x=\"210\" y=\"91\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"15\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">αᵢ₋₁</text><text x=\"290\" y=\"91\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"15\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">dᵢ</text><text x=\"370\" y=\"91\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"15\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">θᵢ</text><text x=\"50\" y=\"128\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">1</text><text x=\"130\" y=\"128\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0</text><text x=\"210\" y=\"128\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0</text><text x=\"290\" y=\"128\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0.333</text><text x=\"370\" y=\"128\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#2f6fd6\" text-anchor=\"middle\">θ₁</text><line x1=\"20\" y1=\"138\" x2=\"420\" y2=\"138\" stroke=\"#d5d2c8\" stroke-width=\"1\" stroke-linecap=\"round\" /><text x=\"50\" y=\"158\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">2</text><text x=\"130\" y=\"158\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0</text><text x=\"210\" y=\"158\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">−90°</text><text x=\"290\" y=\"158\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0</text><text x=\"370\" y=\"158\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#2f6fd6\" text-anchor=\"middle\">θ₂</text><line x1=\"20\" y1=\"168\" x2=\"420\" y2=\"168\" stroke=\"#d5d2c8\" stroke-width=\"1\" stroke-linecap=\"round\" /><text x=\"50\" y=\"188\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">3</text><text x=\"130\" y=\"188\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0</text><text x=\"210\" y=\"188\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">90°</text><text x=\"290\" y=\"188\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0.316</text><text x=\"370\" y=\"188\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#2f6fd6\" text-anchor=\"middle\">θ₃</text><line x1=\"20\" y1=\"198\" x2=\"420\" y2=\"198\" stroke=\"#d5d2c8\" stroke-width=\"1\" stroke-linecap=\"round\" /><text x=\"50\" y=\"218\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">4</text><text x=\"130\" y=\"218\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0.0825</text><text x=\"210\" y=\"218\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">90°</text><text x=\"290\" y=\"218\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0</text><text x=\"370\" y=\"218\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#2f6fd6\" text-anchor=\"middle\">θ₄</text><line x1=\"20\" y1=\"228\" x2=\"420\" y2=\"228\" stroke=\"#d5d2c8\" stroke-width=\"1\" stroke-linecap=\"round\" /><text x=\"220\" y=\"268\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"18\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">⁰T₄ = ⁰T₁ · ¹T₂ · ²T₃ · ³T₄</text></svg>"}},{"id":"fk-poe","name":"Product of exponentials (PoE)","plain":"Product of exponentials uses one screw axis per joint and multiplies joint exponentials with a home configuration.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 4 §4.1","quote":"The forward kinematics of open chains can be expressed as the product of matrix exponentials.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"svg":{"card":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect width=\"440\" height=\"300\" rx=\"10\" fill=\"#f6f4ef\"/><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#1f2430\" font-weight=\"700\">Forward kinematics</text><text x=\"20\" y=\"54\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#7a7f8c\">Product of exponentials: one screw axis per joint</text><text x=\"220\" y=\"120\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"18\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">T(θ) = e^[S₁]θ₁ · e^[S₂]θ₂ ··· e^[Sₙ]θₙ · M</text><text x=\"60\" y=\"170\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"15\" fill=\"#2f6fd6\" font-weight=\"700\">S₁</text><text x=\"100\" y=\"170\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#2a2530\">(0,0,1, 0,0,0)</text><text x=\"60\" y=\"198\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"15\" fill=\"#2f6fd6\" font-weight=\"700\">S₂</text><text x=\"100\" y=\"198\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#2a2530\">(0,1,0, −0.33,0,0)</text><text x=\"60\" y=\"226\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"15\" fill=\"#2f6fd6\" font-weight=\"700\">S₃</text><text x=\"100\" y=\"226\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#2a2530\">(0,1,0, −0.65,0,0)</text><text x=\"60\" y=\"262\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"14\" fill=\"#7a7f8c\">M = home pose of the tool</text></svg>"}}]}],"sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 4 §§4.1–4.3","quote":"For an open chain, the position and orientation of the end-effector are uniquely determined from the joint positions. The forward kinematics problem is to find the position and orientation of the reference frame attached to the end-effector given the set of joint positions.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"deeper":"Next level: transform products, joint screw axes, DH parameters and numerical validation against measured poses.","id":"forward-kinematics","look":{"parts":[{"shape":"box","size":[1.4,0.9545,0.02],"pos":[0,0,-0.012],"color":"#cfccc2","material":"matte","slot":"card-back"},{"shape":"plane","size":[1.4,0.9545],"pos":[0,0,0],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect width=\"440\" height=\"300\" rx=\"10\" fill=\"#f6f4ef\"/><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#1f2430\" font-weight=\"700\">Forward kinematics</text><text x=\"20\" y=\"54\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#7a7f8c\">Denavit–Hartenberg table, one row per link</text><rect x=\"20\" y=\"70\" width=\"400\" height=\"30\" rx=\"3\" fill=\"#e9e6dd\" stroke=\"none\" stroke-width=\"0\"/><text x=\"50\" y=\"91\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"15\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">i</text><text x=\"130\" y=\"91\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"15\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">aᵢ₋₁</text><text x=\"210\" y=\"91\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"15\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">αᵢ₋₁</text><text x=\"290\" y=\"91\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"15\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">dᵢ</text><text x=\"370\" y=\"91\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"15\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">θᵢ</text><text x=\"50\" y=\"128\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">1</text><text x=\"130\" y=\"128\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0</text><text x=\"210\" y=\"128\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0</text><text x=\"290\" y=\"128\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0.333</text><text x=\"370\" y=\"128\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#2f6fd6\" text-anchor=\"middle\">θ₁</text><line x1=\"20\" y1=\"138\" x2=\"420\" y2=\"138\" stroke=\"#d5d2c8\" stroke-width=\"1\" stroke-linecap=\"round\" /><text x=\"50\" y=\"158\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">2</text><text x=\"130\" y=\"158\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0</text><text x=\"210\" y=\"158\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">−90°</text><text x=\"290\" y=\"158\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0</text><text x=\"370\" y=\"158\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#2f6fd6\" text-anchor=\"middle\">θ₂</text><line x1=\"20\" y1=\"168\" x2=\"420\" y2=\"168\" stroke=\"#d5d2c8\" stroke-width=\"1\" stroke-linecap=\"round\" /><text x=\"50\" y=\"188\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">3</text><text x=\"130\" y=\"188\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0</text><text x=\"210\" y=\"188\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">90°</text><text x=\"290\" y=\"188\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0.316</text><text x=\"370\" y=\"188\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#2f6fd6\" text-anchor=\"middle\">θ₃</text><line x1=\"20\" y1=\"198\" x2=\"420\" y2=\"198\" stroke=\"#d5d2c8\" stroke-width=\"1\" stroke-linecap=\"round\" /><text x=\"50\" y=\"218\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">4</text><text x=\"130\" y=\"218\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0.0825</text><text x=\"210\" y=\"218\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">90°</text><text x=\"290\" y=\"218\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#1f2430\" text-anchor=\"middle\">0</text><text x=\"370\" y=\"218\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#2f6fd6\" text-anchor=\"middle\">θ₄</text><line x1=\"20\" y1=\"228\" x2=\"420\" y2=\"228\" stroke=\"#d5d2c8\" stroke-width=\"1\" stroke-linecap=\"round\" /><text x=\"220\" y=\"268\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"18\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">⁰T₄ = ⁰T₁ · ¹T₂ · ²T₃ · ³T₄</text></svg>","slot":"card"}]}},{"term":"Inverse kinematics","aka":["IK"],"kind":"process","plain":"Inverse kinematics finds joint coordinates that produce a desired tool pose.","does":"It turns a grasp or placement pose into joint commands.","ask":"Are there zero, one or many solutions, and which solution respects limits and avoids collisions?","trouble":"Targets can be unreachable, solutions can switch between branches, or an iterative solver can stop in a poor local solution.","at":[0.4136,-0.1273,0.02],"links":[{"to":"jacobian","rel":"made from"}],"variants":[{"label":"Solver","items":[{"id":"ik-analytic","name":"Analytic (closed form)","plain":"An analytic solver uses geometry-specific formulas and can enumerate all solutions for that robot family.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 6 §6.1","quote":"We first examine a popular class of six-dof open-chain structures whose inverse kinematics admits a closed-form analytic solution.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"svg":{"card":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect width=\"440\" height=\"300\" rx=\"10\" fill=\"#f6f4ef\"/><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#1f2430\" font-weight=\"700\">Inverse kinematics</text><text x=\"20\" y=\"54\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#7a7f8c\">one target, two arm shapes</text><g opacity=\"0.55\"><rect x=\"118\" y=\"250\" width=\"44\" height=\"14\" rx=\"3\" fill=\"#9aa0aa\" stroke=\"none\" stroke-width=\"0\"/><line x1=\"140\" y1=\"250\" x2=\"252.763114494309\" y2=\"208.95758280091974\" stroke=\"#2f6fd6\" stroke-width=\"10\" stroke-linecap=\"round\" /><line x1=\"252.763114494309\" y1=\"208.95758280091974\" x2=\"206.2751057028321\" y2=\"109.26372622688824\" stroke=\"#2f6fd6\" stroke-width=\"10\" stroke-linecap=\"round\" /><circle cx=\"140\" cy=\"250\" r=\"9\" fill=\"#fff\" stroke=\"#2f6fd6\" stroke-width=\"3\"/><circle cx=\"252.763114494309\" cy=\"208.95758280091974\" r=\"8\" fill=\"#fff\" stroke=\"#2f6fd6\" stroke-width=\"3\"/><circle cx=\"206.2751057028321\" cy=\"109.26372622688824\" r=\"5\" fill=\"#2f6fd6\" stroke=\"none\" stroke-width=\"2\"/></g><g opacity=\"1\"><rect x=\"118\" y=\"250\" width=\"44\" height=\"14\" rx=\"3\" fill=\"#9aa0aa\" stroke=\"none\" stroke-width=\"0\"/><line x1=\"140\" y1=\"250\" x2=\"171.0582854123025\" y2=\"134.0889008453118\" stroke=\"#1f2430\" stroke-width=\"10\" stroke-linecap=\"round\" /><line x1=\"171.0582854123025\" y1=\"134.0889008453118\" x2=\"274.4244736987524\" y2=\"171.71111661113537\" stroke=\"#1f2430\" stroke-width=\"10\" stroke-linecap=\"round\" /><circle cx=\"140\" cy=\"250\" r=\"9\" fill=\"#fff\" stroke=\"#1f2430\" stroke-width=\"3\"/><circle cx=\"171.0582854123025\" cy=\"134.0889008453118\" r=\"8\" fill=\"#fff\" stroke=\"#1f2430\" stroke-width=\"3\"/><circle cx=\"274.4244736987524\" cy=\"171.71111661113537\" r=\"5\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/></g><g><circle cx=\"274.4245\" cy=\"171.7111\" r=\"14\" fill=\"none\" stroke=\"#c8463d\" stroke-width=\"2.5\"/><line x1=\"254.42450000000002\" y1=\"171.7111\" x2=\"294.4245\" y2=\"171.7111\" stroke=\"#c8463d\" stroke-width=\"2\" stroke-linecap=\"round\" /><line x1=\"274.4245\" y1=\"151.7111\" x2=\"274.4245\" y2=\"191.7111\" stroke=\"#c8463d\" stroke-width=\"2\" stroke-linecap=\"round\" /></g><text x=\"101.0583\" y=\"128.0889\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#1f2430\">elbow up</text><text x=\"262.7631\" y=\"238.9576\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#2f6fd6\">elbow down</text><text x=\"280\" y=\"92\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"14\" fill=\"#2a2530\" font-weight=\"700\">Closed form:</text><text x=\"280\" y=\"114\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"14\" fill=\"#2a2530\">both solutions</text><text x=\"280\" y=\"134\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"14\" fill=\"#2a2530\">listed at once</text></svg>"}},{"id":"ik-numerical","name":"Numerical (iterative)","plain":"A numerical solver iterates a velocity or Jacobian update from an initial guess; damping improves behavior near singularities.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 6 §§6.2–6.3","quote":"The result is an iterative numerical algorithm which, provided that an initial guess of the joint variables is sufficiently close to a true solution, converges quickly to that solution.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"svg":{"card":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect width=\"440\" height=\"300\" rx=\"10\" fill=\"#f6f4ef\"/><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#1f2430\" font-weight=\"700\">Inverse kinematics</text><text x=\"20\" y=\"54\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#7a7f8c\">one target, two arm shapes</text><g opacity=\"0.55\"><rect x=\"118\" y=\"250\" width=\"44\" height=\"14\" rx=\"3\" fill=\"#9aa0aa\" stroke=\"none\" stroke-width=\"0\"/><line x1=\"140\" y1=\"250\" x2=\"252.763114494309\" y2=\"208.95758280091974\" stroke=\"#2f6fd6\" stroke-width=\"10\" stroke-linecap=\"round\" /><line x1=\"252.763114494309\" y1=\"208.95758280091974\" x2=\"206.2751057028321\" y2=\"109.26372622688824\" stroke=\"#2f6fd6\" stroke-width=\"10\" stroke-linecap=\"round\" /><circle cx=\"140\" cy=\"250\" r=\"9\" fill=\"#fff\" stroke=\"#2f6fd6\" stroke-width=\"3\"/><circle cx=\"252.763114494309\" cy=\"208.95758280091974\" r=\"8\" fill=\"#fff\" stroke=\"#2f6fd6\" stroke-width=\"3\"/><circle cx=\"206.2751057028321\" cy=\"109.26372622688824\" r=\"5\" fill=\"#2f6fd6\" stroke=\"none\" stroke-width=\"2\"/></g><g opacity=\"1\"><rect x=\"118\" y=\"250\" width=\"44\" height=\"14\" rx=\"3\" fill=\"#9aa0aa\" stroke=\"none\" stroke-width=\"0\"/><line x1=\"140\" y1=\"250\" x2=\"171.0582854123025\" y2=\"134.0889008453118\" stroke=\"#1f2430\" stroke-width=\"10\" stroke-linecap=\"round\" /><line x1=\"171.0582854123025\" y1=\"134.0889008453118\" x2=\"274.4244736987524\" y2=\"171.71111661113537\" stroke=\"#1f2430\" stroke-width=\"10\" stroke-linecap=\"round\" /><circle cx=\"140\" cy=\"250\" r=\"9\" fill=\"#fff\" stroke=\"#1f2430\" stroke-width=\"3\"/><circle cx=\"171.0582854123025\" cy=\"134.0889008453118\" r=\"8\" fill=\"#fff\" stroke=\"#1f2430\" stroke-width=\"3\"/><circle cx=\"274.4244736987524\" cy=\"171.71111661113537\" r=\"5\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/></g><g><circle cx=\"274.4245\" cy=\"171.7111\" r=\"14\" fill=\"none\" stroke=\"#c8463d\" stroke-width=\"2.5\"/><line x1=\"254.42450000000002\" y1=\"171.7111\" x2=\"294.4245\" y2=\"171.7111\" stroke=\"#c8463d\" stroke-width=\"2\" stroke-linecap=\"round\" /><line x1=\"274.4245\" y1=\"151.7111\" x2=\"274.4245\" y2=\"191.7111\" stroke=\"#c8463d\" stroke-width=\"2\" stroke-linecap=\"round\" /></g><text x=\"101.0583\" y=\"128.0889\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#1f2430\">elbow up</text><text x=\"262.7631\" y=\"238.9576\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#2f6fd6\">elbow down</text><text x=\"280\" y=\"92\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"14\" fill=\"#2a2530\" font-weight=\"700\">Iterative:</text><text x=\"280\" y=\"114\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" fill=\"#2a2530\">Δθ = J⁺ · error</text><text x=\"280\" y=\"134\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"14\" fill=\"#2a2530\">finds the nearest one</text><circle cx=\"204.42450000000002\" cy=\"221.7111\" r=\"4\" fill=\"#e07a2d\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"224.42450000000002\" cy=\"206.7111\" r=\"4\" fill=\"#e07a2d\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"244.42450000000002\" cy=\"191.7111\" r=\"4\" fill=\"#e07a2d\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"264.4245\" cy=\"176.7111\" r=\"4\" fill=\"#e07a2d\" stroke=\"none\" stroke-width=\"2\"/></svg>"}}]}],"sources":[{"label":"Kevin M. Lynch and Frank C. 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Lynch and Frank C. 