A dynamical formulation based upon the undetermined force method is presented for analyzing redundant robotic manipulators. The equivalence between this dynamical formulation and the general solution of kinematic constraint equations is then obtained through use of a normalized generalized inverse. This leads to a special form of the dynamical equations, called the N-inverse form of the dynamical equations. A class of problems, associated with the optimization of quadratic objective functions, are then studied. We find that the N-inverse form of the dynamical equations is the solution of this class of problems. Examples, including local minimization of joint torques and global minimization of kinetic energy, are presented.

1.
Baillieul, J., 1985, “Kinematic Programming Alternatives for Redundant Manipulators,” IEEE Proceedings of Int. Conf. of Robotics and Automation, pp. 722–728.
2.
Baillieul, J., 1986, “Avoiding Obstacles and Resolving Kinematic Redundancy,” Proc. IEEE Conf. on Robotics and Automation, pp. 1698–1704.
3.
Baillieul, J., Hollerbach, J., and Brockett, R., 1984, “Programming and Control of Kinematically Redundant Manipulators,” Proc. of 23rd Conf. on Decision and Control.
4.
Ben-Israel, A., and Greville, T. N. E., 1980, Generalized Inverse: Theory and Applications, Krieger, New York.
5.
Chang, P. H., 1986, “A Closed-Form Solution for the Control of Manipulators with Kinematic Redundancy,” IEEE Proceedings of Int. Conf. of Robotics and Automation, pp. 722–728.
6.
Goldman
A. J.
, and
Zelen
M.
,
1964
, “
Weak Generalized Inverses and Minimum Variance Linear Unbiased Estimation
,”
Journal of Research of the National Bureau of Standards—B. Mathematics and Mathematical Physics
, Vol.
68B
, No.
4
, pp.
151
172
.
7.
Hollerbach, J. M., and Suh, K. C., 1985, “Redundancy Resolution of Manipulators through Torque Optimization,” IEEE Proceedings of Int. Conf. of Robotics and Automation, pp. 1016–1021.
8.
Kazerounian
K.
, and
Nedungadi
A.
,
1988
, “
Redundancy Resolution of Serial Manipulators Based on Robot Dynamics
,”
Mech. Mach. Theory
, Vol.
23
, No.
4
, pp.
295
303
.
9.
Kazerounian
K.
, and
Wang
Z.
,
1988
, “
Global versus Local Optimization in Redundancy Resolution of Robotic Manipulators
,”
International Journal of Robotics Research
, Vol.
7
, No.
5
, pp.
3
12
.
10.
Klein
C. A.
, and
Huang
C.-H.
,
1983
, “
Review of Pseudoinverse Control for Use with Kinematically Redundant Manipulators
,”
IEEE Transactions on Systems, Man, and Cybernetics
, Vol.
SMC-13
, No.
3
, pp.
245
250
.
11.
Liegeois
A.
,
1977
, “
Automatic Supervisory Control of the Configuration and Behavior of Multibody Mechanisms
,”
IEEE Transactions on Systems, Man, and Cybernetics
, Vol.
SMC-7
, No.
12
, pp.
868
871
.
12.
Luh, J. Y. S., and Gu, Y. L., 1984, “Industrial Robots with Seven Joints,” Proc. IEEE Conf. on Robotics and Automation, pp. 1010–1015.
13.
Maciejewski
A. A.
, and
Klein
C. A.
,
1985
, “
Obstacle Avoidance for Kinematically Redundant Manipulators in Dynamically Varying Environments
,”
Int. Journal of Robotics Research
, Vol.
4
, No.
3
, pp.
109
117
.
14.
Martin, D. P., Baillieul, J., and Hollerback, J. M., 1989, “Resolution of Kinematic Redundancy Using Optimization Techniques,” IEEE Transactions on Robotics and Automation, Vol. 5, No. 4.
15.
Passerello
C. E.
, and
Huston
R. L.
,
1973
, “
Another Look at Nonholonomic Systems
,”
ASME Journal of Applied Mechanics
, Vol.
40
, pp.
101
104
.
16.
Rohde
C. A.
,
1965
, “
Generalized Inverses of Partitioned Matrices
,”
J. Soc. Indust. Appl. Math.
, Vol.
13
, No.
4
, pp.
1033
1035
.
17.
Rohde
C. A.
,
1966
, “
Some Results on Generalized Inverses
,”
SIAM Review
, Vol.
8
, No.
2
, pp.
201
205
.
18.
Wang
J. T.
,
1990
, “
Inverse Dynamics of Constrained Multibody Systems
,”
ASME Journal of Applied Mechanics
, Vol.
112
, pp.
750
757
.
19.
Wang
J. T.
, and
Huston
R. L.
,
1987
, “
Kane’s Equations with Undetermined Multipliers-Application to Constrained Multibody Systems
,”
ASME Journal of Applied Mechanics
, Vol.
54
, pp.
424
429
.
20.
Whitney, D. E., 1972, “The Mathematics of Coordinated Control of Prosthetic Arms and Manipulators,” ASME Journal of Dynamic Systems, Measurement, and Control, pp. 303–309.
21.
Yoshikawa, T., 1983, “Analysis and Control of Robot Manipulators with Redundancy,” Robotics Research: The first Inter. Symp., MIT press, pp. 735–748.
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