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Singularity Handling on PUMA in Operational Space Formulation

Singularity Handling on PUMA in Operational Space Formulation. Author: Denny Oetomo*, Marcelo Ang Jr*, Lim Ser Yong** * National University of Singapore, ** Gintic Institute of Manufacturing Technology. ISER 2000, Honolulu, HI, Dec 12, 2000. Problem Statement Singularity.

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Singularity Handling on PUMA in Operational Space Formulation

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  1. Singularity Handling on PUMA in Operational Space Formulation Author: Denny Oetomo*, Marcelo Ang Jr*, Lim Ser Yong** * National University of Singapore, ** Gintic Institute of Manufacturing Technology ISER 2000, Honolulu, HI, Dec 12, 2000

  2. Problem Statement Singularity • Motion across singularities • increased usable workspace for task execution • Traditional methods • motion-based • forcing Jacobian to be non-singular, etc • Task (operational) space methods • Motion/Forces at End-Effector are directly controlled via Joint Torques

  3. Force on hand/tool virtual - to cause motion real - actual forces exerted Singularity handling needs to be in both motion and force control Actuation signals to robot joints computed to effect forces Task-Based Control Operational space

  4. Operational Space vs Inverse Kinematics • Differential Motion • Operational Space Formulation [Chang and Khatib, 1994]

  5. Work Done • Analysis and resolution of singularities in operational space • Remove degenerate directions • lower order (in terms of task space) non-singular but redundant mechanism • Graceful escape algorithms using null space motion • stable and smooth motions from singular to non-singular regions • Experimental verification

  6. Z4, Z6 Y4, Z5 d4 X4, X5 Z2 d2 Z1 Y1 X2 Z3 X1 d3 X3 a2 Y3 PUMA Singularities • Singularities in PUMA 500 series: • Wrist • Elbow • Head Det(J) = a2(d4C3 - a3S3) (d4S23 + a2C2 + a3C23) S5

  7. 1J = Z1 X1 Jacobian in Frame 0, 0J Head Singularity Remove 2nd row 0 at head singularity

  8. Wrist point Degenerate direction d4 b d3 a2 XB ZB d2 Elbow Singularity

  9. Z4 q6 q5 q4 Y4 X4 Wrist Singularity

  10. Experimental Sets • Four sets of result were collected, consisting of the position and • orientation (tracking) error in: • PUMA tracing a non-singular trajectory • PUMA going through wrist singularity, not in the singular direction. • PUMA escaping from wrist singularity into a path in singular direction • PUMA escaping from elbow singularity into a path in singular direction

  11. Desired path and non-feasible path The initially non-feasible direction Joint 3 Desired path Escape into Singular Direction Utilising Null Space Motion: Type 1: Null Space Motion creates motion in singular direction Type 2: Null Space Motion creates internal motion which shifts the singular direction.

  12. Polishing Application

  13. Conclusions • The singularity handling algorithm implemented. • By removing the singular component in operational space • Graceful escape algorithms using null space motion • stable and smooth motions from singular to non-singular regions • Experimental Verification

  14. Future Work • This is one of the ‘infra structure’ of a larger project. • (further work would be done on the larger project). • Extension of the work into inherently redundant robots.

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