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Murray, Zexiang Li and S. Shankar Sastry, A Mathematical Introduction to Robotic Manipulation","url":"http://www.cds.caltech.edu/~murray/mlswiki/images/mlswiki/0/02/Mls94-complete.pdf","kind":"book","isbn":"9780849379819","page":"Ch. 5, Multifingered Hand Kinematics","quote":"A multifingered hand is a set of robots which is attached to the end of a larger robot arm for the purpose of manipulation.","flag":"electronic edition","work":"richard-m-murray-zexiang-li-and-s-shankar-sastry"}],"look":{"parts":[{"shape":"cylinder","radiusTop":0.16,"radiusBottom":0.16,"height":0.06,"pos":[0,0.62,0],"color":"#9aa0aa","material":"metal","slot":"gripper"},{"shape":"cylinder","radiusTop":0.15,"radiusBottom":0.15,"height":0.18,"pos":[0,0.5,0],"color":"#2b3038","material":"gloss","slot":"gripper"},{"shape":"cylinder","radiusTop":0.03,"radiusBottom":0.03,"height":0.18,"pos":[0,0.31,0.1],"rot":[180,0,0],"color":"#5b616b","material":"metal","slot":"gripper"},{"shape":"sphere","radius":0.035,"pos":[0,0.22,0.1],"color":"#2f6fd6","slot":"gripper"},{"shape":"cylinder","radiusTop":0.026,"radiusBottom":0.026,"height":0.1897,"pos":[0,0.13,0.07],"rot":[-161.57,0,0],"color":"#5b616b","material":"metal","slot":"gripper"},{"shape":"cylinder","radiusTop":0.03,"radiusBottom":0.03,"height":0.18,"pos":[0.0866,0.31,-0.05],"rot":[180,0,0],"color":"#5b616b","material":"metal","slot":"gripper"},{"shape":"sphere","radius":0.035,"pos":[0.0866,0.22,-0.05],"color":"#2f6fd6","slot":"gripper"},{"shape":"cylinder","radiusTop":0.026,"radiusBottom":0.026,"height":0.1897,"pos":[0.0606,0.13,-0.035],"rot":[17.12,57.51,149.33],"color":"#5b616b","material":"metal","slot":"gripper"},{"shape":"cylinder","radiusTop":0.03,"radiusBottom":0.03,"height":0.18,"pos":[-0.0866,0.31,-0.05],"rot":[180,0,0],"color":"#5b616b","material":"metal","slot":"gripper"},{"shape":"sphere","radius":0.035,"pos":[-0.0866,0.22,-0.05],"color":"#2f6fd6","slot":"gripper"},{"shape":"cylinder","radiusTop":0.026,"radiusBottom":0.026,"height":0.1897,"pos":[-0.0606,0.13,-0.035],"rot":[17.12,-57.51,-149.33],"color":"#5b616b","material":"metal","slot":"gripper"},{"shape":"sphere","radius":0.09,"pos":[0,0.12,0],"color":"#c8463d","material":"gloss","slot":"gripper"}]}},{"id":"grip-soft","name":"Soft gripper","plain":"A soft gripper uses compliant fingers or silicone tools to conform to irregular or delicate objects.","sources":[{"label":"OnRobot, One-stop shop for collaborative robots","url":"https://onrobot.com/en","kind":"maker","page":"Soft Gripper for Delicate Handling","quote":"The OnRobot Soft Gripper uses interchangeable silicone tools to handle delicate and irregular items.","work":"onrobot-one-stop-shop-for-collaborative-robots"}],"look":{"parts":[{"shape":"cylinder","radiusTop":0.16,"radiusBottom":0.16,"height":0.06,"pos":[0,0.62,0],"color":"#9aa0aa","material":"metal","slot":"gripper"},{"shape":"box","size":[0.36,0.14,0.18],"pos":[0,0.5,0],"color":"#f2f2f2","material":"gloss","radius":0.03,"slot":"gripper"},{"shape":"box","size":[0.07,0.07,0.1],"pos":[-0.1,0.36,0],"color":"#e7a0b0","material":"matte","rot":[0,0,0],"slot":"gripper"},{"shape":"box","size":[0.07,0.07,0.1],"pos":[-0.112,0.29,0],"color":"#e7a0b0","material":"matte","rot":[0,0,-6],"slot":"gripper"},{"shape":"box","size":[0.07,0.07,0.1],"pos":[-0.124,0.21999999999999997,0],"color":"#e7a0b0","material":"matte","rot":[0,0,-12],"slot":"gripper"},{"shape":"box","size":[0.07,0.07,0.1],"pos":[-0.10600000000000001,0.14999999999999997,0],"color":"#e7a0b0","material":"matte","rot":[0,0,-18],"slot":"gripper"},{"shape":"box","size":[0.07,0.07,0.1],"pos":[-0.08800000000000002,0.07999999999999996,0],"color":"#e7a0b0","material":"matte","rot":[0,0,-24],"slot":"gripper"},{"shape":"box","size":[0.07,0.07,0.1],"pos":[0.1,0.36,0],"color":"#e7a0b0","material":"matte","rot":[0,0,0],"slot":"gripper"},{"shape":"box","size":[0.07,0.07,0.1],"pos":[0.112,0.29,0],"color":"#e7a0b0","material":"matte","rot":[0,0,6],"slot":"gripper"},{"shape":"box","size":[0.07,0.07,0.1],"pos":[0.124,0.21999999999999997,0],"color":"#e7a0b0","material":"matte","rot":[0,0,12],"slot":"gripper"},{"shape":"box","size":[0.07,0.07,0.1],"pos":[0.10600000000000001,0.14999999999999997,0],"color":"#e7a0b0","material":"matte","rot":[0,0,18],"slot":"gripper"},{"shape":"box","size":[0.07,0.07,0.1],"pos":[0.08800000000000002,0.07999999999999996,0],"color":"#e7a0b0","material":"matte","rot":[0,0,24],"slot":"gripper"},{"shape":"sphere","radius":0.1,"pos":[0,0.12,0],"color":"#d6453d","material":"gloss","slot":"gripper"}]}}]}],"sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Chs. 4 and 12","quote":"A robot arm is typically equipped with a hand or gripper, more generally called an end-effector, which interacts with objects in the surrounding world.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"deeper":"Next level: jaw geometry, contact friction, suction seal, compliance, tooling and changeover.","id":"end-effector","look":{"parts":[{"shape":"cylinder","radiusTop":0.16,"radiusBottom":0.16,"height":0.06,"pos":[0,0.62,0],"color":"#9aa0aa","material":"metal","slot":"gripper"},{"shape":"box","size":[0.5,0.18,0.22],"pos":[0,0.48,0],"color":"#2b3038","material":"gloss","radius":0.03,"slot":"gripper"},{"shape":"box","size":[0.06,0.34,0.12],"pos":[-0.12,0.22,0],"color":"#5b616b","material":"metal","slot":"gripper"},{"shape":"box","size":[0.06,0.34,0.12],"pos":[0.12,0.22,0],"color":"#5b616b","material":"metal","slot":"gripper"},{"shape":"box","size":[0.18,0.18,0.18],"pos":[0,0.16,0],"color":"#e07a2d","material":"matte","slot":"gripper"}]}},{"term":"Grip force","aka":["how hard it squeezes"],"kind":"knob","plain":"Grip force is the normal force a contact applies to the object.","does":"It must resist gravity and acceleration through friction, without damaging the object.","ask":"What is the lowest force that holds with a measured friction and safety margin?","cues":["Object held without slip","Slip from too little force","Deformation or crushing from too much force"],"range":"Robotiq lists 20–235 N grip force for its 2F-85 parallel gripper. 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Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 12 §§12.2.1–12.2.3","quote":"If the finger slides to the right, the force it applies lies on the right-hand edge of the friction cone, with magnitude determined by the normal force.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"},{"label":"Robotiq, Adaptive Grippers","url":"https://robotiq.com/products/adaptive-grippers","kind":"maker","page":"2F-85 specification","quote":"20 TO 235 N GRIP FORCE","work":"robotiq-adaptive-grippers"}],"id":"grip-force","look":{"parts":[{"shape":"box","size":[1.2,1,0.02],"pos":[0,0,-0.012],"color":"#0d0f14","material":"matte"},{"shape":"plane","size":[1.2,1],"pos":[0,0,0],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 360 300\"><rect width=\"360\" height=\"300\" rx=\"10\" fill=\"#161a22\"/><text x=\"20\" y=\"34\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"14\" fill=\"#9aa3b5\" font-weight=\"700\" letter-spacing=\"2\">GRIPPER</text><text x=\"20\" y=\"80\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"16\" fill=\"#d7dae0\">Force</text><text x=\"340\" y=\"80\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"30\" fill=\"#ffffff\" font-weight=\"700\" text-anchor=\"end\">50 N</text><rect x=\"20\" y=\"100\" width=\"320\" height=\"14\" rx=\"7\" fill=\"#2c3240\" stroke=\"none\" stroke-width=\"0\"/><rect x=\"20\" y=\"100\" width=\"44.64\" height=\"14\" rx=\"7\" fill=\"#2f6fd6\" stroke=\"none\" stroke-width=\"0\"/><circle cx=\"64.64\" cy=\"107\" r=\"13\" fill=\"#ffffff\" stroke=\"none\" stroke-width=\"2\"/><text x=\"20\" y=\"140\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"12\" fill=\"#9aa3b5\">20 N</text><text x=\"340\" y=\"140\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"12\" fill=\"#9aa3b5\" text-anchor=\"end\">235 N</text><text x=\"20\" y=\"190\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"16\" fill=\"#d7dae0\">Width</text><text x=\"340\" y=\"190\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"22\" fill=\"#ffffff\" font-weight=\"700\" text-anchor=\"end\">42 mm</text><text x=\"20\" y=\"236\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"16\" fill=\"#d7dae0\">Speed</text><text x=\"340\" y=\"236\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"22\" fill=\"#ffffff\" font-weight=\"700\" text-anchor=\"end\">60 mm/s</text><rect x=\"20\" y=\"256\" width=\"150\" height=\"32\" rx=\"6\" fill=\"#3f9a5b\" stroke=\"none\" stroke-width=\"0\"/><text x=\"95\" y=\"278\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"15\" fill=\"#fff\" font-weight=\"700\" text-anchor=\"middle\">GRIP</text><rect x=\"190\" y=\"256\" width=\"150\" height=\"32\" rx=\"6\" fill=\"#3a4150\" stroke=\"none\" stroke-width=\"0\"/><text x=\"265\" y=\"278\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"15\" fill=\"#fff\" font-weight=\"700\" text-anchor=\"middle\">RELEASE</text></svg>"}]}},{"term":"Grasp quality","aka":["force closure"],"kind":"measure","plain":"Grasp quality measures how well contacts resist external forces and torques. Force closure means the contact set can resist an arbitrary object wrench under the contact model.","does":"It lets a grasp planner rank candidate contacts before execution.","ask":"Is this grasp in force closure, and how much margin remains?","at":[-0.09,0.16,0.08],"sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 12 §§12.1.7 and 12.2.3","quote":"We say the contacts result in force closure if the composite wrench cone contains the entire wrench space","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"},{"label":"Richard M. Murray, Zexiang Li and S. Shankar Sastry, A Mathematical Introduction to Robotic Manipulation","url":"http://www.cds.caltech.edu/~murray/mlswiki/images/mlswiki/0/02/Mls94-complete.pdf","kind":"book","isbn":"9780849379819","page":"Ch. 5 §§2–3","quote":"One is to assign a quality measure to a grasp and choose the grasp which maximizes this quality measure and is also force-closure.","flag":"electronic edition","work":"richard-m-murray-zexiang-li-and-s-shankar-sastry"}],"deeper":"Next level: grasp maps, friction cones, wrench-space convex hulls, force-closure tests and quality metrics.","id":"grasp-quality","look":{"parts":[{"shape":"box","size":[1.4,0.9545,0.02],"pos":[0,0,-0.012],"color":"#cfccc2","material":"matte"},{"shape":"plane","size":[1.4,0.9545],"pos":[0,0,0],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect width=\"440\" height=\"300\" rx=\"10\" fill=\"#f6f4ef\"/><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#1f2430\" font-weight=\"700\">Grasp quality</text><text x=\"20\" y=\"54\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#7a7f8c\">contacts and friction cones: force closure</text><path d=\"M150 110 L290 100 L310 220 L140 230 Z\" stroke=\"#1f2430\" stroke-width=\"3\" fill=\"#e9e6dd\" stroke-linecap=\"round\" stroke-linejoin=\"round\" /><path d=\"M146 170 L210.9029 143.7775 L210.9029 196.2225 Z\" stroke=\"#2f6fd6\" stroke-width=\"1.5\" fill=\"#2f6fd6\" stroke-linecap=\"round\" stroke-linejoin=\"round\" fill-opacity=\"0.18\"/><circle cx=\"146\" cy=\"170\" r=\"7\" fill=\"#c8463d\" stroke=\"none\" stroke-width=\"2\"/><path d=\"M300 160 L235.0971 186.2225 L235.0971 133.7775 Z\" stroke=\"#2f6fd6\" stroke-width=\"1.5\" fill=\"#2f6fd6\" stroke-linecap=\"round\" stroke-linejoin=\"round\" fill-opacity=\"0.18\"/><circle cx=\"300\" cy=\"160\" r=\"7\" fill=\"#c8463d\" stroke=\"none\" stroke-width=\"2\"/><path d=\"M220 104 L243.9414 169.7785 L191.5284 167.9482 Z\" stroke=\"#2f6fd6\" stroke-width=\"1.5\" fill=\"#2f6fd6\" stroke-linecap=\"round\" stroke-linejoin=\"round\" fill-opacity=\"0.18\"/><circle cx=\"220\" cy=\"104\" r=\"7\" fill=\"#c8463d\" stroke=\"none\" stroke-width=\"2\"/><text x=\"220\" y=\"272\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"14\" fill=\"#1f2430\" text-anchor=\"middle\">Cones cover every direction: the grasp resists any push</text></svg>"}]}},{"term":"Drive base","aka":["wheels","mobile base","locomotion"],"kind":"part","plain":"A drive base produces the robot's gross motion with wheels, legs or rotors.","does":"It moves the arm and tool to the work area and determines which body motions are direct.","ask":"Which body velocities can the base command without a manoeuvre?","cues":["Wheels, legs or rotors under the robot","Gross motion toward the work area"],"at":[0.34,0.1,0.04],"variants":[{"label":"Drive","items":[{"id":"drive-differential","name":"Differential drive","plain":"Two driven wheels give forward motion and turning, but no instantaneous sideways motion; Stretch 3 uses this base type.","why":"A base with two driven wheels that gives forward motion and turning without instantaneous sideways motion defines it; Stretch 3 is one example.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 13 §13.1","quote":"Many mobile bases, however, such as cars and differential-drive robots, use more typical wheels, which do not slip sideways.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"},{"label":"Hello Robot, Stretch 3 Mobile Manipulator","url":"https://docs-arch.hello-robot.com/0.3/hardware/hardware_guide_stretch_3/","kind":"maker","page":"Base","quote":"The base is a two wheel differential drive with a passive omniwheel for a caster.","work":"hello-robot-stretch-3-mobile-manipulator"}],"look":{"parts":[{"shape":"cylinder","radiusTop":0.13,"radiusBottom":0.13,"height":0.08,"pos":[-0.45,0.13,0],"color":"#16181c","rot":[0,0,90],"material":"matte","slot":"wheels"},{"shape":"cylinder","radiusTop":0.0585,"radiusBottom":0.0585,"height":0.09,"pos":[-0.45,0.13,0],"color":"#9aa0aa","rot":[0,0,90],"material":"metal","slot":"wheels"},{"shape":"cylinder","radiusTop":0.13,"radiusBottom":0.13,"height":0.08,"pos":[0.45,0.13,0],"color":"#16181c","rot":[0,0,90],"material":"matte","slot":"wheels"},{"shape":"cylinder","radiusTop":0.0585,"radiusBottom":0.0585,"height":0.09,"pos":[0.45,0.13,0],"color":"#9aa0aa","rot":[0,0,90],"material":"metal","slot":"wheels"},{"shape":"sphere","radius":0.05,"pos":[0,0.05,0.24],"color":"#555555","slot":"wheels"},{"shape":"sphere","radius":0.05,"pos":[0,0.05,-0.24],"color":"#555555","slot":"wheels"}]}},{"id":"drive-mecanum","name":"Mecanum / omni wheels","plain":"Mecanum or omni wheels use angled rollers to create planar motion in more directions than a conventional wheel.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 13 §§13.1–13.2","quote":"Mecanum wheels are similar, except that the spin axes of the circumferential rollers are not in the plane of the wheel.","flag":"author 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(car-like)","plain":"Ackermann steering is car-like: steering geometry constrains the instantaneous turn and normally prevents turning in place.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 13 §13.1","quote":"To prevent slipping of the front wheels, they are steered using Ackermann steering.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"look":{"parts":[{"shape":"cylinder","radiusTop":0.13,"radiusBottom":0.13,"height":0.08,"pos":[-0.45,0.13,0.24],"color":"#16181c","rot":[0,20,90],"material":"matte","slot":"wheels"},{"shape":"cylinder","radiusTop":0.0585,"radiusBottom":0.0585,"height":0.09,"pos":[-0.45,0.13,0.24],"color":"#9aa0aa","rot":[0,20,90],"material":"metal","slot":"wheels"},{"shape":"cylinder","radiusTop":0.13,"radiusBottom":0.13,"height":0.08,"pos":[0.45,0.13,0.24],"color":"#16181c","rot":[0,20,90],"material":"matte","slot":"wheels"},{"shape":"cylinder","radiusTop":0.0585,"radiusBottom":0.0585,"height":0.09,"pos":[0.45,0.13,0.24],"color":"#9aa0aa","rot":[0,20,90],"material":"metal","slot":"wheels"},{"shape":"cylinder","radiusTop":0.13,"radiusBottom":0.13,"height":0.08,"pos":[-0.45,0.13,-0.24],"color":"#16181c","rot":[0,0,90],"material":"matte","slot":"wheels"},{"shape":"cylinder","radiusTop":0.0585,"radiusBottom":0.0585,"height":0.09,"pos":[-0.45,0.13,-0.24],"color":"#9aa0aa","rot":[0,0,90],"material":"metal","slot":"wheels"},{"shape":"cylinder","radiusTop":0.13,"radiusBottom":0.13,"height":0.08,"pos":[0.45,0.13,-0.24],"color":"#16181c","rot":[0,0,90],"material":"matte","slot":"wheels"},{"shape":"cylinder","radiusTop":0.0585,"radiusBottom":0.0585,"height":0.09,"pos":[0.45,0.13,-0.24],"color":"#9aa0aa","rot":[0,0,90],"material":"metal","slot":"wheels"}]}},{"id":"drive-legged","name":"Legs","plain":"Legged bases place feet and shift body balance to cross terrain that wheels may not traverse; Spot is a four-legged example.","why":"A base that places feet and shifts body balance across terrain wheels may not traverse defines it; Spot is one example.","sources":[{"label":"Boston Dynamics, Spot","url":"https://bostondynamics.com/products/spot","kind":"maker","page":"Locomotion and terrain sensing","quote":"Our agile mobile robot for dynamic sensing and industrial inspection","work":"boston-dynamics-spot"}],"look":{"parts":[{"shape":"sphere","radius":0.05,"pos":[-0.3,0.22,0.3],"color":"#2b3038","slot":"wheels"},{"shape":"cylinder","radiusTop":0.035,"radiusBottom":0.035,"height":0.1673,"pos":[-0.27,0.17,0.36],"rot":[111.2,-39.72,-27.79],"color":"#2b3038","slot":"wheels"},{"shape":"sphere","radius":0.035,"pos":[-0.24,0.12,0.42],"color":"#2f6fd6","slot":"wheels"},{"shape":"cylinder","radiusTop":0.028,"radiusBottom":0.028,"height":0.2506,"pos":[-0.27,0,0.44],"rot":[21.87,64.63,146.03],"color":"#2b3038","slot":"wheels"},{"shape":"sphere","radius":0.035,"pos":[-0.3,-0.12,0.45999999999999996],"color":"#16181c","slot":"wheels"},{"shape":"sphere","radius":0.05,"pos":[0.3,0.22,0.3],"color":"#2b3038","slot":"wheels"},{"shape":"cylinder","radiusTop":0.035,"radiusBottom":0.035,"height":0.1673,"pos":[0.33,0.17,0.36],"rot":[111.2,-39.72,-27.79],"color":"#2b3038","slot":"wheels"},{"shape":"sphere","radius":0.035,"pos":[0.36,0.12,0.42],"color":"#2f6fd6","slot":"wheels"},{"shape":"cylinder","radiusTop":0.028,"radiusBottom":0.028,"height":0.2506,"pos":[0.33,0,0.44],"rot":[21.87,64.63,146.03],"color":"#2b3038","slot":"wheels"},{"shape":"sphere","radius":0.035,"pos":[0.3,-0.12,0.45999999999999996],"color":"#16181c","slot":"wheels"},{"shape":"sphere","radius":0.05,"pos":[-0.3,0.22,-0.3],"color":"#2b3038","slot":"wheels"},{"shape":"cylinder","radiusTop":0.035,"radiusBottom":0.035,"height":0.1673,"pos":[-0.27,0.17,-0.36],"rot":[-111.2,39.72,-27.79],"color":"#2b3038","slot":"wheels"},{"shape":"sphere","radius":0.035,"pos":[-0.24,0.12,-0.42],"color":"#2f6fd6","slot":"wheels"},{"shape":"cylinder","radiusTop":0.028,"radiusBottom":0.028,"height":0.2506,"pos":[-0.27,0,-0.44],"rot":[-21.87,-64.63,146.03],"color":"#2b3038","slot":"wheels"},{"shape":"sphere","radius":0.035,"pos":[-0.3,-0.12,-0.45999999999999996],"color":"#16181c","slot":"wheels"},{"shape":"sphere","radius":0.05,"pos":[0.3,0.22,-0.3],"color":"#2b3038","slot":"wheels"},{"shape":"cylinder","radiusTop":0.035,"radiusBottom":0.035,"height":0.1673,"pos":[0.33,0.17,-0.36],"rot":[-111.2,39.72,-27.79],"color":"#2b3038","slot":"wheels"},{"shape":"sphere","radius":0.035,"pos":[0.36,0.12,-0.42],"color":"#2f6fd6","slot":"wheels"},{"shape":"cylinder","radiusTop":0.028,"radiusBottom":0.028,"height":0.2506,"pos":[0.33,0,-0.44],"rot":[-21.87,-64.63,146.03],"color":"#2b3038","slot":"wheels"},{"shape":"sphere","radius":0.035,"pos":[0.3,-0.12,-0.45999999999999996],"color":"#16181c","slot":"wheels"}]}}]}],"sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 13 §§13.1–13.2","quote":"Mecanum wheels are similar, except that the spin axes of the circumferential rollers are not in the plane of the wheel.