Concept
Jacobian and singularities
You might say: velocity map
The Jacobian maps joint velocities to tool twist and maps tool wrench to joint torque through its transpose.
- What it does
- It supports velocity control, numerical IK, force control and singularity analysis.
- Ask
- How close is the current configuration to losing a task-space direction?
- Typical
- For a full-row-rank Jacobian, manipulability can be written w = sqrt(det(J J^T)); it falls to zero at a singularity.
- Trouble
- At a singularity the Jacobian loses rank; some tool motions become unavailable and joint speeds can become very large near it.
Sources
- Kevin M. Lynch and Frank C. Park, Modern Robotics: Mechanics, Planning, and Control, Ch. 5 §§5.1–5.5
Kinematic singularities, which are configurations in which the end-effector frame loses the ability to move or rotate in one or more directions, correspond to those configurations at which the Jacobian matrix fails to have maximal rank.
- Peter Corke, Robotics, Vision and Control, Ch. 8, Velocity Relationships
The joint velocity and the end-effector velocity are related by the manipulator Jacobian matrix which is a function of manipulator pose.
Use it on your project
teardown-apply: hold "Jacobian and singularities" (jacobian) from the teardown at https://teardownatlas.com/robotics/ against my project
Paste it into a coding agent that has the teardown skills.
An AI agent wrote this map with the teardown skill. It can contain errors: check the sources before you rely on a part. About and legal