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A unified approach to the inverse kinematic solution for a redundant manipulator

Published online by Cambridge University Press:  09 March 2009

J. H. Won
Affiliation:
Dept. of Electrical Engineering, KAIST, 373-1, Kusongdong, Yusunggu, Taejon (Korea)
B. W. Choi
Affiliation:
Dept. of Electrical Engineering, KAIST, 373-1, Kusongdong, Yusunggu, Taejon (Korea)
M. J. Chung
Affiliation:
Dept. of Electrical Engineering, KAIST, 373-1, Kusongdong, Yusunggu, Taejon (Korea)

Summary

For a kinematically redundant manipulator, some performance indices can be optimized while carrying out a given task. So far, the redundancy resolution has been solved at the joint angle level, the joint velocity level, or joint acceleration level depending on the performance indices. According to the resolution level, the solution is represented by high-order differential equations or superfluous number of equations. We propose a unified approach to the inverse kinematic solution which optimizes it at the joint velocity level regardless of the types of the performance indices. A unified approach to obtain an optimal joint velocity is derived by using the necessary condition for optimality so that the proposed method provides an optimal solution for any performance indices and tasks. The optimal solution becomes a set of the minimum number of first-order differential equations which requires a minimum search dimension.To show the validity of the approach, it is applied to a three-link planar manipulator for various types of performance indices.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1993

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References

1.Whitneyz, D.E., Resolved motion rate control of manipulators and human prostheses IEEE Trans. Man-Machine Systems MMS-10 4753 (1969).Google Scholar
2.Liégeois, A., Automatic supervisory control of the configuration and behavior of multibody mechanisms IEEE Trans. Systems. Man, Cyber. SMC-7 868871 (1977).Google Scholar
3.Hanafusa, H., Yoshikawa, T. and Nakamura, Y., Analysis and control of articulated robot arms with redundancy Prepr. 8th Triennial IFAC World Congress, XIV. (Kyoto, Japan) 7883 (1981).Google Scholar
4.Yoshikawa, T., Analysis and control of robotic man- ipulators with redundancy In:Robotics Research: the First Int. Symp. (eds. Brady, and Paul, ) (Cambridge MIT Press 1984). pp. 735748.Google Scholar
5.Dubey, R.V. and Luh, J.Y.S., Redundant robot control for higher flexibility. Proc. of IEEE Int. Conf. on Robotics and Automation 10661072 (1987).Google Scholar
6.Dubey, R.V., Euler, J.A. and Badcock, S.M., An efficient gradient projection optimization scheme for a seven-degree of freedom redundant robot with spherical wrist Proc. of IEEE Int. Conf. on Robotics and Automation2836 (1988).Google Scholar
7.Klein, C.A. and Huang, C.H.,Review of pseudoinverse control for use with kinematically redundant manipulators IEEE Trans, on System, Man, Cybern SMC-13 No. 3, 245250 (1983).Google Scholar
8.Baillieul, J., Kinematic programming alternatives for redundant manipulators Proc. of IEEE Int. Conf. on Robotics and Automation (March, St. Louis) 722728 (1985).Google Scholar
9.Sciavicco, L. and Sicilliano, B., A solution algorithm to the inverse kinematic problem of redundant manipulators Proc. of IEEE Trans, on Robotics and Automation 4, No. 4, 403410 (1988).Google Scholar
10.Anderson, K. and Angeles, J., The kinematic inversion of robot manipulators in the presence of redundancies Int. J. Robotics Research 8, No. 6, 8097 (1989).Google Scholar
11.Chang, P.H., A closed-form solution for the control of manipulators with kinematic redundancy Proc. of IEEE Int. Conf. on Robotics and Automation(San Francisco, CA,Apr. 7–10 1986)914.Google Scholar
12.Uchiyama, M., Shimizu, K. and Hakomori, K., Performance evaluation of manipulators using the Jacobian and its application to trajectory planning In:Robotics Research: the Second Int. Symp. (eds. Hanafusa, H. and Inoue, H.) (Cambridge MIT Press 1985) pp. 446454.Google Scholar
13.Nakamura, Y. and Hanafusa, H., Optimal redundancy control of robot manipulators Int. J. Robotics Res. 6(1), 3242 (1987).Google Scholar
14.Suh, K.C. and Hollerbach, J.M., Local versus global torque optimization of redundant manipulators. Proc. of IEEE Int. Conf. on Robotics and Automation(Raleigh. N.C.)619624 (1987).Google Scholar
15.Kazerounian, K. and Wang, Z., Global versus local optimization in redundancy resolution of robotic manipulators Int. J. Robotics Res. 7(5) 312 (1988).Google Scholar
16.Martin, D.P., Baillieul, J. and Hollerbach, J.M., Resolution of kinematic redundancy using optimization techniques. IEEE Trans, on Robotics and Automation 5, No. 4, 529533 (1989).Google Scholar
17.Kirk, D.E., Optimal Control Theory (New Jersey Prentice-Hall 1970).Google Scholar
18.Ben-Israel, A. and Greville, T.N.E., Generalized Inverses: theory and applications (New York Krieger 1980).Google Scholar
19.Vetterlinkg, W.T. et al. Numerical Recipes in C (Cambridge Univ. Press, Cambridge, 1988).Google Scholar
20.Choi, B.W., Won, J.H. and Chung, M.J., A study on the optimal redundancy resolution of a kinematically redundant manipulator Korean Automatic Control Conf.(Oct. Seoul, Korea)11451149 (1990).Google Scholar