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"deeper":"Next level: wheel geometry, nonholonomic constraints, odometry, traction, gait or flight dynamics and safety limits.","id":"drive-base","look":{"parts":[{"shape":"box","size":[0.8,0.22,0.6],"pos":[0,0.26,0],"color":"#3a3f47","material":"matte","radius":0.04},{"shape":"box","size":[0.82,0.03,0.62],"pos":[0,0.15,0],"color":"#e8b82e","material":"matte"},{"shape":"cylinder","radiusTop":0.13,"radiusBottom":0.13,"height":0.08,"pos":[-0.45,0.13,0],"color":"#16181c","rot":[0,0,90],"material":"matte","slot":"wheels"},{"shape":"cylinder","radiusTop":0.0585,"radiusBottom":0.0585,"height":0.09,"pos":[-0.45,0.13,0],"color":"#9aa0aa","rot":[0,0,90],"material":"metal","slot":"wheels"},{"shape":"cylinder","radiusTop":0.13,"radiusBottom":0.13,"height":0.08,"pos":[0.45,0.13,0],"color":"#16181c","rot":[0,0,90],"material":"matte","slot":"wheels"},{"shape":"cylinder","radiusTop":0.0585,"radiusBottom":0.0585,"height":0.09,"pos":[0.45,0.13,0],"color":"#9aa0aa","rot":[0,0,90],"material":"metal","slot":"wheels"},{"shape":"sphere","radius":0.05,"pos":[0,0.05,0.24],"color":"#555555","slot":"wheels"},{"shape":"sphere","radius":0.05,"pos":[0,0.05,-0.24],"color":"#555555","slot":"wheels"}]}},{"term":"Actuators","aka":["motors","drives","muscles"],"kind":"part","plain":"Actuation is the chain that converts electrical or fluid power into controlled joint motion. A common electric unit combines a motor, transmission and driver.","does":"It supplies joint torque and speed while setting heat, mass, compliance and backdrivability.","ask":"Is there enough continuous and peak torque at the required speed without overheating?","cues":["Controlled joint motion","Joint torque and speed","Heat, compliance or backdrivability changes"],"children":["electric-motor","gearbox","motor-driver"],"at":[0.17,0.58,0.05],"variants":[{"label":"Actuator design","items":[{"id":"act-geared","name":"High-ratio geared servo","plain":"A high-ratio geared servo uses a fast motor and reducer to obtain larger joint torque at lower output speed; UR5 is described with 100:1 harmonic gearing.","why":"A fast motor and reducer producing larger joint torque at lower output speed defines it; UR5 is one example.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 4 Example 4.5; Ch. 8 §8.9","quote":"Each joint is directly driven by a brushless motor combined with 100:1 zero-backlash harmonic drive gearing, which greatly increases the torque available at the joint while reducing its maximum speed.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"},{"label":"Harmonic Drive LLC, CSG/CSF Component Sets Reducer Catalog","url":"https://www.harmonicdrive.net/_hd/content/documents1/CSG-CSF_Component.pdf","kind":"maker","page":"p. 6, ratios and zero backlash","quote":"The high-performance attributes of this gearing technology including, zero-backlash, high-torque-to-weight ratio, compact size, and excellent positional accuracy.","work":"harmonic-drive-llc-csg-csf-component-sets"}]},{"id":"act-qdd","name":"Quasi-direct drive","plain":"Quasi-direct drive couples a high-torque-density motor to a transmission below 10:1; Blue uses a 7.125:1 belt reduction and emphasizes backdrivability.","why":"A high-torque-density motor coupled to a transmission below 10:1 defines it; Blue is one example.","sources":[{"label":"David V. Gealy et al., Quasi-Direct Drive for Low-Cost Compliant Robotic Manipulation","url":"https://arxiv.org/pdf/1904.03815","kind":"research","page":"pp. 3–4","quote":"Quasi-Direct Drive (QDD) actuators (transmission ratios < 1:10) have been used for legged locomotion and have the desirable properties of low friction, high backdrivability.","flag":"arXiv preprint","work":"david-v-gealy-et-al-quasi-direct-drive-for-low"}]},{"id":"act-sea","name":"Series elastic","plain":"A series elastic actuator places a compliant element between the transmission and load; measured deflection gives force through F = kx.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 8 §8.9","quote":"A series elastic actuator (SEA) consists of an electric motor with a gearhead (often a harmonic drive gearhead) and a torsional spring attaching the output of the gearhead to the output of the actuator.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}]},{"id":"act-hydraulic","name":"Hydraulic","plain":"Hydraulic actuation is a high-power architecture used in Boston Dynamics' research Hydraulic Atlas; the current Atlas product page is all-electric.","sources":[{"label":"Boston Dynamics, History and Legacy","url":"https://bostondynamics.com/about/history/","kind":"maker","page":"Hydraulic Atlas","quote":"The hydraulic Atlas pushed the limits of dynamic motion and manipulation.","work":"boston-dynamics-history-and-legacy"}]}]}],"sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 8 §8.9","quote":"Most robots are driven by actuators that apply a force or torque to each joint.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"id":"actuation","look":{"parts":[{"shape":"cylinder","radiusTop":0.22,"radiusBottom":0.22,"height":0.6,"pos":[-0.42,0,0],"color":"#3a3f47","rot":[0,0,90],"material":"matte"},{"shape":"cylinder","radiusTop":0.23,"radiusBottom":0.23,"height":0.04,"pos":[-0.12,0,0],"color":"#9aa0aa","rot":[0,0,90],"material":"metal"},{"shape":"cylinder","radiusTop":0.26,"radiusBottom":0.26,"height":0.4,"pos":[0.12,0,0],"color":"#8b919b","rot":[0,0,90],"material":"metal"},{"shape":"cylinder","radiusTop":0.2,"radiusBottom":0.2,"height":0.06,"pos":[0.35,0,0],"color":"#c9ccd2","rot":[0,0,90],"material":"metal"},{"shape":"cylinder","radiusTop":0.02,"radiusBottom":0.02,"height":0.07,"pos":[0.36,0,0.14],"color":"#5b616b","rot":[0,0,90],"material":"metal"},{"shape":"cylinder","radiusTop":0.02,"radiusBottom":0.02,"height":0.07,"pos":[0.36,0.1212,0.07],"color":"#5b616b","rot":[0,0,90],"material":"metal"},{"shape":"cylinder","radiusTop":0.02,"radiusBottom":0.02,"height":0.07,"pos":[0.36,0.1212,-0.07],"color":"#5b616b","rot":[0,0,90],"material":"metal"},{"shape":"cylinder","radiusTop":0.02,"radiusBottom":0.02,"height":0.07,"pos":[0.36,0,-0.14],"color":"#5b616b","rot":[0,0,90],"material":"metal"},{"shape":"cylinder","radiusTop":0.02,"radiusBottom":0.02,"height":0.07,"pos":[0.36,-0.1212,-0.07],"color":"#5b616b","rot":[0,0,90],"material":"metal"},{"shape":"cylinder","radiusTop":0.02,"radiusBottom":0.02,"height":0.07,"pos":[0.36,-0.1212,0.07],"color":"#5b616b","rot":[0,0,90],"material":"metal"},{"shape":"box","size":[0.5,0.03,0.34],"pos":[-0.42,0.24,0],"color":"#1b5e3b","material":"matte"},{"shape":"box","size":[0.1,0.04,0.1],"pos":[-0.5,0.275,0],"color":"#15171c"},{"shape":"box","size":[0.08,0.06,0.06],"pos":[-0.3,0.29,0.1],"color":"#9aa0aa","material":"metal"}]}},{"term":"Electric motor","aka":["motor"],"kind":"part","plain":"An electric motor converts current into torque. In the linear motor model, torque is proportional to current through the torque constant until saturation and thermal limits matter.","does":"It provides the raw speed and torque that the transmission and controller use.","ask":"What continuous and peak torque are available at the required speed and temperature?","cues":["Current entering a motor","Torque and speed at the output","Winding heat or current limiting"],"range":"The linear model uses torque proportional to current; winding heat grows with current squared.","trouble":"Winding temperature, current limiting, saturation or demagnetization reduce torque; a driver can trip before the task is complete.","at":[-0.42,0,0],"variants":[{"label":"Motor","items":[{"id":"motor-bldc","name":"Brushless DC (BLDC/PMSM)","plain":"A BLDC/PMSM motor uses electronic commutation and is common in robot servos.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 8 §8.9","quote":"This commutation of the windings occurs mechanically using brushes (brushed motors) or electrically using control circuitry (brushless motors).","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"look":{"parts":[{"shape":"cylinder","radiusTop":0.5,"radiusBottom":0.5,"height":0.7,"pos":[0,0.35,0],"color":"#3a3f47","material":"matte","cut":110,"slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[0.36,0.35,0],"color":"#b8732e","rot":[0,0,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[0.3118,0.35,-0.18],"color":"#b8732e","rot":[0,30,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[0.18,0.35,-0.3118],"color":"#b8732e","rot":[0,60,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[0,0.35,-0.36],"color":"#b8732e","rot":[0,90,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[-0.18,0.35,-0.3118],"color":"#b8732e","rot":[0,120,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[-0.3118,0.35,-0.18],"color":"#b8732e","rot":[0,150,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[-0.36,0.35,0],"color":"#b8732e","rot":[0,180,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[-0.3118,0.35,0.18],"color":"#b8732e","rot":[0,210,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[-0.18,0.35,0.3118],"color":"#b8732e","rot":[0,240,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[0,0.35,0.36],"color":"#b8732e","rot":[0,270,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[0.18,0.35,0.3118],"color":"#b8732e","rot":[0,300,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[0.3118,0.35,0.18],"color":"#b8732e","rot":[0,330,0],"material":"metal","slot":"body"},{"shape":"cylinder","radiusTop":0.24,"radiusBottom":0.24,"height":0.5,"pos":[0,0.35,0],"color":"#5b616b","material":"metal","slot":"body"},{"shape":"cylinder","radiusTop":0.05,"radiusBottom":0.05,"height":1.1,"pos":[0,0.5,0],"color":"#c9ccd2","material":"metal","motion":"spin","slot":"body"}]}},{"id":"motor-brushed","name":"Brushed DC","plain":"A brushed DC motor commutates through brushes and a commutator.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 8 §8.9","quote":"Figure 8.9 shows a brushed DC motor with an encoder and a gearhead.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"look":{"parts":[{"shape":"cylinder","radiusTop":0.42,"radiusBottom":0.42,"height":0.8,"pos":[0,0.4,0],"color":"#9aa0aa","material":"metal","cut":110,"slot":"body"},{"shape":"cylinder","radiusTop":0.43,"radiusBottom":0.43,"height":0.12,"pos":[0,0.86,0],"color":"#1d2027","material":"matte","slot":"body"},{"shape":"cylinder","radiusTop":0.24,"radiusBottom":0.24,"height":0.6,"pos":[0,0.4,0],"color":"#b8732e","material":"metal","slot":"body"},{"shape":"cylinder","radiusTop":0.05,"radiusBottom":0.05,"height":1.2,"pos":[0,0.55,0],"color":"#c9ccd2","material":"metal","slot":"body"},{"shape":"box","size":[0.06,0.08,0.06],"pos":[0.2,0.94,0],"color":"#2b2b2b","slot":"body"},{"shape":"box","size":[0.06,0.08,0.06],"pos":[-0.2,0.94,0],"color":"#2b2b2b","slot":"body"}]}},{"id":"motor-stepper","name":"Stepper","plain":"A stepper motor advances in commanded steps from input pulses; in open loop it can lose synchronism under excess load.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 11, velocity control","quote":"The links are moved by actuators, which typically are electrically driven (e.g., by DC or AC motors, stepper motors, or shape memory alloys) but can also be driven by pneumatic or hydraulic cylinders.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"look":{"parts":[{"shape":"box","size":[0.84,0.7,0.84],"pos":[0,0.35,0],"color":"#1d2027","material":"matte","slot":"body"},{"shape":"box","size":[0.86,0.08,0.86],"pos":[0,0.04,0],"color":"#8b919b","material":"metal","slot":"body"},{"shape":"box","size":[0.86,0.08,0.86],"pos":[0,0.66,0],"color":"#8b919b","material":"metal","slot":"body"},{"shape":"cylinder","radiusTop":0.04,"radiusBottom":0.04,"height":1,"pos":[0,0.6,0],"color":"#c9ccd2","material":"metal","slot":"body"},{"shape":"cylinder","radiusTop":0.18,"radiusBottom":0.18,"height":0.04,"pos":[0,0.72,0],"color":"#8b919b","material":"metal","slot":"body"}]}}]}],"sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 8 §§8.9.1–8.9.2","quote":"Since DC electric motors nominally provide a torque proportional to the current through the motor, this torque command is equivalent to a current command.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"deeper":"Next level: torque-speed curves, winding resistance, thermal time constants, commutation, current limits and motor sizing.","id":"electric-motor","look":{"parts":[{"shape":"cylinder","radiusTop":0.5,"radiusBottom":0.5,"height":0.7,"pos":[0,0.35,0],"color":"#3a3f47","material":"matte","cut":110,"slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[0.36,0.35,0],"color":"#b8732e","rot":[0,0,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[0.3118,0.35,-0.18],"color":"#b8732e","rot":[0,30,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[0.18,0.35,-0.3118],"color":"#b8732e","rot":[0,60,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[0,0.35,-0.36],"color":"#b8732e","rot":[0,90,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[-0.18,0.35,-0.3118],"color":"#b8732e","rot":[0,120,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[-0.3118,0.35,-0.18],"color":"#b8732e","rot":[0,150,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[-0.36,0.35,0],"color":"#b8732e","rot":[0,180,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[-0.3118,0.35,0.18],"color":"#b8732e","rot":[0,210,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[-0.18,0.35,0.3118],"color":"#b8732e","rot":[0,240,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[0,0.35,0.36],"color":"#b8732e","rot":[0,270,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[0.18,0.35,0.3118],"color":"#b8732e","rot":[0,300,0],"material":"metal","slot":"body"},{"shape":"box","size":[0.08,0.5,0.09],"pos":[0.3118,0.35,0.18],"color":"#b8732e","rot":[0,330,0],"material":"metal","slot":"body"},{"shape":"cylinder","radiusTop":0.24,"radiusBottom":0.24,"height":0.5,"pos":[0,0.35,0],"color":"#5b616b","material":"metal","slot":"body"},{"shape":"cylinder","radiusTop":0.05,"radiusBottom":0.05,"height":1.1,"pos":[0,0.5,0],"color":"#c9ccd2","material":"metal","motion":"spin","slot":"body"}]}},{"term":"Gearbox","aka":["reducer","transmission"],"kind":"part","plain":"A gearbox trades motor speed for output torque. 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Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 4 Example 4.5","quote":"Each joint is directly driven by a brushless motor combined with 100:1 zero-backlash harmonic drive gearing.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}]}]}],"sources":[{"label":"Kevin M. Lynch and Frank C. 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Barfoot, State Estimation for Robotics","url":"https://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser24.pdf","kind":"book","isbn":"9781009299893","page":"Chs. 3, 6–8","quote":"This classic technique for linear systems (whose measurements are corrupted by Gaussian noise) is famously known as the Kalman filter, and has been the workhorse of estimation for the more than 60 years since its inception.","flag":"author PDF","work":"timothy-d-barfoot-state-estimation-for-robotics"}],"id":"state-estimation","look":{"parts":[{"shape":"box","size":[1.4,0.9545,0.02],"pos":[0,0,-0.012],"color":"#cfccc2","material":"matte"},{"shape":"plane","size":[1.4,0.9545],"pos":[0,0,0],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect width=\"440\" height=\"300\" rx=\"10\" fill=\"#f6f4ef\"/><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#1f2430\" font-weight=\"700\">State estimate</text><text x=\"20\" y=\"54\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#7a7f8c\">pose ± uncertainty, every step</text><path d=\"M60 240 L120 210 L180 200 L240 170 L300 150 L360 110\" stroke=\"#7a7f8c\" stroke-width=\"2\" fill=\"none\" stroke-linecap=\"round\" stroke-linejoin=\"round\" stroke-dasharray=\"6 6\"/><ellipse cx=\"60\" cy=\"240\" rx=\"8\" ry=\"5\" fill=\"#2f6fd6\" fill-opacity=\"0.18\" stroke=\"#2f6fd6\" stroke-width=\"1.5\"/><circle cx=\"60\" cy=\"240\" r=\"4\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/><ellipse cx=\"120\" cy=\"210\" rx=\"13\" ry=\"8\" fill=\"#2f6fd6\" fill-opacity=\"0.18\" stroke=\"#2f6fd6\" stroke-width=\"1.5\"/><circle cx=\"120\" cy=\"210\" r=\"4\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/><ellipse cx=\"180\" cy=\"200\" rx=\"18\" ry=\"11\" fill=\"#2f6fd6\" fill-opacity=\"0.18\" stroke=\"#2f6fd6\" stroke-width=\"1.5\"/><circle cx=\"180\" cy=\"200\" r=\"4\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/><ellipse cx=\"240\" cy=\"170\" rx=\"23\" ry=\"14\" fill=\"#2f6fd6\" fill-opacity=\"0.18\" stroke=\"#2f6fd6\" stroke-width=\"1.5\"/><circle cx=\"240\" cy=\"170\" r=\"4\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/><ellipse cx=\"300\" cy=\"150\" rx=\"28\" ry=\"17\" fill=\"#2f6fd6\" fill-opacity=\"0.18\" stroke=\"#2f6fd6\" stroke-width=\"1.5\"/><circle cx=\"300\" cy=\"150\" r=\"4\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/><ellipse cx=\"360\" cy=\"110\" rx=\"33\" ry=\"20\" fill=\"#2f6fd6\" fill-opacity=\"0.18\" stroke=\"#2f6fd6\" stroke-width=\"1.5\"/><circle cx=\"360\" cy=\"110\" r=\"4\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/><g transform=\"translate(360 110) rotate(-35)\"><rect x=\"-14\" y=\"-10\" width=\"28\" height=\"20\" rx=\"4\" fill=\"#e07a2d\" stroke=\"#1f2430\" stroke-width=\"2\"/><path d=\"M14 0 L24 0\" stroke=\"#1f2430\" stroke-width=\"3\" fill=\"none\" stroke-linecap=\"round\" stroke-linejoin=\"round\" /></g><text x=\"300\" y=\"270\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"16\" fill=\"#2a2530\" font-weight=\"700\">x̂ = (x, y, θ),  Σ</text></svg>"}]}},{"term":"Bayes filter","aka":["Kalman filter","sensor fusion"],"kind":"loop","plain":"A Bayes filter predicts a belief through a motion model and then conditions it on a new measurement.","does":"Fuses sensors into one state estimate with an explicit belief or covariance.","ask":"Which filter matches the motion, measurement, and uncertainty distributions?","children":["prediction-step","update-step","noise-covariances"],"at":[0.2545,0,0.02],"pattern":"pattern-predict-correct","loop":{"type":"cycle","through":["prediction-step","update-step"]},"variants":[{"label":"Filter","items":[{"id":"filter-ekf","name":"Extended Kalman filter","plain":"Linearizes nonlinear motion and measurement models near the current estimate and propagates a Gaussian mean and covariance.","sources":[{"label":"Timothy D. Barfoot, State Estimation for Robotics","url":"https://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser24.pdf","kind":"book","isbn":"9781009299893","page":"Ch. 6","quote":"The EKF is still the mainstay of estimation and data fusion in many circles, and can often be effective for mildly nonlinear, non-Gaussian systems.","flag":"author PDF","work":"timothy-d-barfoot-state-estimation-for-robotics"}]},{"id":"filter-ukf","name":"Unscented Kalman filter","plain":"The unscented Kalman filter is a nonlinear Gaussian filtering method in the state-estimation family.","sources":[{"label":"Timothy D. 