Most of the robot task space control methods based on inverse Jacobian matrix suffer from instability in singular regions of workspace. Methods based on damped least-squares algorithm (DLS) for matrix inversion have been developed but not experimentally confirmed. The application of DLS method at the kinematic control level has been reported in (Chiaverini et al., 1994). In this article, a modified DLS method combined with the resolved-acceleration control scheme, is experimentally verified on two degrees of freedom of a PUMA-560 robot. In order to decrease the position error introduced by the damping, only small singular values are damped, in contrast to the conventional damping method were all the singular values are damped. The symbolic expressions of the singular value decomposition of the Jacobian matrix were used, to decrease the computational burden.

1.
Chiaverini
S.
,
Siciliano
B.
, and
Egeland
O.
,
1994
, “
Review of the Damped Least-Squares Inverse Kinematics with Experiments on an Industrial Robot Manipulator
,”
IEEE Trans. on Control Systems Technology
, Vol.
2
, No.
2
, pp.
123
134
.
2.
Golub, G. H., and Van Loan, Ch. P., 1989, Matrix Computations, The John Hopkins University Press, Baltimore.
3.
Kirc´anski, M., 1995, “Symbolic Singular Value Decomposition for Simple Redundant Manipulators and its Application to Robot Control,” Int. J. Robotics Research, Vol. 14, No. 4.
4.
Kirc´anski
M.
, and
Boric´
M.
,
1993
, “
Symbolic Singular Value Decomposition for PUMA Robot and its Application to Robot Operation Near Singularities
,”
Int. J. of Robotics Research
, Vol.
12
, No.
5
, pp.
460
472
.
5.
Kirc´anski, N., 1995, “Stability of Damped Resolved Acceleration Controlled Robots in Singularities,” RAL Int. Report, University of Toronto, Toronto.
6.
La Salle, J., and Lefschetz, S., 1961, Stability by Liapunov’s Direct Method, Academic Press, New York.
7.
Lu
Z.
,
Shimoga
K.
, and
Goldenberg
A.
,
1993
, “
Experimental Determination of the Dynamic Parameters of Robotic Arms
,”
J. of Robotic Systems
, Vol.
10
, No.
8
, pp.
1009
1029
.
8.
Luh
J. Y. S.
,
Walker
M. W.
, and
Paul
R. P.
,
1980
, “
Resolved-Acceleration Control of Mechanical Manipulators
,”
IEEE Trans. on Automatic Control
, Vol.
AC-25
, pp.
195
200
.
9.
Maciejewski
A. A.
, and
Klein
Ch. A.
,
1988
, “
Numerical Filtering for the Operation of Robotic Manipulators Through Kinematically Singular Configurations
,”
J. of Robotic Systems
, Vol.
5
, No.
6
, pp.
527
552
.
10.
Nakamura
Y.
, and
Hanafusa
H.
,
1986
, “
Inverse Kinematic Solutions with Singularity Robustness for Robot Manipulator Control
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
108
, pp.
163
171
.
11.
Wampler
Ch. W.
,
1986
, “
Manipulator Inverse Kinematic Solutions Based on Vector Formulations and Damped Least-Squares Methods
,”
IEEE Trans. on Systems, Man, and Cybernetics
, Vol.
SMC-16
, No.
1
, pp.
93
101
.
12.
Wampler
C. W.
, and
Leifer
L. J.
,
1988
, “
Application of Damped Least-Squares Methods to Resolved-Rate and Resolved-Acceleration Control of Manipulators
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
110
, pp.
31
38
.
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