1 Singularity Handling on PUMA in Operational Space Formulation Author: Denny Oetomo*, Marcelo Ang...
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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
1 Singularity Handling on PUMA in Operational Space Formulation Author: Denny Oetomo*, Marcelo Ang Jr*, Lim Ser Yong** * National University of Singapore,
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
Slide 2
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Slide 3
3 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
Slide 4
4 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
Slide 5
5 Operational Space vs Inverse Kinematics Differential Motion
Operational Space Formulation [Chang and Khatib, 1994]
Slide 6
6 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
Slide 7
7 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.
Slide 8
8 Singularities in PUMA 500 series: Wrist Elbow Head Z1Z1 X1X1
Y1Y1 Z2Z2 X2X2 Z3Z3 X3X3 Y3Y3 Z 4, Z 6 Y 4, Z 5 X 4, X 5 d2 d4 d3
a2 PUMA Singularities Det(J) = a 2 (d 4 C 3 - a 3 S 3 ) (d 4 S 23 +
a 2 C 2 + a 3 C 23 ) S 5
Slide 9
9 Jacobian in Frame 0, 0 J Z1Z1 X1X1 Head Singularity 1 J = 0
at head singularity Remove 2nd row
Slide 10
10 Elbow Singularity Wrist point d2 d3 XBXB ZBZB Degenerate
direction d4 a2
Slide 11
11 Wrist Singularity q4q4 q5q5 q6q6 Z4 Y4 X4
Slide 12
12 ISER 2000: Singularity Handling on Puma in Operational Space
Formulation 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.
Collapsing the Jacobian q4q4 q5q5 q6q6 Z4 Y4 X4 Wrist point d2 d3
XBXB ZBZB Degenerate direction d4 a2 Zo Xo Wrist Elbow Head
Slide 13
13 Four sets of result were collected, consisting of the
position and orientation (tracking) error in: 1.PUMA tracing a
non-singular trajectory 2.PUMA going through wrist singularity, not
in the singular direction. 3.PUMA escaping from wrist singularity
into a path in singular direction 4.PUMA escaping from elbow
singularity into a path in singular direction Experimental
Sets
Slide 14
14 Escape into Singular Direction Utilising Null Space Motion:
Type 1: Null Space Motion creates motion in singular direction
Joint 3 Desired path Desired path and non-feasible path The
initially non-feasible direction Type 2: Null Space Motion creates
internal motion which shifts the singular direction.
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18 Polishing Application
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19 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
Slide 20
20 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.
Slide 21
21 ISER 2000: Singularity Handling on Puma in Operational Space
Formulation Removing the Singular Component(s) Example on Head
singularity: The resulting Jacobian: 1 J =