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Barfoot, State Estimation for Robotics","url":"https://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser24.pdf","kind":"book","isbn":"9781009299893","page":"Chs. 8–9","quote":"The fixed-interval smoother is usually presented in a recursive formulation.","flag":"author PDF","work":"timothy-d-barfoot-state-estimation-for-robotics"},{"label":"Cesar Cadena et al., Past, Present, and Future of Simultaneous Localization and Mapping: Toward the Robust-Perception Age","url":"https://robotics.caltech.edu/wiki/images/1/1a/PastPresentFutureSLAM.pdf","kind":"research","page":"Survey of SLAM back ends","quote":"The variables correspond to nodes in the factor graph. The terms p ( z k |X k ) and the prior p ( X ) are called factors, and they encode probabilistic constraints over a subset of nodes.","flag":"open PDF","work":"cesar-cadena-et-al-past-present-and-future-of"}]}]}],"sources":[{"label":"Timothy D. Barfoot, State Estimation for Robotics","url":"https://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser24.pdf","kind":"book","isbn":"9781009299893","page":"Chs. 6–8","quote":"The Bayes filter seeks to come up with an entire PDF to represent the likelihood of the state","flag":"author PDF","work":"timothy-d-barfoot-state-estimation-for-robotics"}],"id":"bayes-filter"},{"term":"Prediction step","aka":["motion update","propagate"],"kind":"process","plain":"The prediction step propagates the prior belief through the motion model and adds process uncertainty.","does":"Keeps the estimate current between measurement updates.","ask":"Is the motion model valid over the time and control gap?","sources":[{"label":"Timothy D. 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Barfoot, State Estimation for Robotics","url":"https://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser24.pdf","kind":"book","isbn":"9781009299893","page":"Ch. 3 §3.3.3","quote":"Next, for the correction step, we express the joint density of our state and latest measurement, at time k, as a Gaussian.","flag":"author PDF","work":"timothy-d-barfoot-state-estimation-for-robotics"}],"deeper":"The next level would hold residuals, innovation covariance, measurement Jacobians, and robust gating.","id":"update-step","look":{"parts":[{"shape":"box","size":[1.4,0.9545,0.02],"pos":[0,0,-0.012],"color":"#cfccc2","material":"matte"},{"shape":"plane","size":[1.4,0.9545],"pos":[0,0,0],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect width=\"440\" height=\"300\" rx=\"10\" fill=\"#f6f4ef\"/><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#1f2430\" font-weight=\"700\">Update step</text><text x=\"20\" y=\"54\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#7a7f8c\">combine prediction and measurement; 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R models uncertainty in a sensor measurement.","does":"Controls how much prediction and measurement compete in the filter.","ask":"Do residuals and state errors agree with the stated covariance?","trouble":"If R is too small, noisy measurements cause jumps. If Q is too small, real motion is ignored and the estimate becomes overconfident.","sources":[{"label":"Timothy D. Barfoot, State Estimation for Robotics","url":"https://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser24.pdf","kind":"book","isbn":"9781009299893","page":"Chs. 6–7","quote":"There are Jacobians embedded in the Q k and R k covariances for the noise.","flag":"author PDF","work":"timothy-d-barfoot-state-estimation-for-robotics"}],"deeper":"The next level would hold covariance calibration, innovation tests, cross-correlation, and adaptive noise models.","id":"noise-covariances","look":{"parts":[{"shape":"box","size":[1.4,0.9545,0.02],"pos":[0,0,-0.012],"color":"#0d0f14","material":"matte"},{"shape":"plane","size":[1.4,0.9545],"pos":[0,0,0],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect x=\"0\" y=\"0\" width=\"440\" height=\"300\" rx=\"10\" fill=\"#1e222b\" stroke=\"none\" stroke-width=\"0\"/><rect x=\"0\" y=\"0\" width=\"440\" height=\"34\" rx=\"10\" fill=\"#2a2f3a\" stroke=\"none\" stroke-width=\"0\"/><rect x=\"0\" y=\"20\" width=\"440\" height=\"14\" rx=\"0\" fill=\"#2a2f3a\" stroke=\"none\" stroke-width=\"0\"/><circle cx=\"18\" cy=\"17\" r=\"5\" fill=\"#e06c5f\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"36\" cy=\"17\" r=\"5\" fill=\"#e5c07b\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"54\" cy=\"17\" r=\"5\" fill=\"#7fc06f\" stroke=\"none\" stroke-width=\"2\"/><text x=\"76\" y=\"22\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"13\" fill=\"#9aa3b5\">ekf.yaml</text><text x=\"18\" y=\"64\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"#e5c07b\">ekf_filter_node:</tspan></text><text x=\"18\" y=\"86\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"#e5c07b\">  ros__parameters:</tspan></text><text x=\"18\" y=\"108\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"#d7dae0\">    frequency: </tspan><tspan fill=\"#d19a66\">30.0</tspan></text><text x=\"18\" y=\"130\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"#7f8794\">    # Q: how much to distrust the model</tspan></text><text x=\"18\" y=\"152\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"#d7dae0\">    process_noise_covariance:</tspan></text><text x=\"18\" y=\"174\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"#d19a66\">      [0.05, 0, 0, …  </tspan><tspan fill=\"#7f8794\"># x</tspan></text><text x=\"18\" y=\"196\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"#d19a66\">       0, 0.05, 0, … </tspan><tspan fill=\"#7f8794\"># y</tspan></text><text x=\"18\" y=\"218\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"#7f8794\">    # R comes with each sensor message</tspan></text><text x=\"18\" y=\"240\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"#d7dae0\">    odom0_config: </tspan><tspan fill=\"#98c379\">[true, true, …]</tspan></text></svg>"}]}},{"term":"Odometry","aka":["dead reckoning"],"kind":"process","plain":"Odometry estimates incremental motion by accumulating wheel, image, inertial, or scan-matching measurements.","does":"Provides smooth, high-rate motion between absolute fixes.","ask":"How quickly does each odometry source drift on this floor, scene, or route?","cues":["Wheel, image, inertial or scan-matching measurements","Incremental path between absolute fixes","Drift along a floor, scene or route"],"children":["drift"],"at":[-0.3182,-0.1909,0.02],"links":[{"to":"encoder","rel":"made from"},{"to":"imu","rel":"made from"}],"variants":[{"label":"Odometry","items":[{"id":"odom-wheel","name":"Wheel","plain":"Integrates encoder increments with the wheel geometry; slip and calibration error create drift.","sources":[{"label":"Timothy D. Barfoot, State Estimation for Robotics","url":"https://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser24.pdf","kind":"book","isbn":"9781009299893","page":"Ch. 3","quote":"Measurements of this type can arise from a lower-level dead-reckoning method such as wheel odometry, visual odometry, or inertial sensing.","flag":"author PDF","work":"timothy-d-barfoot-state-estimation-for-robotics"}]},{"id":"odom-visual","name":"Visual","plain":"Tracks image motion or features across frames to estimate camera motion.","sources":[{"label":"Timothy D. 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Barfoot, State Estimation for Robotics","url":"https://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser24.pdf","kind":"book","isbn":"9781009299893","page":"Chs. 6–8","quote":"An inertial measurement unit has three linear accelerometers and three rate gyros that measure quantities in the sensor frame.","flag":"author PDF","work":"timothy-d-barfoot-state-estimation-for-robotics"}]},{"id":"odom-lidar","name":"Lidar","plain":"Registers consecutive lidar scans to estimate their relative transform.","sources":[{"label":"Point Cloud Library, The PCL Registration API","url":"https://pointclouds.org/documentation/tutorials/registration_api.html","kind":"maker","page":"Registration API","quote":"Estimate a (rigid) transformation between camera poses (motion estimate) and minimize error metric.","work":"point-cloud-library-the-pcl-registration-api"}]}]}],"sources":[{"label":"Timothy D. Barfoot, State Estimation for Robotics","url":"https://asrl.utias.utoronto.ca/~tdb/bib/barfoot_ser24.pdf","kind":"book","isbn":"9781009299893","page":"Chs. 3 and 6","quote":"Measurements of this type can arise from a lower-level dead-reckoning method such as wheel odometry, visual odometry, or inertial sensing.","flag":"author PDF","work":"timothy-d-barfoot-state-estimation-for-robotics"},{"label":"Point Cloud Library, The PCL Registration API","url":"https://pointclouds.org/documentation/tutorials/registration_api.html","kind":"maker","page":"Registration API","quote":"The last step is to actually compute the transformation.","work":"point-cloud-library-the-pcl-registration-api"}],"id":"odometry","look":{"parts":[{"shape":"box","size":[1.4,0.9545,0.02],"pos":[0,0,-0.012],"color":"#cfccc2","material":"matte"},{"shape":"plane","size":[1.4,0.9545],"pos":[0,0,0],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect width=\"440\" height=\"300\" rx=\"10\" fill=\"#f6f4ef\"/><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#1f2430\" font-weight=\"700\">Odometry</text><text x=\"20\" y=\"54\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#7a7f8c\">add up small steps; error accumulates</text><path d=\"M50 250 L150 250 L250 250 L330 230 L380 170 L380 90\" stroke=\"#1f2430\" stroke-width=\"3\" fill=\"none\" stroke-linecap=\"round\" stroke-linejoin=\"round\" /><path d=\"M50 250 L150 246 L250 236 L334 206 L376 140 L364 64\" stroke=\"#e07a2d\" stroke-width=\"3\" fill=\"none\" stroke-linecap=\"round\" stroke-linejoin=\"round\" stroke-dasharray=\"2 8\"/><circle cx=\"50\" cy=\"250\" r=\"4\" fill=\"#e07a2d\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"150\" cy=\"246\" r=\"4\" fill=\"#e07a2d\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"250\" cy=\"236\" r=\"4\" fill=\"#e07a2d\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"334\" cy=\"206\" r=\"4\" fill=\"#e07a2d\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"376\" cy=\"140\" r=\"4\" fill=\"#e07a2d\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"364\" cy=\"64\" r=\"4\" fill=\"#e07a2d\" stroke=\"none\" stroke-width=\"2\"/><line x1=\"380\" y1=\"90\" x2=\"364\" y2=\"64\" stroke=\"#c8463d\" stroke-width=\"2\" stroke-linecap=\"round\" /><text x=\"140\" y=\"274\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#1f2430\" font-weight=\"700\">true path</text><text x=\"250\" y=\"220\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#e07a2d\" font-weight=\"700\">odometry</text><text x=\"396\" y=\"80\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#c8463d\" font-weight=\"700\">drift</text></svg>"}]}},{"term":"Drift","aka":["accumulated error"],"kind":"measure","plain":"Drift is accumulated trajectory error from integrating imperfect incremental motion.","does":"Indicates how often the robot needs an absolute reference or loop closure.","ask":"What translational drift percentage occurs per 100 m on this robot and route?","cues":["Accumulated trajectory error","Estimated path diverging from a reference","Error growing along a route"],"range":"KITTI reports average translational error in percent over all 100–800 m subsequences.","at":[0.5409,0.2291,0.02],"sources":[{"label":"Jürgen Sturm et al., Evaluating Egomotion and Structure-from-Motion Approaches Using the TUM RGB-D Benchmark","url":"https://cvg.cit.tum.de/_media/spezial/bib/sturm12iros_ws.pdf","kind":"research","page":"Sec. V, Relative Pose Error","quote":"The relative pose error measures the local accuracy of the trajectory over a fixed time interval Δ.","flag":"open PDF","work":"jurgen-sturm-et-al-evaluating-egomotion-and"},{"label":"Johann Borenstein and Liqiang Feng, UMBmark: A Benchmark Test for Measuring Odometry Errors in Mobile Robots","url":"https://www.cs.columbia.edu/~allen/F15/NOTES/borenstein.pdf","kind":"research","page":"Secs. 3.2, 4.1; Table I; 4×4 m path","quote":"Systematic errors are a property of the robot itself, and they stay almost constant over prolonged periods of time, while non-systematic errors are a function of the properties of the floor.","flag":"open PDF","work":"johann-borenstein-and-liqiang-feng-umbmark-a"}],"deeper":"The next level would hold error definitions, alignment choices, trajectory segments, and benchmark protocols.","id":"drift","plot":{"x":"Distance travelled (m)","y":"Position error (m)","series":[{"name":"Wheel (UMBmark, uncalibrated LabMate) (1.94%)","points":[[0,0],[500,9.7],[1000,19.4]]},{"name":"Stereo visual (KITTI, Stereo DSO) (0.93%)","points":[[0,0],[500,4.65],[1000,9.3]]},{"name":"Visual-inertial (KITTI, VINS-Fusion) (1.09%)","points":[[0,0],[500,5.45],[1000,10.9]]},{"name":"Lidar (KITTI, LOAM) (0.55%)","points":[[0,0],[500,2.75],[1000,5.5]]}]}},{"term":"SLAM","aka":["simultaneous localisation and mapping"],"kind":"process","plain":"SLAM estimates a robot trajectory and a map together from observations, so the map and pose constrain one another.","does":"Builds a reusable spatial reference when no prior map or reliable absolute position exists.","ask":"What representation, loop-closure evidence and uncertainty are acceptable for this environment?","cues":["Robot trajectory and map together","Pose constrained by the map","Reusable spatial reference"],"children":["map-representation","loop-closure","trajectory-error"],"sources":[{"label":"Cesar Cadena et al., Past, Present, and Future of Simultaneous Localization and Mapping: Toward the Robust-Perception Age","url":"https://robotics.caltech.edu/wiki/images/1/1a/PastPresentFutureSLAM.pdf","kind":"research","page":"Survey of SLAM","quote":"Topological mapping drops the metric information and only leverages place recognition to build a graph in which the nodes represent distinguishable places.","flag":"open PDF","work":"cesar-cadena-et-al-past-present-and-future-of"},{"label":"Timothy D. 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representation","aka":["map type"],"kind":"concept","plain":"A map representation is the data structure used to store the world for localization, mapping, and planning.","does":"Sets which spatial questions the planner can ask and how much memory and computation the map needs.","ask":"Does the planner need occupancy, landmarks, raw geometry, or a surface?","cues":["Occupation probabilities assigned to cells","Distinctive landmarks across observations","Registered 3D samples from scans","Smooth surfaces from a depth volume"],"at":[-0.3182,0,0.02],"variants":[{"label":"Map","items":[{"id":"map-grid","name":"Occupancy grid","plain":"An occupancy grid discretizes the environment into cells and assigns a probability of occupation to each cell.","sources":[{"label":"Cesar Cadena et al., Past, Present, and Future of Simultaneous Localization and Mapping: Toward the Robust-Perception 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Lynch and Frank C. 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redeployment.","id":"data-flywheel"},{"term":"Control","aka":["feedback control"],"kind":"process","plain":"A controller reads a target and measured robot state, computes a correction, and updates actuator commands.","does":"Feedback makes the robot follow a motion or force objective while reducing disturbance and model error.","ask":"Is the loop stable, how quickly does it respond, and how large is the tracking error?","cues":["Target and measured robot state","Motion or force objective followed"],"range":"A representative robot controller evaluates its law about 1,000 times per second; exact rates depend on the drive and robot.","children":["control-loop","robot-dynamics","interaction-control","model-predictive-control"],"at":[0.62,0.82,0.05],"sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 11, robot control","quote":"We can combine the advantages of feedforward control, which commands motion even when there is no error, with the advantages of feedback control, which limits the accumulation of error.