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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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slide1

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

Stefano Chiaverini

outline
Outline

Redundancy

Inverse differential kinematic control

Robust techniques for kinematic control

Task-priority redundancy resolution

Numerical analysis of existing solutions.

redundancy
Redundancy

N > M

Workspace

Degrees of Freedom

redundancy1
Redundancy

Example:

7 DOF arm vs. 6 DOF Trajectory

redundancy2
Redundancy

Many solutions per problem.

redundancy3
Redundancy

Which one to pick?

kinematic control
Kinematic Control

Gives an end-effector velocity which minimizes joint velocities.

Jacobian Pseudo-Inverse:

kinematic control1
Kinematic Control

Generalized:

Arbitrary

Span

Min Norm

Null space

x

Null

kinematic control2
Kinematic Control

Problem: singularites

Min Norm

Null space

singularities1
Singularities

How to deal with kinematic singularities?

robust techniques
Robust Techniques

First Technique: Damping

From SVD

Damping term

robust techniques1
Robust Techniques

***

First Technique: Damping

Null Space

Damped Norm

robust techniques2
Robust Techniques

First Technique: Damping

robust techniques3
Robust Techniques

How to deal with error?

Filter out singularities.

slide17

How to choose q0?

Consequence of redundancy

task priority redundancy resolution
Task Priority Redundancy Resolution

How to choose q0?

Minimizes an objective function H(q)

task priority redundancy resolution1
Task Priority Redundancy Resolution

Or, define a task-space constraint:

Complicates the update rule:

task priority redundancy resolution2
Task Priority Redundancy Resolution

Task space constraint:

Can satisfy (N – M) parameters

task priority redundancy resolution3
Task Priority Redundancy Resolution

Problem: Leads to Algorithmic Singularities

Might approach singular

task priority redundancy resolution4
Task Priority Redundancy Resolution

Condition for algorithmic singularities

Null spaces linearly dependant

task priority redundancy resolution5
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 resolution6
Task Priority Redundancy Resolution

Solve for the constraint instead:

A lot of math later….

Zeros out at singularities…

numerical analysis
Numerical Analysis

For a 7-dof manipulator:

Exact solution (796 flops):

Chiaverni’s robust simplification (632 flops):

Naïve minimum norm (519 flops):

numerical analysis1
Numerical Analysis

Experiments:

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