Stefano Chiaverini
Post on 23-Feb-2016
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Singularity-Robust Task Priority Redundancy Resolution for Real-time Kinematic Control of Robot Manipulators
Stefano Chiaverini
Outline
1.Redundancy2. Inverse differential kinematic control 3. Robust techniques for kinematic control4. Task-priority redundancy resolution5. Numerical analysis of existing solutions.
Redundancy
N > M
Degrees of Freedom Workspace
Redundancy
Example:7 DOF arm vs. 6 DOF Trajectory
Redundancy
Many solutions per problem.
Redundancy
Which one to pick?
Inverse Differential Kinematic Control:
A redundant system!
Kinematic Control
Gives an end-effector velocity which minimizes joint velocities.
Jacobian Pseudo-Inverse:
Kinematic Control
Generalized:
Min Norm Null space
Arbitrary
x
Null
Span
Kinematic Control
Problem: singularites
Min Norm Null space
Singularities
Kinematic Singularities
•Occur when Jacobian has null singular values•Inherent to all techniques.
Algorithmic Singularities
•Occur when no solution exists which satisfies constraints and provides desired EE motion.
Singularities
How to deal with kinematic singularities?
Robust Techniques
First Technique: Damping
Damping term
From SVD
Robust Techniques***
First Technique: Damping
Damped Norm Null Space
Robust Techniques
Pros•Good performance•Robust to singularities
Cons•Accumulates error
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
Task space constraint: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:
Numerical Analysis
Constraint:
(damped)
(undamped)
(damped)
(undamped)
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
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