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"id":"control","look":{"parts":[{"shape":"box","size":[1.5,0.8125,0.02],"pos":[0,0,-0.012],"color":"#cfccc2","material":"matte"},{"shape":"plane","size":[1.5,0.8125],"pos":[0,0,0],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 480 260\"><rect width=\"480\" height=\"260\" rx=\"10\" fill=\"#f6f4ef\"/><defs><marker id=\"ah\" viewBox=\"0 0 10 10\" refX=\"8\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\"><path d=\"M0 0 L10 5 L0 10 z\" fill=\"#1f2430\"/></marker><marker id=\"ahb\" viewBox=\"0 0 10 10\" refX=\"8\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\"><path d=\"M0 0 L10 5 L0 10 z\" fill=\"#2f6fd6\"/></marker><marker id=\"ahr\" viewBox=\"0 0 10 10\" refX=\"8\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\"><path d=\"M0 0 L10 5 L0 10 z\" fill=\"#c8463d\"/></marker></defs><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#1f2430\" font-weight=\"700\">Control</text><text x=\"20\" y=\"120\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#7a7f8c\">setpoint</text><line x1=\"20\" y1=\"130\" x2=\"76\" y2=\"130\" stroke=\"#1f2430\" stroke-width=\"2\" stroke-linecap=\"round\" marker-end=\"url(#ah)\"/><circle cx=\"92\" cy=\"130\" r=\"15\" fill=\"#fff\" stroke=\"#1f2430\" stroke-width=\"2\"/><text x=\"92\" y=\"135\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"16\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">Σ</text><text x=\"70\" y=\"158\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#2a2530\" font-weight=\"700\">−</text><line x1=\"107\" y1=\"130\" x2=\"150\" y2=\"130\" stroke=\"#1f2430\" stroke-width=\"2\" stroke-linecap=\"round\" marker-end=\"url(#ah)\"/><text x=\"128\" y=\"120\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"14\" fill=\"#c8463d\" font-weight=\"700\" text-anchor=\"middle\">e</text><rect x=\"150\" y=\"108\" width=\"110\" height=\"44\" rx=\"6\" fill=\"#dce6f7\" stroke=\"#1f2430\" stroke-width=\"2\"/><text x=\"205\" y=\"135\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"14\" fill=\"#1f2430\" font-weight=\"600\" text-anchor=\"middle\">Controller</text><line x1=\"260\" y1=\"130\" x2=\"300\" y2=\"130\" stroke=\"#1f2430\" stroke-width=\"2\" stroke-linecap=\"round\" marker-end=\"url(#ah)\"/><text x=\"280\" y=\"120\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"14\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">u</text><rect x=\"300\" y=\"108\" width=\"110\" height=\"44\" rx=\"6\" fill=\"#f3dfcc\" stroke=\"#1f2430\" stroke-width=\"2\"/><text x=\"355\" y=\"135\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"14\" fill=\"#1f2430\" font-weight=\"600\" text-anchor=\"middle\">Robot</text><line x1=\"410\" y1=\"130\" x2=\"460\" y2=\"130\" stroke=\"#1f2430\" stroke-width=\"2\" stroke-linecap=\"round\" marker-end=\"url(#ah)\"/><text x=\"440\" y=\"120\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"14\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">y</text><path d=\"M440 130 L440 210 L92 210 L92 147\" stroke=\"#1f2430\" stroke-width=\"2\" fill=\"none\" stroke-linecap=\"round\" stroke-linejoin=\"round\" marker-end=\"url(#ah)\"/><rect x=\"210\" y=\"190\" width=\"110\" height=\"40\" rx=\"6\" fill=\"#fff\" stroke=\"#1f2430\" stroke-width=\"2\"/><text x=\"265\" y=\"215\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"14\" fill=\"#1f2430\" font-weight=\"600\" text-anchor=\"middle\">Sensor</text></svg>"}]}},{"term":"Feedback control loop","aka":["servo loop","closed loop"],"kind":"loop","plain":"A closed loop measures the robot, compares the measurement with a target, computes a correction, commands an actuator, and measures again.","does":"It rejects errors and disturbances by feeding the measured result back to the controller.","ask":"What bandwidth, delay and stability margin remain?","cues":["Target compared with measurement","Repeated measurement after the command"],"children":["pid-controller","control-rate","tracking-error"],"at":[0.0625,-0.25,0.02],"pattern":"pattern-negative-feedback","loop":{"type":"balancing","through":["pid-controller","motor-driver","electric-motor","encoder","tracking-error"]},"sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 8 §8.9","quote":"The amplifier uses a local feedback control loop to adjust the time-averaged voltage across the motor to achieve the desired current.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"id":"control-loop"},{"term":"PID controller","aka":["proportional-integral-derivative"],"kind":"process","plain":"A PID law combines proportional error, accumulated error and error-rate terms into a command.","does":"It gives a joint or drive loop a compact, tunable feedback law.","ask":"Are the gains, sample time and derivative filtering matched to this plant and payload?","children":["pid-gains"],"sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 11 §11.4.1.1","quote":"A common feedback controller is linear proportional-integral-derivative control, or PID control.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"},{"label":"Karl J. Åström and Richard M. Murray, Feedback Systems: An Introduction for Scientists and Engineers","url":"https://web.archive.org/web/20251008125640id_/https://fbswiki.org/wiki/index.php/PID_Control","kind":"book","page":"PID control","quote":"Proportional-integral-derivative (PID) control is by far the most common way of using feedback in engineering systems.","work":"karl-j-astrom-and-richard-m-murray-feedback"}],"id":"pid-controller","look":{"parts":[{"shape":"box","size":[1.4,0.9545,0.02],"pos":[0,0,-0.012],"color":"#cfccc2","material":"matte"},{"shape":"plane","size":[1.4,0.9545],"pos":[0,0,0],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect width=\"440\" height=\"300\" rx=\"10\" fill=\"#f6f4ef\"/><defs><marker id=\"ah\" viewBox=\"0 0 10 10\" refX=\"8\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\"><path d=\"M0 0 L10 5 L0 10 z\" fill=\"#1f2430\"/></marker><marker id=\"ahb\" viewBox=\"0 0 10 10\" refX=\"8\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\"><path d=\"M0 0 L10 5 L0 10 z\" fill=\"#2f6fd6\"/></marker><marker id=\"ahr\" viewBox=\"0 0 10 10\" refX=\"8\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\"><path d=\"M0 0 L10 5 L0 10 z\" fill=\"#c8463d\"/></marker></defs><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#1f2430\" font-weight=\"700\">PID controller</text><text x=\"36\" y=\"156\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"14\" fill=\"#c8463d\" font-weight=\"700\">error e</text><path d=\"M100 150 L120 150 L120 80 L150 80 M120 150 L150 150 M120 150 L120 220 L150 220\" stroke=\"#1f2430\" stroke-width=\"2\" fill=\"none\" stroke-linecap=\"round\" stroke-linejoin=\"round\" /><rect x=\"150\" y=\"58\" width=\"170\" height=\"44\" rx=\"6\" fill=\"#fff\" stroke=\"#2f6fd6\" stroke-width=\"2.5\"/><text x=\"166\" y=\"86\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"20\" fill=\"#2f6fd6\" font-weight=\"700\">P</text><text x=\"196\" y=\"86\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#2a2530\">Kp · e</text><rect x=\"150\" y=\"128\" width=\"170\" height=\"44\" rx=\"6\" fill=\"#fff\" stroke=\"#e07a2d\" stroke-width=\"2.5\"/><text x=\"166\" y=\"156\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"20\" fill=\"#e07a2d\" font-weight=\"700\">I</text><text x=\"196\" y=\"156\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#2a2530\">Ki · ∫e dt</text><rect x=\"150\" y=\"198\" width=\"170\" height=\"44\" rx=\"6\" fill=\"#fff\" stroke=\"#3f9a5b\" stroke-width=\"2.5\"/><text x=\"166\" y=\"226\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"20\" fill=\"#3f9a5b\" font-weight=\"700\">D</text><text x=\"196\" y=\"226\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"15\" fill=\"#2a2530\">Kd · de/dt</text><path d=\"M320 80 L350 80 L350 150 M320 150 L350 150 M320 220 L350 220 L350 150 L366 150\" stroke=\"#1f2430\" stroke-width=\"2\" fill=\"none\" stroke-linecap=\"round\" stroke-linejoin=\"round\" /><circle cx=\"380\" cy=\"150\" r=\"14\" fill=\"#fff\" stroke=\"#1f2430\" stroke-width=\"2\"/><text x=\"380\" y=\"155\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">+</text><line x1=\"394\" y1=\"150\" x2=\"428\" y2=\"150\" stroke=\"#1f2430\" stroke-width=\"2\" stroke-linecap=\"round\" marker-end=\"url(#ah)\"/><text x=\"410\" y=\"140\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"14\" fill=\"#2a2530\" font-weight=\"700\">u</text></svg>"}]}},{"term":"PID gains","aka":["tuning","Kp Ki Kd"],"kind":"knob","plain":"The three weights Kp, Ki and Kd set the proportional, integral and derivative contributions.","does":"They trade response speed, steady-state error and transient overshoot or settling.","ask":"After a step, what are the steady-state error, rise time, overshoot and settling time?","cues":["Step response reaching the target","Overshoot or ringing","Settling and steady-state error"],"trouble":"Excessive gain can cause overshoot or oscillation; insufficient gain can leave a slow or inaccurate response.","links":[{"to":"tracking-error","rel":"lowers"}],"variants":[{"label":"Tuning","items":[{"id":"tune-low","name":"Soft (overdamped)","plain":"This tuning choice is evaluated by its settling time, overshoot and steady-state error.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://modernrobotics.northwestern.edu/nu-gm-book-resource/11-2-1-error-response/","kind":"book","isbn":"9781107156302","page":"§11.2.1 Error Response: Transient response and settling time","quote":"This video introduces the error response for a controlled system and characterizes the error response in terms of its steady-state error and its transient response (overshoot and settling time).","flag":"book resource page","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}]},{"id":"tune-good","name":"Well tuned (near critical damping)","plain":"A well-tuned response reaches the target quickly with small overshoot and short settling time.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://modernrobotics.northwestern.edu/nu-gm-book-resource/11-2-1-error-response/","kind":"book","isbn":"9781107156302","page":"§11.2.1 Error Response: Good controller response","quote":"A better response would have no steady-state error, no overshoot, and a faster settling time.","flag":"book resource page","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}]},{"id":"tune-high","name":"Aggressive (underdamped)","plain":"Aggressive gains can shorten rise time but may increase overshoot, ringing and settling time.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://modernrobotics.northwestern.edu/nu-gm-book-resource/11-2-1-error-response/","kind":"book","isbn":"9781107156302","page":"§11.2.1 Error Response: Overshoot, oscillation and settling time","quote":"We can also see that the error response overshoots its steady-state value before settling.","flag":"book resource page","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}]}]}],"sources":[{"label":"Karl J. Åström and Richard M. Murray, Feedback Systems: An Introduction for Scientists and Engineers","url":"https://web.archive.org/web/20251008125640id_/https://fbswiki.org/wiki/index.php/PID_Control","kind":"book","page":"Ch. 11, PID tuning, integral windup and implementation","quote":"Proportional-integral-derivative (PID) control is by far the most common way of using feedback in engineering systems.","work":"karl-j-astrom-and-richard-m-murray-feedback"},{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://modernrobotics.northwestern.edu/nu-gm-book-resource/11-2-1-error-response/","kind":"book","isbn":"9781107156302","page":"§11.2.1 Error Response","quote":"In summary, the error response can be characterized by its steady-state response, which refers to the final error achieved, and its transient response, which consists of the overshoot and settling time.","flag":"book resource page","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"deeper":"The next level would hold plant models, sample time, gain units, anti-windup and derivative filtering.","id":"pid-gains","plot":{"x":"Time (s)","y":"Joint position (fraction of step)","series":[{"name":"Soft: Kp 25, Kd 20","item":"tune-low","points":[[0,0],[0.025,0.0068],[0.05,0.0232],[0.075,0.0451],[0.1,0.0701],[0.125,0.0968],[0.15,0.124],[0.175,0.1513],[0.2,0.1782],[0.225,0.2047],[0.25,0.2305],[0.275,0.2556],[0.3,0.2799],[0.325,0.3036],[0.35,0.3264],[0.375,0.3486],[0.4,0.37],[0.425,0.3907],[0.45,0.4108],[0.475,0.4302],[0.5,0.4489],[0.525,0.4671],[0.55,0.4846],[0.575,0.5016],[0.6,0.518],[0.625,0.5339],[0.65,0.5492],[0.675,0.5641],[0.7,0.5784],[0.725,0.5923],[0.75,0.6057],[0.775,0.6187],[0.8,0.6313],[0.825,0.6434],[0.85,0.6551],[0.875,0.6665],[0.9,0.6775],[0.925,0.6881],[0.95,0.6984],[0.975,0.7083],[1,0.7179],[1.025,0.7272],[1.05,0.7362],[1.075,0.7449],[1.1,0.7533],[1.125,0.7614],[1.15,0.7692],[1.175,0.7768],[1.2,0.7842],[1.225,0.7913],[1.25,0.7982],[1.275,0.8048],[1.3,0.8112],[1.325,0.8175],[1.35,0.8235],[1.375,0.8293],[1.4,0.8349],[1.425,0.8403],[1.45,0.8456],[1.475,0.8507],[1.5,0.8556]]},{"name":"Well tuned: Kp 100, Kd 16","item":"tune-good","points":[[0,0],[0.025,0.0279],[0.05,0.0966],[0.075,0.189],[0.1,0.2925],[0.125,0.3982],[0.15,0.4999],[0.175,0.5936],[0.2,0.6772],[0.225,0.7498],[0.25,0.8112],[0.275,0.862],[0.3,0.9031],[0.325,0.9356],[0.35,0.9607],[0.375,0.9795],[0.4,0.9931],[0.425,1.0026],[0.45,1.0088],[0.475,1.0125],[0.5,1.0143],[0.525,1.0148],[0.55,1.0144],[0.575,1.0134],[0.6,1.012],[0.625,1.0104],[0.65,1.0089],[0.675,1.0074],[0.7,1.006],[0.725,1.0048],[0.75,1.0037],[0.775,1.0028],[0.8,1.002],[0.825,1.0014],[0.85,1.0009],[0.875,1.0006],[0.9,1.0003],[0.925,1.0001],[0.95,1],[0.975,0.9999],[1,0.9998],[1.025,0.9998],[1.05,0.9998],[1.075,0.9998],[1.1,0.9998],[1.125,0.9998],[1.15,0.9998],[1.175,0.9999],[1.2,0.9999],[1.225,0.9999],[1.25,0.9999],[1.275,0.9999],[1.3,1],[1.325,1],[1.35,1],[1.375,1],[1.4,1],[1.425,1],[1.45,1],[1.475,1],[1.5,1]]},{"name":"Aggressive: Kp 400, Kd 10","item":"tune-high","points":[[0,0],[0.025,0.1152],[0.05,0.397],[0.075,0.7472],[0.1,1.0747],[0.125,1.3133],[0.15,1.4311],[0.175,1.4291],[0.2,1.3344],[0.225,1.1881],[0.25,1.0334],[0.275,0.9057],[0.3,0.8269],[0.325,0.803],[0.35,0.8273],[0.375,0.8836],[0.4,0.9527],[0.425,1.0168],[0.45,1.063],[0.475,1.0853],[0.5,1.0841],[0.525,1.065],[0.55,1.0359],[0.575,1.0055],[0.6,0.9807],[0.625,0.9655],[0.65,0.9612],[0.675,0.9663],[0.7,0.9776],[0.725,0.9912],[0.75,1.0037],[0.775,1.0127],[0.8,1.0169],[0.825,1.0165],[0.85,1.0126],[0.875,1.0069],[0.9,1.0009],[0.925,0.996],[0.95,0.9931],[0.975,0.9924],[1,0.9934],[1.025,0.9957],[1.05,0.9984],[1.075,1.0008],[1.1,1.0025],[1.125,1.0033],[1.15,1.0032],[1.175,1.0024],[1.2,1.0013],[1.225,1.0001],[1.25,0.9992],[1.275,0.9986],[1.3,0.9985],[1.325,0.9987],[1.35,0.9992],[1.375,0.9997],[1.4,1.0002],[1.425,1.0005],[1.45,1.0007],[1.475,1.0006],[1.5,1.0005]]}]}},{"term":"Control rate","aka":["loop frequency","servo rate"],"kind":"knob","plain":"Control rate is the number of control updates made each second.","does":"It limits reaction speed and the bandwidth that a loop can achieve.","ask":"Is the loop fast enough for the dynamics, with enough time left to compute each update?","range":"Modern Robotics gives about 1 kHz for a robot controller; exact rates are drive-dependent.","links":[{"to":"fieldbus","rel":"see also"},{"to":"onboard-computer","rel":"see also"}],"pattern":"pattern-cascade","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://modernrobotics.northwestern.edu/nu-gm-book-resource/11-1-control-system-overview/","kind":"book","isbn":"9781107156302","page":"§11.1 Control System Overview: Representative controller and current-loop rates","quote":"At a rate of perhaps a thousand times per second, the controller evaluates a control law and requests joint torques from each motor amplifier.","flag":"book resource page","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"deeper":"The next level would hold scheduler jitter, sample-and-hold effects, computation deadlines and rate ratios between nested loops.","id":"control-rate","look":{"parts":[{"shape":"box","size":[1.4,0.9545,0.02],"pos":[0,0,-0.012],"color":"#0d0f14","material":"matte"},{"shape":"plane","size":[1.4,0.9545],"pos":[0,0,0],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect x=\"0\" y=\"0\" width=\"440\" height=\"300\" rx=\"10\" fill=\"#1e222b\" stroke=\"none\" stroke-width=\"0\"/><rect x=\"0\" y=\"0\" width=\"440\" height=\"34\" rx=\"10\" fill=\"#2a2f3a\" stroke=\"none\" stroke-width=\"0\"/><rect x=\"0\" y=\"20\" width=\"440\" height=\"14\" rx=\"0\" fill=\"#2a2f3a\" stroke=\"none\" stroke-width=\"0\"/><circle cx=\"18\" cy=\"17\" r=\"5\" fill=\"#e06c5f\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"36\" cy=\"17\" r=\"5\" fill=\"#e5c07b\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"54\" cy=\"17\" r=\"5\" fill=\"#7fc06f\" stroke=\"none\" stroke-width=\"2\"/><text x=\"76\" y=\"22\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"13\" fill=\"#9aa3b5\">controllers.yaml</text><text x=\"18\" y=\"64\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"#e5c07b\">controller_manager:</tspan></text><text x=\"18\" y=\"86\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"#e5c07b\">  ros__parameters:</tspan></text><text x=\"18\" y=\"108\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"#d7dae0\">    update_rate: </tspan><tspan fill=\"#d19a66\">1000</tspan><tspan fill=\"#7f8794\">  # Hz</tspan></text><text x=\"18\" y=\"130\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"undefined\">undefined</tspan></text><text x=\"18\" y=\"152\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"#e5c07b\">    arm_controller:</tspan></text><text x=\"18\" y=\"174\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"#d7dae0\">      type: </tspan><tspan fill=\"#98c379\">joint_trajectory_controller/</tspan></text><text x=\"18\" y=\"196\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"#d7dae0\">            </tspan><tspan fill=\"#98c379\">JointTrajectoryController</tspan></text><text x=\"18\" y=\"218\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"#7f8794\">    # perception runs at ~30 Hz</tspan></text><text x=\"18\" y=\"240\" font-family=\"Liberation Mono, Courier New, monospace\" font-size=\"14\" xml:space=\"preserve\"><tspan fill=\"#7f8794\">    # current loop in the drive: ~20 kHz</tspan></text></svg>"}]}},{"term":"Tracking error","aka":["following error"],"kind":"measure","plain":"Tracking error is the difference between the desired motion and the measured motion over time.","does":"It exposes steady-state accuracy and transient response during tuning.","ask":"What are the peak and RMS errors, and does the error settle?","cues":["Desired and measured motion traces","Peak and RMS error","Overshoot and settling"],"range":"Feedback Systems defines rise time, overshoot and settling time from a chosen final-value tolerance; state the tolerance used.","links":[{"to":"encoder","rel":"measured by"}],"sources":[{"label":"Karl J. Åström and Richard M. Murray, Feedback Systems: An Introduction for Scientists and Engineers","url":"http://www.cds.caltech.edu/~murray/books/AM08/pdf/fbs-principles_24Jul2020.pdf","kind":"book","page":"Ch. 2 §2.4","quote":"There are situations where only the error signal e = r − y can be measured; typical examples are DVD players, optical memories, and atomic force microscopes.","work":"karl-j-astrom-and-richard-m-murray-feedback"},{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://modernrobotics.northwestern.edu/nu-gm-book-resource/11-2-1-error-response/","kind":"book","isbn":"9781107156302","page":"§11.2.1 Error Response","quote":"The error response can be characterized by its steady-state response, which refers to the final error achieved, and its transient response, which consists of the overshoot and settling time.","flag":"book resource page","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"deeper":"The next level would hold error norms, steady-state and transient decompositions, step tests and disturbance tests.","id":"tracking-error","look":{"parts":[{"shape":"box","size":[1.4,0.9545,0.02],"pos":[0,0,-0.012],"color":"#0d0f14","material":"matte"},{"shape":"plane","size":[1.4,0.9545],"pos":[0,0,0],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect x=\"0\" y=\"0\" width=\"440\" height=\"300\" rx=\"10\" fill=\"#0e1a14\" stroke=\"none\" 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x=\"420\" y=\"34\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"15\" fill=\"#ffd166\" font-weight=\"700\" text-anchor=\"end\">peak 1.8 mm</text></svg>"}]}},{"term":"Robot dynamics","aka":["equations of motion","M(q)q̈ + C + g = τ"],"kind":"concept","plain":"Robot dynamics describe how joint forces and torques produce acceleration from link mass, inertia, Coriolis effects, gravity and friction.","does":"They let a controller predict required torque and add feedforward such as gravity compensation.","ask":"Are the masses, inertias and friction parameters identified, or only guessed?","range":"For an open chain, Modern Robotics writes the equations as M(q)q̈ + h(q,q̇) = τ, with h collecting centripetal, Coriolis, gravity and friction terms.","at":[0.3594,0,0.02],"sources":[{"label":"Kevin M. 