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Stefano Chiaverini

Singularity-Robust Task Priority Redundancy Resolution for Real-time Kinematic Control of Robot Manipulators. Stefano Chiaverini. Outline. R edundancy Inverse d ifferential k inematic c ontrol Robust techniques for kinematic c ontrol Task-priority r edundancy r esolution

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Stefano Chiaverini

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  1. Singularity-Robust Task Priority Redundancy Resolution for Real-time Kinematic Control of Robot Manipulators Stefano Chiaverini

  2. Outline Redundancy Inverse differential kinematic control Robust techniques for kinematic control Task-priority redundancy resolution Numerical analysis of existing solutions.

  3. Redundancy N > M Workspace Degrees of Freedom

  4. Redundancy Example: 7 DOF arm vs. 6 DOF Trajectory

  5. Redundancy Many solutions per problem.

  6. Redundancy Which one to pick?

  7. Inverse Differential Kinematic Control: A redundant system!

  8. Kinematic Control Gives an end-effector velocity which minimizes joint velocities. Jacobian Pseudo-Inverse:

  9. Kinematic Control Generalized: Arbitrary Span Min Norm Null space x Null

  10. Kinematic Control Problem: singularites Min Norm Null space

  11. Singularities

  12. Singularities How to deal with kinematic singularities?

  13. Robust Techniques First Technique: Damping From SVD Damping term

  14. Robust Techniques *** First Technique: Damping Null Space Damped Norm

  15. Robust Techniques First Technique: Damping

  16. Robust Techniques How to deal with error? Filter out singularities.

  17. How to choose q0? Consequence of redundancy

  18. Task Priority Redundancy Resolution How to choose q0? Minimizes an objective function H(q)

  19. Task Priority Redundancy Resolution Or, define a task-space constraint: Complicates the update rule:

  20. Task Priority Redundancy Resolution Task space constraint: Can satisfy (N – M) parameters

  21. Task Priority Redundancy Resolution Problem: Leads to Algorithmic Singularities Might approach singular

  22. Task Priority Redundancy Resolution Condition for algorithmic singularities Null spaces linearly dependant

  23. Task Priority Redundancy Resolution • Algorithmic Singularities • Difficult to predict. • Arise because of competing demands. • Leads to extreme joint velocities. How do we get rid of them?

  24. Task Priority Redundancy Resolution Solve for the constraint instead: A lot of math later…. Zeros out at singularities…

  25. Numerical Analysis For a 7-dof manipulator: Exact solution (796 flops): Chiaverni’s robust simplification (632 flops): Naïve minimum norm (519 flops):

  26. Numerical Analysis Experiments:

  27. Numerical Analysis Constraint:

  28. (damped)

  29. (undamped)

  30. (damped)

  31. (undamped)

  32. Conclusion • Need to avoid two kinds of singularities. • Presented approach which handles both. • New approach is more computationally efficient.

  33. Limitations • Null space motions only • Constraints always prioritized lower

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