Stefano Chiaverini

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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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Singularity-Robust Task Priority Redundancy Resolution for Real-time Kinematic Control of Robot Manipulators

Stefano Chiaverini

Outline

Redundancy

Inverse differential kinematic control

Robust techniques for kinematic control

Numerical analysis of existing solutions.

Redundancy

N > M

Workspace

Degrees of Freedom

Redundancy

Example:

7 DOF arm vs. 6 DOF Trajectory

Redundancy

Many solutions per problem.

Redundancy

Which one to pick?

Kinematic Control

Gives an end-effector velocity which minimizes joint velocities.

Jacobian Pseudo-Inverse:

Kinematic Control

Generalized:

Arbitrary

Span

Min Norm

Null space

x

Null

Kinematic Control

Problem: singularites

Min Norm

Null space

Singularities

How to deal with kinematic singularities?

Robust Techniques

First Technique: Damping

From SVD

Damping term

Robust Techniques

***

First Technique: Damping

Null Space

Damped Norm

Robust Techniques

First Technique: Damping

Robust Techniques

How to deal with error?

Filter out singularities.

How to choose q0?

Consequence of redundancy

Task Priority Redundancy Resolution

How to choose q0?

Minimizes an objective function H(q)

Task Priority Redundancy Resolution

Or, define a task-space constraint:

Complicates the update rule:

Task Priority Redundancy Resolution

Can satisfy (N – M) parameters

Task Priority Redundancy Resolution

Problem: Leads to Algorithmic Singularities

Might approach singular

Task Priority Redundancy Resolution

Condition for algorithmic singularities

Null spaces linearly dependant

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?

Task Priority Redundancy Resolution

Solve for the constraint instead:

A lot of math later….

Zeros out at singularities…

Numerical Analysis

For a 7-dof manipulator:

Exact solution (796 flops):

Chiaverni’s robust simplification (632 flops):

Naïve minimum norm (519 flops):

Numerical Analysis

Experiments:

Conclusion
• Need to avoid two kinds of singularities.
• Presented approach which handles both.
• New approach is more computationally efficient.
Limitations
• Null space motions only
• Constraints always prioritized lower