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Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 1 Preview","quote":"If the robot imposes a motion then the environment determines the force, and vice versa.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}]},{"id":"ic-impedance","name":"Impedance control","plain":"Impedance control is a robot control objective involving a chosen motion–force relationship.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://modernrobotics.northwestern.edu/nu-gm-book-resource/11-1-control-system-overview/","kind":"book","isbn":"9781107156302","page":"§11.1 Control System Overview","quote":"This video introduces different robot control objectives (motion control, force control, hybrid motion-force control, and impedance control).","flag":"book resource page","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}]},{"id":"ic-admittance","name":"Admittance control","plain":"Admittance control is a force-to-motion control mode.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 11 §11.7.2","quote":"In an admittance-control algorithm the force f ext applied by the user is sensed by the wrist load cell, and the robot responds with an end-effector acceleration satisfying Equation (11.64).","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}]},{"id":"ic-force","name":"Direct force control","plain":"Direct force control regulates contact force toward a setpoint along selected task directions.","sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://modernrobotics.northwestern.edu/nu-gm-book-resource/11-1-control-system-overview/","kind":"book","isbn":"9781107156302","page":"§11.1 Control System Overview: Force-control objective","quote":"This video introduces different robot control objectives (motion control, force control, hybrid motion-force control, and impedance control).","flag":"book resource page","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}]}]}],"sources":[{"label":"Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://hades.mech.northwestern.edu/images/7/7f/MR.pdf","kind":"book","isbn":"9781107156302","page":"Ch. 11 §§11.5–11.7, force, hybrid and impedance control","quote":"A force-control goal makes sense when the end-effector is in contact with something, but not when it is moving in free space.","flag":"author preprint","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"},{"label":"Bruno Siciliano and Oussama Khatib (eds.), Springer Handbook of Robotics","url":"https://link.springer.com/chapter/10.1007/978-3-319-32552-1_9","kind":"book","isbn":"978-3-319-32552-1","page":"Ch. 9, Force Control","quote":"Pure motion control turns out to be inadequate because the unavoidable modeling errors and uncertainties may cause a rise of the contact force.","work":"bruno-siciliano-and-oussama-khatib-eds-springer"}],"id":"interaction-control","look":{"parts":[{"shape":"box","size":[1.4,0.08,0.7],"pos":[0,-0.04,0],"color":"#8b919b","material":"matte"},{"shape":"box","size":[0.9,0.06,0.3],"pos":[0,0.95,0],"color":"#2b3038","material":"gloss"},{"shape":"torus","radius":0.12,"tube":0.018,"pos":[-0.25,0.42,0],"rot":[90,0,0],"color":"#c9a227","material":"metal"},{"shape":"torus","radius":0.12,"tube":0.018,"pos":[-0.25,0.48,0],"rot":[90,0,0],"color":"#c9a227","material":"metal"},{"shape":"torus","radius":0.12,"tube":0.018,"pos":[-0.25,0.54,0],"rot":[90,0,0],"color":"#c9a227","material":"metal"},{"shape":"torus","radius":0.12,"tube":0.018,"pos":[-0.25,0.6,0],"rot":[90,0,0],"color":"#c9a227","material":"metal"},{"shape":"torus","radius":0.12,"tube":0.018,"pos":[-0.25,0.66,0],"rot":[90,0,0],"color":"#c9a227","material":"metal"},{"shape":"torus","radius":0.12,"tube":0.018,"pos":[-0.25,0.72,0],"rot":[90,0,0],"color":"#c9a227","material":"metal"},{"shape":"torus","radius":0.12,"tube":0.018,"pos":[-0.25,0.78,0],"rot":[90,0,0],"color":"#c9a227","material":"metal"},{"shape":"torus","radius":0.12,"tube":0.018,"pos":[-0.25,0.84,0],"rot":[90,0,0],"color":"#c9a227","material":"metal"},{"shape":"cylinder","radiusTop":0.012,"radiusBottom":0.012,"height":0.56,"pos":[-0.25,0.64,0],"rot":[0,0,0],"color":"#5b616b"},{"shape":"cylinder","radiusTop":0.07,"radiusBottom":0.07,"height":0.3,"pos":[0.25,0.78,0],"color":"#3a3f47","material":"gloss"},{"shape":"cylinder","radiusTop":0.025,"radiusBottom":0.025,"height":0.28,"pos":[0.25,0.5,0],"rot":[0,0,0],"color":"#c9ccd2","material":"metal"},{"shape":"box","size":[0.8,0.06,0.3],"pos":[0,0.33,0],"color":"#5b616b","material":"metal"},{"shape":"cylinder","radiusTop":0.08,"radiusBottom":0.08,"height":0.3,"pos":[0,0.15,0],"color":"#e07a2d","material":"matte"}]}},{"term":"Virtual stiffness and damping","aka":["impedance gains"],"kind":"knob","plain":"Virtual stiffness K maps displacement from an equilibrium to a restoring force; damping D adds a velocity-dependent term.","does":"It sets how compliant the robot feels and how quickly contact force grows with displacement.","ask":"What force will the robot apply if the target is 1 cm inside the surface?","cues":["Displacement from equilibrium","Restoring force","Contact force growing with displacement","Push response at a stiffness setting"],"range":"libfranka documents Cartesian stiffness/compliance and gives an impedance example with 150 N/m translational stiffness and 10 Nm/rad rotational stiffness.","at":[-0.25,0.6,0.14],"links":[{"to":"force-torque-sensor","rel":"measured by"}],"variants":[{"label":"Stiffness","items":[{"id":"k-soft","name":"Soft","plain":"200 N/m is a low translational stiffness example; a 1 cm displacement gives about 2 N before other terms.","sources":[{"label":"Franka Robotics, libfranka: cartesian_impedance_control.cpp","url":"https://frankarobotics.github.io/libfranka/0.15.0/cartesian_impedance_control_8cpp-example.html","kind":"maker","page":"Example introduction","quote":"After starting the controller try to push the robot around and try different stiffness levels.","work":"franka-robotics-libfranka-cartesian-impedance"}]},{"id":"k-medium","name":"Medium","plain":"1000 N/m is a middle-of-range translational stiffness example; a 1 cm displacement gives about 10 N before damping.","sources":[{"label":"Franka Robotics, libfranka: franka::Robot Class Reference","url":"https://frankarobotics.github.io/libfranka/latest/classfranka_1_1Robot.html","kind":"maker","page":"Stiffness frame","quote":"This frame allows to modify the compliance behavior of the robot (e.g. to have a low stiffness around a specific point which is not the end effector).","work":"franka-robotics-libfranka-franka-robot-class"}]},{"id":"k-stiff","name":"Stiff","plain":"3000 N/m is an upper translational stiffness example; a 1 cm displacement gives about 30 N before damping.","sources":[{"label":"Franka Robotics, libfranka: franka::Robot Class Reference","url":"https://frankarobotics.github.io/libfranka/latest/classfranka_1_1Robot.html","kind":"maker","page":"setCartesianImpedance parameter bounds","quote":"Sets the Cartesian stiffness/compliance (for x, y, z, roll, pitch, yaw) in the internal controller.","work":"franka-robotics-libfranka-franka-robot-class"}]}]}],"sources":[{"label":"Franka Robotics, libfranka: cartesian_impedance_control.cpp","url":"https://frankarobotics.github.io/libfranka/0.15.0/cartesian_impedance_control_8cpp-example.html","kind":"maker","page":"Example introduction","quote":"After starting the controller try to push the robot around and try different stiffness levels.","work":"franka-robotics-libfranka-cartesian-impedance"},{"label":"Franka Robotics, libfranka: franka::Robot Class Reference","url":"https://frankarobotics.github.io/libfranka/latest/classfranka_1_1Robot.html","kind":"maker","page":"setCartesianImpedance parameter bounds","quote":"Sets the Cartesian stiffness/compliance (for x, y, z, roll, pitch, yaw) in the internal controller.","work":"franka-robotics-libfranka-franka-robot-class"}],"id":"stiffness","plot":{"x":"Displacement (mm)","y":"Contact force (N)","series":[{"name":"200 N/m","item":"k-soft","points":[[0,0],[10,2],[20,4]]},{"name":"1000 N/m","item":"k-medium","points":[[0,0],[10,10],[20,20]]},{"name":"3000 N/m","item":"k-stiff","points":[[0,0],[10,30],[20,60]]}]}},{"term":"Model predictive control","aka":["MPC","receding horizon control"],"kind":"process","plain":"At each update, model predictive control optimizes a future command sequence, applies the first command, then repeats with a fresh state estimate.","does":"It plans ahead while enforcing model, input and contact constraints.","ask":"Can the optimization finish before the next control update?","range":"The MIT Cheetah 3 implementation is a convex model-predictive-control study; timing and horizon are implementation details.","at":[-0.1094,0,0.02],"links":[{"to":"robot-dynamics","rel":"made from"}],"pattern":"pattern-predict-correct","sources":[{"label":"Jared Di Carlo, Patrick M. 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9.2.3.3","quote":"1 Controlled stop A controlled stop with power available to the machine actuators to achieve the stop, and then removal of power when the stop is achieved","work":"idec-group-safety-standard-iec-60204-1-2016"}]},{"id":"stop-2","name":"Category 2","plain":"Stop category 2 is a controlled stop that leaves actuator power available after the stop.","sources":[{"label":"IDEC, Group Safety Standard: IEC 60204-1:2016","url":"https://www.idec.com/en-us/solutions/safety/law/iso-iec/iec60204","kind":"maker","page":"Stop categories, 9.2.3.3","quote":"2 At-rest state Controlled stop with power remaining available to the machine actuators even after the stop is completed","work":"idec-group-safety-standard-iec-60204-1-2016"}]}]}],"sources":[{"label":"Universal Robots, Emergency Stop","url":"https://www.universal-robots.com/manuals/EN/HTML/SW10_15/Content/prod-usr-man/complianceUR18/H_g5_sections/safety_g5/emergency_stop.htm","kind":"maker","page":"Emergency Stop","quote":"Do not use the emergency stop for routine stopping or as a substitute for normal shutdown or power-off procedures.","work":"universal-robots-emergency-stop"},{"label":"IDEC, Group Safety Standard: IEC 60204-1:2016","url":"https://www.idec.com/en-us/solutions/safety/law/iso-iec/iec60204","kind":"maker","page":"Stop categories and emergency stop, 9.2.3.3–9.2.3.4.2","quote":"An emergency stop function shall stop the hazardous motion as quickly as practicable without creating other hazards.","work":"idec-group-safety-standard-iec-60204-1-2016"}],"deeper":"The next level would hold button layout, stop-category selection, safe outputs, latching and reset, diagnostics, and validation tests.","id":"emergency-stop","look":{"parts":[{"shape":"box","size":[0.8,0.6,0.8],"pos":[0,0.3,0],"color":"#e8b82e","material":"matte","radius":0.05},{"shape":"cylinder","radiusTop":0.22,"radiusBottom":0.22,"height":0.12,"pos":[0,0.66,0],"color":"#c8261d","material":"gloss"},{"shape":"lathe","profile":[[0,0],[0.26,0],[0.34,0.04],[0.36,0.1],[0.3,0.16],[0,0.18]],"smooth":true,"pos":[0,0.72,0],"color":"#d22a20","material":"gloss"},{"shape":"plane","size":[0.6,0.2],"pos":[0,0.3,0.402],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 300 100\"><rect width=\"300\" height=\"100\" fill=\"#e8b82e\"/><text x=\"150\" y=\"66\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"44\" font-weight=\"700\" text-anchor=\"middle\" fill=\"#111\">STOP</text></svg>"}]}},{"term":"Collaborative operation","aka":["cobot safety"],"kind":"concept","plain":"Collaborative operation is a deliberately designed state in which a robot and a person can work in a shared workspace.","does":"Sets which monitored stop, guiding, separation, or force-limiting functions the application needs.","ask":"Which collaborative mode and contact assumptions did the application risk assessment justify?","children":["contact-force-limit"],"at":[0.62,0.37,0.12],"links":[{"to":"interaction-control","rel":"see also"}],"variants":[{"label":"Collaborative mode","items":[{"id":"collab-sms","name":"Safety-rated monitored stop","plain":"Safety-rated monitored stop is one of the four collaborative operation types described by FANUC America.","why":"It counts here because the collaborative function is a safety-rated monitored stop; the shared workspace is not the defining feature.","sources":[{"label":"FANUC America, Collaborative Robots: Options and Safety Explained","url":"https://www.fanucamerica.com/articles/what-you-need-to-know-to-work-with-a-collaborative-robot-system","kind":"practitioner","page":"Collaborative robot operations","quote":"there are four different types of collaborative robot operation: Safety rated monitored stop Hand guiding Speed and separation monitoring Power and force limiting by inherent design.","work":"fanuc-collaborative-robot-options-safety"}],"svg":{"mode":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect width=\"440\" height=\"300\" rx=\"10\" fill=\"#f6f4ef\"/><clipPath id=\"cl\"><rect x=\"20\" y=\"50\" width=\"400\" height=\"215\"/></clipPath><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#1f2430\" font-weight=\"700\">Monitored stop</text><g clip-path=\"url(#cl)\"><circle cx=\"170\" cy=\"170\" r=\"110\" fill=\"#e0705f\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"170\" cy=\"170\" r=\"22\" fill=\"#e07a2d\" stroke=\"none\" stroke-width=\"2\"/><line x1=\"170\" y1=\"170\" x2=\"210\" y2=\"140\" stroke=\"#1f2430\" stroke-width=\"8\" stroke-linecap=\"round\" /><circle cx=\"210\" cy=\"140\" r=\"6\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"250\" cy=\"176\" r=\"9\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/><rect x=\"240\" y=\"186\" width=\"20\" height=\"26\" rx=\"6\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"0\"/></g><text x=\"220\" y=\"286\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">person inside: robot holds a monitored stop</text></svg>"}},{"id":"collab-hand","name":"Hand guiding","plain":"Hand guiding is one of the four collaborative operation types described by FANUC America.","why":"It counts here because the collaborative function lets a person hand-guide the robot; the shared workspace is not the defining feature.","sources":[{"label":"FANUC America, Collaborative Robots: Options and Safety Explained","url":"https://www.fanucamerica.com/articles/what-you-need-to-know-to-work-with-a-collaborative-robot-system","kind":"practitioner","page":"Collaborative robot operations","quote":"there are four different types of collaborative robot operation: Safety rated monitored stop Hand guiding Speed and separation monitoring Power and force limiting by inherent design.","work":"fanuc-collaborative-robot-options-safety"}],"svg":{"mode":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect width=\"440\" height=\"300\" rx=\"10\" fill=\"#f6f4ef\"/><clipPath id=\"cl\"><rect x=\"20\" y=\"50\" width=\"400\" height=\"215\"/></clipPath><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#1f2430\" font-weight=\"700\">Hand guiding</text><g clip-path=\"url(#cl)\"><circle cx=\"170\" cy=\"170\" r=\"22\" fill=\"#e07a2d\" stroke=\"none\" stroke-width=\"2\"/><line x1=\"170\" y1=\"170\" x2=\"210\" y2=\"140\" stroke=\"#1f2430\" stroke-width=\"8\" stroke-linecap=\"round\" /><circle cx=\"210\" cy=\"140\" r=\"6\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"230\" cy=\"146\" r=\"9\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/><rect