Report

Singularity-Robust Task Priority Redundancy Resolution for Real-time Kinematic Control of Robot Manipulators Stefano Chiaverini Outline 1.Redundancy 2. Inverse differential kinematic control 3. Robust techniques for kinematic control 4. Task-priority redundancy resolution 5. 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 Jacobian Pseudo-Inverse: Gives an end-effector velocity which minimizes joint velocities. Kinematic Control Generalized: Span Min Norm x Null Arbitrary Null space Kinematic Control Min Norm Null space Problem: singularites Singularities Kinematic Singularities Algorithmic Singularities • Occur when Jacobian has null singular values • Inherent to all techniques. • 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 From SVD Damping term Robust Techniques *** First Technique: Damping Damped Norm Null Space Robust Techniques First Technique: Damping Pros Cons • Good performance • Robust to singularities • Accumulates error 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