Singularity Handling on PUMA in Operational Space Formulation

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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
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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

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Task-Based Control
Operational space

• 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

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Operational Space vs Inverse Kinematics

• Differential Motion
• Operational Space Formulation

Chang and Khatib, 1994
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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

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ISER 2000 Singularity Handling on Puma in
Operational Space Formulation
Handling of Singularity Problem existence of
the inverse of the Jacobian matrix at singular
configuration. Cause Manipulator loses DOF(s).
Jacobian is not full rank. There is a degenerate
direction. Proposed Solution Remove the
degenerate component(s) from the Jacobian and
collapse the Jacobian into a matrix of smaller
dimension but with full rank.
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PUMA Singularities

• Singularities in PUMA 500 series
• Wrist
• Elbow
• Head

Det(J) a2(d4C3 - a3S3) (d4S23 a2C2 a3C23) S5
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Jacobian in Frame 0, 0J
Head Singularity
Remove 2nd row
0 at head singularity
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Elbow Singularity
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Wrist Singularity
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ISER 2000 Singularity Handling on Puma in
Operational Space Formulation
Collapsing the Jacobian
The forces (and the Jacobian) is resolved into
the frame which one of the axis represents the
singular direction. The row of the Jacobian
matrix that contains all zero is then removed.
Wrist Elbow Head
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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

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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.
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Polishing Application
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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

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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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ISER 2000 Singularity Handling on Puma in
Operational Space Formulation
Removing the Singular Component(s)
Example on Head singularity

The resulting Jacobian