x=\"220\" y=\"156\" width=\"20\" height=\"26\" rx=\"6\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"0\"/><line x1=\"214\" y1=\"142\" x2=\"224\" y2=\"150\" stroke=\"#1f2430\" stroke-width=\"4\" stroke-linecap=\"round\" /></g><text x=\"220\" y=\"286\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">person moves the robot by hand</text></svg>"}},{"id":"collab-ssm","name":"Speed and separation monitoring","plain":"Speed and separation monitoring is one of the four collaborative operation types described by FANUC America.","why":"It counts here because the function monitors speed and separation; the shared workspace is not the defining feature.","sources":[{"label":"FANUC America, Collaborative Robots: Options and Safety Explained","url":"https://www.fanucamerica.com/articles/what-you-need-to-know-to-work-with-a-collaborative-robot-system","kind":"practitioner","page":"Collaborative robot operations","quote":"there are four different types of collaborative robot operation: Safety rated monitored stop Hand guiding Speed and separation monitoring Power and force limiting by inherent design.","work":"fanuc-collaborative-robot-options-safety"}],"svg":{"mode":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect width=\"440\" height=\"300\" rx=\"10\" fill=\"#f6f4ef\"/><clipPath id=\"cl\"><rect x=\"20\" y=\"50\" width=\"400\" height=\"215\"/></clipPath><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#1f2430\" font-weight=\"700\">Speed and separation</text><g clip-path=\"url(#cl)\"><circle cx=\"170\" cy=\"170\" r=\"120\" fill=\"#7fc28f\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"170\" cy=\"170\" r=\"85\" fill=\"#f0cf5a\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"170\" cy=\"170\" r=\"50\" fill=\"#e0705f\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"170\" cy=\"170\" r=\"22\" fill=\"#e07a2d\" stroke=\"none\" stroke-width=\"2\"/><line x1=\"170\" y1=\"170\" x2=\"210\" y2=\"140\" stroke=\"#1f2430\" stroke-width=\"8\" stroke-linecap=\"round\" /><circle cx=\"210\" cy=\"140\" r=\"6\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"360\" cy=\"156\" r=\"9\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/><rect x=\"350\" y=\"166\" width=\"20\" height=\"26\" rx=\"6\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"0\"/></g><text x=\"220\" y=\"286\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">closer = slower; too close = stop</text></svg>"}},{"id":"collab-pfl","name":"Power and force limiting","plain":"Power and force limiting is one of the four collaborative operation types described by FANUC America.","why":"It counts here because the function limits power and force; the shared workspace is not the defining feature.","sources":[{"label":"FANUC America, Collaborative Robots: Options and Safety Explained","url":"https://www.fanucamerica.com/articles/what-you-need-to-know-to-work-with-a-collaborative-robot-system","kind":"practitioner","page":"Collaborative robot operations","quote":"there are four different types of collaborative robot operation: Safety rated monitored stop Hand guiding Speed and separation monitoring Power and force limiting by inherent design.","work":"fanuc-collaborative-robot-options-safety"}],"svg":{"mode":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect width=\"440\" height=\"300\" rx=\"10\" fill=\"#f6f4ef\"/><clipPath id=\"cl\"><rect x=\"20\" y=\"50\" width=\"400\" height=\"215\"/></clipPath><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#1f2430\" font-weight=\"700\">Power and force limiting</text><g clip-path=\"url(#cl)\"><circle cx=\"170\" cy=\"170\" r=\"22\" fill=\"#e07a2d\" stroke=\"none\" stroke-width=\"2\"/><line x1=\"170\" y1=\"170\" x2=\"210\" y2=\"140\" stroke=\"#1f2430\" stroke-width=\"8\" stroke-linecap=\"round\" /><circle cx=\"210\" cy=\"140\" r=\"6\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"222\" cy=\"138\" r=\"9\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/><rect x=\"212\" y=\"148\" width=\"20\" height=\"26\" rx=\"6\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"0\"/><circle cx=\"214\" cy=\"140\" r=\"16\" fill=\"none\" stroke=\"#c8463d\" stroke-width=\"3\"/><text x=\"260\" y=\"120\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"16\" fill=\"#c8463d\" font-weight=\"700\">≤ 140 N</text></g><text x=\"220\" y=\"286\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">contact allowed below body-region limits</text></svg>"}}]}],"sources":[{"label":"FANUC America, Collaborative Robots: Options and Safety Explained","url":"https://www.fanucamerica.com/articles/what-you-need-to-know-to-work-with-a-collaborative-robot-system","kind":"practitioner","page":"Collaborative robot operations","quote":"there are four different types of collaborative robot operation","work":"fanuc-collaborative-robot-options-safety"}],"id":"collaborative-operation","look":{"parts":[{"shape":"box","size":[1.4,0.9545,0.02],"pos":[0,0,-0.012],"color":"#cfccc2","material":"matte","slot":"mode-back"},{"shape":"plane","size":[1.4,0.9545],"pos":[0,0,0],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 300\"><rect width=\"440\" height=\"300\" rx=\"10\" fill=\"#f6f4ef\"/><clipPath id=\"cl\"><rect x=\"20\" y=\"50\" width=\"400\" height=\"215\"/></clipPath><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#1f2430\" font-weight=\"700\">Monitored stop</text><g clip-path=\"url(#cl)\"><circle cx=\"170\" cy=\"170\" r=\"110\" fill=\"#e0705f\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"170\" cy=\"170\" r=\"22\" fill=\"#e07a2d\" stroke=\"none\" stroke-width=\"2\"/><line x1=\"170\" y1=\"170\" x2=\"210\" y2=\"140\" stroke=\"#1f2430\" stroke-width=\"8\" stroke-linecap=\"round\" /><circle cx=\"210\" cy=\"140\" r=\"6\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/><circle cx=\"250\" cy=\"176\" r=\"9\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"2\"/><rect x=\"240\" y=\"186\" width=\"20\" height=\"26\" rx=\"6\" fill=\"#1f2430\" stroke=\"none\" stroke-width=\"0\"/></g><text x=\"220\" y=\"286\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">person inside: robot holds a monitored stop</text></svg>","slot":"mode"}]}},{"term":"Contact force limits","aka":["biomechanical limits"],"kind":"knob","plain":"Contact-force limits constrain power and force in a power-and-force-limited application; body-specific limits require a risk assessment.","does":"Constrain speed, energy, and contact behavior after the application risk assessment.","ask":"Which body region could be hit or clamped, and which limit applies?","at":[0.0955,-0.0954,0.02],"variants":[{"label":"Body region","items":[{"id":"region-hand","name":"Hand and fingers","plain":"The body model lists hand and finger as an individual body region.","sources":[{"label":"DGUV, BG/BGIA Risk Assessment Recommendations: Design of Workplaces with Collaborative Robots","url":"https://publikationen.dguv.de/widgets/pdf/download/article/4387","kind":"standard","page":"p. 14, body model explanatory text","quote":"The body model establishes 4 main body regions and 15 individual body regions within the main regions so all anthropometric points of the body surface can be allocated in the body model.","work":"dguv-bgia-design-of-workplaces-with-collaborative-robots"}]},{"id":"region-forearm","name":"Lower arm","plain":"The body model lists lower arm and hand joint as an individual body region.","sources":[{"label":"DGUV, BG/BGIA Risk Assessment Recommendations: Design of Workplaces with Collaborative Robots","url":"https://publikationen.dguv.de/widgets/pdf/download/article/4387","kind":"standard","page":"p. 14, body model explanatory text","quote":"The body model establishes 4 main body regions and 15 individual body regions within the main regions so all anthropometric points of the body surface can be allocated in the body model.","work":"dguv-bgia-design-of-workplaces-with-collaborative-robots"}]},{"id":"region-chest","name":"Chest","plain":"The body model lists chest as an individual body region.","sources":[{"label":"DGUV, BG/BGIA Risk Assessment Recommendations: Design of Workplaces with Collaborative 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model.","work":"dguv-bgia-design-of-workplaces-with-collaborative-robots"}]}]}],"sources":[{"label":"FANUC America, Collaborative Robots: Options and Safety Explained","url":"https://www.fanucamerica.com/articles/what-you-need-to-know-to-work-with-a-collaborative-robot-system","kind":"practitioner","page":"Power and force limiting","quote":"power or force feedback built in, allowing it to detect contact with a person","work":"fanuc-collaborative-robot-options-safety"},{"label":"DGUV, BG/BGIA Risk Assessment Recommendations: Design of Workplaces with Collaborative Robots","url":"https://publikationen.dguv.de/widgets/pdf/download/article/4387","kind":"standard","page":"p. 13, risk analysis and individual body regions","quote":"In risk analysis, the individual body regions assigned to a collision risk are determined.","work":"dguv-bgia-design-of-workplaces-with-collaborative-robots"}],"deeper":"The next level would hold contact geometry, quasi-static versus transient cases, pressure-force conversion, speed limits, and validation measurements.","id":"contact-force-limit","look":{"parts":[{"shape":"box","size":[1.3,1.0045,0.02],"pos":[0,0,-0.012],"color":"#cfccc2","material":"matte"},{"shape":"plane","size":[1.3,1.0045],"pos":[0,0,0],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 340\"><rect width=\"440\" height=\"340\" rx=\"10\" fill=\"#f6f4ef\"/><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#2a2530\" font-weight=\"700\">Contact limits</text><circle cx=\"220\" cy=\"70\" r=\"26\" fill=\"#cdd3dc\" stroke=\"#1f2430\" stroke-width=\"2\"/><rect x=\"186\" y=\"100\" width=\"68\" height=\"110\" rx=\"18\" fill=\"#cdd3dc\" stroke=\"#1f2430\" stroke-width=\"2\"/><path d=\"M190 110 L150 200 L140 250\" stroke=\"#1f2430\" stroke-width=\"14\" fill=\"none\" stroke-linecap=\"round\" stroke-linejoin=\"round\" /><path d=\"M250 110 L290 200 L300 250\" stroke=\"#1f2430\" stroke-width=\"14\" fill=\"none\" stroke-linecap=\"round\" stroke-linejoin=\"round\" /><path d=\"M200 205 L196 320 M240 205 L244 320\" stroke=\"#1f2430\" stroke-width=\"16\" fill=\"none\" stroke-linecap=\"round\" stroke-linejoin=\"round\" /><line x1=\"220\" y1=\"76\" x2=\"330\" y2=\"60\" stroke=\"#7a7f8c\" stroke-width=\"1.5\" stroke-linecap=\"round\" /><circle cx=\"220\" cy=\"76\" r=\"5\" fill=\"#c8463d\" stroke=\"none\" stroke-width=\"2\"/><text x=\"336\" y=\"58\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"start\">Face</text><text x=\"336\" y=\"76\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#c8463d\" font-weight=\"700\" text-anchor=\"start\">65 N</text><line x1=\"220\" y1=\"140\" x2=\"330\" y2=\"140\" stroke=\"#7a7f8c\" stroke-width=\"1.5\" stroke-linecap=\"round\" /><circle cx=\"220\" cy=\"140\" r=\"5\" fill=\"#c8463d\" stroke=\"none\" stroke-width=\"2\"/><text x=\"336\" y=\"138\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"start\">Chest</text><text x=\"336\" y=\"156\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#c8463d\" font-weight=\"700\" text-anchor=\"start\">140 N</text><line x1=\"150\" y1=\"200\" x2=\"60\" y2=\"180\" stroke=\"#7a7f8c\" stroke-width=\"1.5\" stroke-linecap=\"round\" /><circle cx=\"150\" cy=\"200\" r=\"5\" fill=\"#c8463d\" stroke=\"none\" stroke-width=\"2\"/><text x=\"54\" y=\"178\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"end\">Lower arm</text><text x=\"54\" y=\"196\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#c8463d\" font-weight=\"700\" text-anchor=\"end\">160 N</text><line x1=\"140\" y1=\"252\" x2=\"60\" y2=\"280\" stroke=\"#7a7f8c\" stroke-width=\"1.5\" stroke-linecap=\"round\" /><circle cx=\"140\" cy=\"252\" r=\"5\" fill=\"#c8463d\" stroke=\"none\" stroke-width=\"2\"/><text x=\"54\" y=\"278\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"end\">Hand</text><text x=\"54\" y=\"296\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#c8463d\" font-weight=\"700\" text-anchor=\"end\">140 N</text></svg>"}]}},{"term":"Performance level (PL)","aka":["safety integrity"],"kind":"measure","plain":"Performance Level (PL) is a discrete reliability level for a safety-related control function, from PL a to PL e.","does":"Sets the required architecture, diagnostic coverage, and reliability evidence for that safety function.","ask":"What required performance level (PLr) did the risk assessment assign to each safety function?","range":"The required performance level (PLr) is determined for each safety function by the risk assessment.","at":[0,0.15,0.21],"sources":[{"label":"SICK, What are performance levels?","url":"https://www.sick.com/us/en/what-are-performance-levels/w/blog-safety-standard-performance-levels","kind":"maker","page":"Risk assessment and PLr overview","quote":"For each safety function carried out by a safety-related parts of a control system, the required performance level (PLr) must be determined.","work":"sick-what-are-performance-levels"}],"deeper":"The next level would hold PLr assignment, categories, MTTFd, diagnostic coverage, common-cause measures, and validation.","id":"performance-level","look":{"parts":[{"shape":"box","size":[1.4,0.7,0.02],"pos":[0,0,-0.012],"color":"#cfccc2","material":"matte"},{"shape":"plane","size":[1.4,0.7],"pos":[0,0,0],"svg":"<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 440 220\"><rect width=\"440\" height=\"220\" rx=\"10\" fill=\"#f6f4ef\"/><text x=\"20\" y=\"32\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#1f2430\" font-weight=\"700\">Performance level</text><rect x=\"30\" y=\"80\" 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font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">PL d</text><rect x=\"342\" y=\"80\" width=\"72\" height=\"60\" rx=\"4\" fill=\"hsl(8,55%,48%)\" stroke=\"none\" stroke-width=\"0\"/><text x=\"378\" y=\"120\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"18\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">PL e</text><path d=\"M300 168 L288 150 L312 150 Z\" fill=\"#1f2430\"/><text x=\"300\" y=\"192\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"14\" fill=\"#2a2530\" font-weight=\"700\" text-anchor=\"middle\">required here</text><text x=\"30\" y=\"192\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#7a7f8c\">lower</text><text x=\"410\" y=\"192\" font-family=\"Liberation Sans, Arial, sans-serif\" font-size=\"13\" fill=\"#7a7f8c\" text-anchor=\"end\">higher</text></svg>"}]}},{"term":"Cascade of loops","aka":["nested loops","fast inside 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Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://modernrobotics.northwestern.edu/nu-gm-book-resource/11-1-control-system-overview/","kind":"book","isbn":"9781107156302","page":"§11.1 Control System Overview: Inner current and outer robot-control loops","quote":"These inner control loops can run tens of thousands of times per second.","flag":"book resource page","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"deeper":"The next level would hold inner and outer setpoints, rate ratios, saturation, anti-windup and loop interaction tests.","id":"pattern-cascade","feel":{"shape":0.4,"energy":0.8,"weight":0,"warmth":0.4,"grain":0.3,"motion":"orbit","why":"Fast small orbits inside a slow wide one: inner loops race while the outer loop steers."}},{"term":"Negative feedback (thermostat)","aka":["balancing loop"],"kind":"pattern","plain":"Measure an output, compare it with a reference, and feed the signed error through a controller so the output moves toward the reference.","ask":"What is measured, what is the reference, and how strong and delayed is the correction?","sources":[{"label":"Kevin M. 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Park, Modern Robotics: Mechanics, Planning, and Control","url":"https://modernrobotics.northwestern.edu/nu-gm-book-resource/11-1-control-system-overview/","kind":"book","isbn":"9781107156302","page":"§11.1 Control System Overview: Sensor feedback and closed-loop control","quote":"The controller takes as input a desired motion from the user and sensor feedback from the robot.","flag":"book resource page","work":"kevin-m-lynch-and-frank-c-park-modern-robotics"}],"deeper":"The next level would hold the reference, measured output, error sign, loop gain and stability margin.","id":"pattern-negative-feedback","feel":{"shape":0.2,"energy":0.35,"weight":0.2,"warmth":0.35,"grain":0.15,"motion":"settle","why":"A soft body that sways and settles back to rest, as a corrected error does."}},{"term":"Predict, then correct","aka":["model plus measurement"],"kind":"pattern","plain":"Propagate an estimate with a model, then correct it with a fresh measurement and its residual.","ask":"How accurate is the model, how uncertain is the prediction, and when does a measurement correct it?","sources":[{"label":"Karl J. Åström and Richard M. Murray, Feedback Systems: An Introduction for Scientists and Engineers","url":"https://web.archive.org/web/20251009103828id_/https://fbswiki.org/wiki/index.php/Output_Feedback","kind":"book","page":"Ch. 8, observer correction and Kalman-filter update","quote":"A state feedback controller and linear observer can be combined to form a stabilizing controller for a reachable and observable linear system.","work":"karl-j-astrom-and-richard-m-murray-feedback"}],"id":"pattern-predict-correct","feel":{"shape":0.45,"energy":0.5,"weight":0,"warmth":0.5,"grain":0.35,"motion":"pulse","why":"It swells with a guess and contracts when a measurement arrives: predict, then correct."}}],"assembly":[{"title":"Model the geometry","text":"Give every link a frame. 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check the residual error.","adds":["reprojection-error"],"makes":"calibration"},{"title":"Fit the sensors","text":"The robot can now measure itself and the world in one frame.","adds":["proprioceptive-sensors","exteroceptive-sensors","calibration"],"makes":"sensing"},{"title":"Tune the joint controller","text":"Set PID gains on each joint while watching a step response.","adds":["pid-gains"],"makes":"pid-controller"},{"title":"Close the servo loop","text":"Run the controller at a fixed rate and read the tracking error.","adds":["pid-controller","control-rate","tracking-error"],"makes":"control-loop"},{"title":"Set contact behaviour","text":"Choose a virtual stiffness for tasks that touch the world.","adds":["stiffness"],"makes":"interaction-control"},{"title":"Control the whole body","text":"Add a dynamics model for feedforward torque, interaction control and, where needed, model predictive control.","adds":["control-loop","robot-dynamics","interaction-control","model-predictive-control"],"makes":"control"},{"title":"Build the filter","text":"Write the prediction and update steps and tune the noise covariances.","adds":["prediction-step","update-step","noise-covariances"],"makes":"bayes-filter"},{"title":"Add odometry","text":"Integrate wheel, visual or inertial motion and measure its drift.","adds":["drift"],"makes":"odometry"},{"title":"Map the place","text":"Choose a map type, add loop closure and measure trajectory error against ground truth.","adds":["map-representation","loop-closure","trajectory-error"],"makes":"slam"},{"title":"Know where it is","text":"Fuse odometry and SLAM in the filter to estimate the robot’s pose.","adds":["bayes-filter","odometry","slam"],"makes":"state-estimation"},{"title":"Detect objects","text":"Train or pick a detector and measure precision and recall on the robot’s own images.","adds":["precision-recall"],"makes":"object-detection"},{"title":"See the scene","text":"Add object pose estimation and point cloud processing.","adds":["object-detection","pose-estimation","point-cloud-processing"],"makes":"perception"},{"title":"Plan paths","text":"Plan in configuration space with collision checking.","adds":["configuration-space","collision-checking"],"makes":"motion-planning"},{"title":"Teach a policy","text":"Collect demonstrations, train a policy and feed field failures back into the data.","adds":["demonstrations","data-flywheel"],"makes":"learned-policy"},{"title":"Decide what to do","text":"Sequence skills in a task executive, plan motions, time them, and use a learned policy where hand-written skills fail.","adds":["task-planning","motion-planning","trajectory-generation","learned-policy"],"makes":"planning"},{"title":"Make it safe","text":"Risk assessment starts on day one; here its outcome is built in: emergency stop, collaborative mode with contact limits, and safety functions at the required performance level.","adds":["contact-force-limit"],"makes":"collaborative-operation"},{"title":"Validate safety","text":"Check every safety function against the risk assessment.","adds":["risk-assessment","emergency-stop","collaborative-operation","performance-level"],"makes":"safety"},{"title":"Bridge sim and reality","text":"Randomise the simulator so behaviour transfers to hardware.","adds":["sim-to-real"],"makes":"simulation"},{"title":"Integrate and test","text":"Connect everything over middleware from one robot description, run the sense–plan–act loop, test in simulation and in the field, log every run and iterate.","adds":["middleware","robot-description","sense-plan-act","simulation","field-testing","logging-and-replay","development-cycle"],"makes":"software-stack"},{"title":"Ship the robot","text":"Body, actuators, sensors, power, perception, estimation, planning, control, software and safety now work as one machine.","adds":["mechanism","actuation","sensing","electronics","perception","state-estimation","planning","control","software-stack","safety"],"makes":"robot"}],"survey":{"lists":[{"id":"stanford-cs223a","label":"Stanford CS223A Introduction to Robotics syllabus (manipulation; 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LaValle, Planning Algorithms","url":"https://lavalle.pl/planning/","kind":"book","isbn":"9780521862059","why":"Use one free reference for sampling, kinodynamic, uncertainty-aware, and manipulation motion planning.","named":["awesome-robotics","gatech-rmp","mit-6832","ultimate-robotics-handbook"],"specialism":"motion planning","work":"steven-m-lavalle-planning-algorithms"},{"label":"ANSI/A3, ANSI/RIA R15.06: Industrial Robots and Robot Systems — Safety Requirements","url":"https://www.automate.org/robotics/safety/robot-safety-standard-documents","kind":"standard","why":"Retained as the US industrial-robot safety canon, but no node cites it because this public landing page does not expose the standard text; current node claims use checkable NEN 2025 and practitioner sources instead.","named":["osha-robotics-standards","standardbots-safety","automate-safety-docs"],"specialism":"functional safety","flag":"The opened pages describe both 2012 and revised 2025 editions","work":"ansi-a3-ansi-ria-r15-06-industrial-robots-and"},{"label":"Bruno Siciliano and Oussama Khatib (eds.), Springer Handbook of Robotics","url":"https://link.springer.com/book/10.1007/978-3-319-32552-1","kind":"book","isbn":"978-3-319-32552-1","why":"Raid authoritative chapters when a project needs depth on a particular robotics subsystem or application.","named":["awesome-robotics","corke-books-i-like","springer-handbook-index"],"specialism":"mechanism/actuator design","work":"bruno-siciliano-and-oussama-khatib-eds-springer"},{"label":"International Organization for Standardization, ISO 10218-1 and ISO 10218-2: Robots for industrial environments — Safety requirements","url":"https://www.osha.gov/robotics/standards","kind":"standard","why":"Retained as the ISO 10218-1/-2 canon, but no node cites it because the standard text is paywalled; current node claims use the checkable NEN 2025 Part 2 page and other public sources instead.","named":["osha-robotics-standards","standardbots-safety","automate-safety-docs"],"specialism":"functional safety","flag":"OSHA and practitioner summaries, not the paywalled standard text","work":"international-organization-for-standardization"},{"label":"Morgan Quigley, Brian Gerkey and William D. 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Murray, Zexiang Li and S. Shankar Sastry, A Mathematical Introduction to Robotic Manipulation","url":"https://openlibrary.org/books/OL33749829M/Mathematical_Introduction_to_Robotic_Manipulation","kind":"book","isbn":"9780849379819","why":"Develop the mechanics and mathematics needed for contact, grasping, and manipulation planning.","named":["awesome-robotics","gatech-rmp"],"specialism":"manipulation","work":"richard-m-murray-zexiang-li-and-s-shankar-sastry"},{"label":"Richard S. Sutton and Andrew G. Barto, Reinforcement Learning: An Introduction","url":"https://web.stanford.edu/class/psych209/Readings/SuttonBartoIPRLBook2ndEd.pdf","kind":"book","why":"University-hosted author draft is retained because the publisher page does not expose the cited chapter text publicly.","named":["mit-6832","awesome-robotics"],"specialism":"robot learning","work":"richard-s-sutton-and-andrew-g-barto"},{"label":"Roland Siegwart, Illah R. Nourbakhsh and Davide Scaramuzza, Introduction to Autonomous Mobile Robots","url":"https://penguinrandomhousehighereducation.com/book/?isbn=9780262015356","kind":"book","isbn":"9780262015356","why":"Retained as the canonical mobile-robotics text, but no node cites it because this publisher page exposes no supporting chapter text; node claims use checkable open papers and documentation instead.","named":["awesome-robotics","corke-books-i-like"],"specialism":"mobile robots/SLAM & state estimation","work":"roland-siegwart-illah-r-nourbakhsh-and-davide"},{"label":"Russ Tedrake, Robotic Manipulation","url":"https://manipulation.csail.mit.edu/","kind":"book","why":"Work through perception, grasping, contact, motion planning, control, mobile manipulation, and robot learning in interactive notes.","named":["rosecity-resources","ultimate-robotics-handbook"],"specialism":"manipulation","work":"russ-tedrake-robotic-manipulation"},{"label":"Sisbot et al., A human aware mobile robot motion planner","url":"https://ieeexplore.ieee.org/document/4339546","kind":"research","why":"Study how a mobile robot planner models human presence and social constraints during navigation.","named":["hri-reading-list","hri-more-readings"],"specialism":"HRI","page":"IEEE Transactions on Robotics 23(5), 874-883","flag":"IEEE page opened but its reader was blocked","work":"sisbot-et-al-a-human-aware-mobile-robot-motion"},{"label":"Timothy D. Barfoot, State Estimation for Robotics","url":"https://www.cambridge.org/core/books/state-estimation-for-robotics/00E53274A2F1E6CC1A55CA5C3D1C9718","kind":"book","isbn":"9781009299893","why":"Move from basic filters to Lie groups, batch estimation, inertial navigation, and practical SLAM estimation.","named":["ultimate-robotics-handbook","awesome-slam"],"specialism":"mobile robots/SLAM & state estimation","work":"timothy-d-barfoot-state-estimation-for-robotics"}],"voices":[{"name":"Russ Tedrake","known":"MIT professor who ran the Underactuated Robotics course and publishes executable notes on walking, flying, dynamics, control, and manipulation; practitioners use his notes and lectures to connect theory to working systems.","links":[{"label":"Underactuated Robotics notes","url":"https://underactuated.mit.edu/","kind":"site"},{"label":"MIT Underactuated Robotics lecture","url":"https://www.youtube.com/watch?v=z8oMbo9j1WM","kind":"video"},{"label":"Robotic Manipulation notes","url":"https://manipulation.csail.mit.edu/","kind":"site"}]},{"name":"Kevin M. Lynch","known":"Northwestern professor and Modern Robotics coauthor; his chapter-by-chapter videos and software give practitioners a concise route from rigid-body geometry to manipulation and mobile robots.","links":[{"label":"Modern Robotics video supplements","url":"https://hades.mech.northwestern.edu/index.php/Modern_Robotics_Videos","kind":"video"},{"label":"Foundations of Robot Motion","url":"https://modernrobotics.northwestern.edu/nu-gm-book-resource/foundations-of-robot-motion/","kind":"site"}]},{"name":"Peter Corke","known":"Robotics Toolbox and Robotics, Vision and Control author; his open technical notes, toolboxes, and talks show how to turn robotics mathematics into experiments.","links":[{"label":"Free technical writings","url":"https://docs.petercorke.com/","kind":"site"},{"label":"Videos and interviews","url":"https://petercorke.com/about/videos/","kind":"video"},{"label":"Books I like","url":"https://petercorke.com/interesting-books/","kind":"site"}]},{"name":"Cyrill Stachniss","known":"Bonn professor whose public courses teach mobile robotics, filtering, localization, mapping, and photogrammetry; his short explanations are widely used by engineers who need the estimation intuition quickly.","links":[{"label":"Online mobile-robotics training","url":"https://www.ipb.uni-bonn.de/online-training-robotics/index.html","kind":"site"},{"label":"SLAM course playlist","url":"https://www.youtube.com/playlist?list=PLgnQpQtFTOGQrZ4O5QzbIHgl3b1JHimN_","kind":"video"}]},{"name":"Davide Scaramuzza","known":"University of Zurich Robotics and Perception Group director who helped transfer visual-inertial estimation, event-camera perception, and agile drone navigation into products and demonstrated AI drone racing systems.","links":[{"label":"Robotics and Perception Group profile","url":"https://rpg.ifi.uzh.ch/people_scaramuzza.html","kind":"site"},{"label":"RPG video channel","url":"https://www.youtube.com/ailabRPG/videos","kind":"video"}]},{"name":"Sergey Levine","known":"Berkeley RAIL leader whose research and public courses cover real-world reinforcement learning, imitation, planning, and robotic manipulation; practitioners follow him for sober accounts of what learning systems need in the physical world.","links":[{"label":"Berkeley profile and talks","url":"https://people.eecs.berkeley.edu/~svlevine/","kind":"site"},{"label":"Robotics Foundation Models seminar","url":"https://www.youtube.com/watch?v=EYLdC3a0NHw","kind":"video"}]},{"name":"Steve Macenski","known":"Open Navigation engineer and a central Nav2 maintainer; his ROSCon talks explain production navigation, trajectory planning, controllers, and the integration details that make mobile robots ship.","links":[{"label":"Nav2 documentation","url":"https://docs.nav2.org/","kind":"site"},{"label":"ROSCon Nav2 MPPI talk","url":"https://vimeo.com/879001391","kind":"talk"}]},{"name":"Rodney Brooks","known":"Robotics entrepreneur and researcher associated with iRobot, Rethink Robotics, and Robust AI; his blog gives practitioners a long-horizon view of what survives deployment and scale rather than lab demos alone.","links":[{"label":"Rodney Brooks blog","url":"https://rodneybrooks.com/blog/","kind":"blog"},{"label":"Rodney Brooks site","url":"https://rodneybrooks.com/","kind":"site"}]},{"name":"Chris Atkeson","known":"Carnegie Mellon roboticist whose research, papers, and public lectures span robot learning, humanoids, and assistive systems; practitioners listen for lessons from long-running physical experiments.","links":[{"label":"Research, papers, videos, and talks","url":"https://www.cs.cmu.edu/~cga/publications.html","kind":"site"},{"label":"CMU faculty profile","url":"https://engineering.cmu.edu/directory/bios/atkeson-chris.html","kind":"site"}]},{"name":"Ben Katz","known":"MIT Mini Cheetah actuator designer whose thesis documents a low-cost modular high-performance actuator; builders follow his detailed hardware construction and control notes.","links":[{"label":"Build Its robotics blog","url":"https://build-its.blogspot.com/","kind":"blog"},{"label":"A Low Cost Modular Actuator for Dynamic Robots (MIT thesis)","url":"https://dspace.mit.edu/server/api/core/bitstreams/f3404f79-1cb4-4e61-a51b-1f4ef8bb4e45/content","kind":"site"}]},{"name":"James Bruton","known":"XRobots builder who publishes open, practical projects such as OpenDog, mobile robots, mechanisms, electronics, and 3D-printed machines; his videos expose the iteration cost behind working hardware.","links":[{"label":"XRobots project site","url":"https://www.xrobots.tech/about/","kind":"site"},{"label":"James Bruton YouTube channel","url":"https://www.youtube.com/@jamesbruton","kind":"video"}]},{"name":"Evan Ackerman","known":"IEEE Spectrum editor and Chatbot host who has covered robotics products, research, and deployment for years; practitioners use his reporting and interviews to track what is real outside papers.","links":[{"label":"IEEE Spectrum author page","url":"https://spectrum.ieee.org/u/evan-ackerman","kind":"site"},{"label":"Chatbot robotics podcast","url":"https://spectrum.ieee.org/podcasts/chatbot/","kind":"podcast"}]},{"name":"Marc Raibert","known":"Boston Dynamics founder and former CEO who led dynamic legged-robot programs including Atlas, Spot, and BigDog; his talks make locomotion and whole-body robotics concrete.","links":[{"label":"TED speaker page","url":"https://www.ted.com/speakers/marc_raibert","kind":"talk"},{"label":"Boston Dynamics video library","url":"https://bostondynamics.com/videos/","kind":"video"}]},{"name":"Aaron Ames","known":"Caltech professor and AMBER Lab founder known for safety-critical control of bipedal robots and demonstrations of dynamic walking; practitioners follow his talks for the bridge between formal guarantees and hardware.","links":[{"label":"Towards the Robots of Science Fiction","url":"https://www.ted.com/talks/aaron_ames_towards_the_robots_of_science_fiction","kind":"talk"},{"label":"AMBER Lab research","url":"https://www.bipedalrobotics.com/research.html","kind":"site"}]},{"name":"Jim Fan","known":"NVIDIA robotics researcher who teaches and writes about foundation models, simulation, Isaac tools, and embodied agents; practitioners follow him for the current interface between large models and robot systems.","links":[{"label":"NVIDIA Robotics Lab profile","url":"https://research.nvidia.com/labs/srl/authors/jim-fan/","kind":"site"},{"label":"NVIDIA humanoid-development article","url":"https://blogs.nvidia.com/blog/robot-learning-humanoid-development/","kind":"blog"}]},{"name":"Chelsea Finn","known":"Stanford robot-learning researcher whose work connects meta-learning, imitation, and manipulation; her public explanations help practitioners reason about data, adaptation, and generalization on robots.","links":[{"label":"Stanford Engineering public feature","url":"https://engineering.stanford.edu/news/chelsea-finn-how-make-artificial-intelligence-more-meta","kind":"blog"}]},{"name":"Andrew Davison","known":"MonoSLAM researcher and Imperial College robotic-vision professor; his public lectures and demonstrations explain visual localization, mapping, and the path from SLAM to spatial AI.","links":[{"label":"Microsoft MonoSLAM video","url":"https://www.microsoft.com/en-us/research/video/real-time-visual-localisation-and-mapping-with-a-single-camera/","kind":"video"},{"label":"Imperial robotic-vision lecture","url":"https://www.imperial.ac.uk/events/107364/inaugural-lecture-robotic-vision-professor-andy-davison-imperial-college/","kind":"talk"}]},{"name":"Jessica Burgner-Kahrs","known":"Leads the Continuum Robotics Laboratory and teaches continuum robot design, modelling and control; her primers distinguish rigid-link snake arms, continuously bending backbones and tendon-routing designs.","links":[{"label":"Continuum Robotics 101","url":"https://www.opencontinuumrobotics.com/101/2022/10/21/cr-intro.html","kind":"blog"},{"label":"Tendon-driven continuum robots","url":"https://www.opencontinuumrobotics.com/101/2022/11/11/tdcr-intro.html","kind":"blog"}]},{"name":"Ytec 3D","known":"Built and documented a three-section cable-driven animatronic tentacle with six base winches, printable parts and notes on cable routing and friction.","links":[{"label":"Animatronic tentacle build","url":"https://ytec3d.com/animatronic-tentacle/","kind":"blog"}]},{"name":"Jan at Pololu","known":"Explains hobby-servo pulse commands, calibration, holding behaviour and supply-current measurements for builders.","links":[{"label":"Servo control interface in detail","url":"https://www.pololu.com/blog/17/servo-control-interface-in-detail","kind":"blog"}]}]}}