Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T13:26:48.544Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal conditions for inverse kinematics of a robot manipulator with redundancy

Published online by Cambridge University Press:  09 March 2009

Dong Kwon Cho ,
Byoung Wook Choi  and
Myung Jin Chung
Dong Kwon Cho
Affiliation:
Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, 373–1 Kusong-dong, Yusong-gu, Taejon 305–701 (Korea)
Byoung Wook Choi
Affiliation:
Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, 373–1 Kusong-dong, Yusong-gu, Taejon 305–701 (Korea)
Myung Jin Chung
Affiliation:
Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, 373–1 Kusong-dong, Yusong-gu, Taejon 305–701 (Korea)
Get access Rights & Permissions [Opens in a new window]

Summary

The algorithms of inverse kinematics based on optimality constraints have some problems because those are based only on necessary conditions for optimality. One of the problems is a switching problem, i.e., an undesirable configuration change from a maximum value of a performance measure to a minimum value may occur and cause an inverse kinematic solution to be unstable. In this paper, we derive sufficient conditions for the optimal solution of the kinematic control of a redundant manipulator. In particular, we obtain the explicit forms of the switching condition for the optimality constraintsbased methods. We also show that the configuration at which switching occurs is equivalent to an algorithmic singularity in the extended Jacobian method. Through a numerical example of a cyclic task, we show the problems of the optimality constraints-based methods. To obtain good configurations without switching and kinematical singularities, we propose a simple algorithm of inverse kinematics.

Keywords

Redundant manipulatorInverse kinematicsRedundancy resolutionSingularity avoidanceAlgorithmic singularity
Type
Articles
Information
Robotica , Volume 13 , Issue 1 , January 1995 , pp. 95 - 101
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

references

1.Won, J.H., Choi, B.W. and Chung, M.J., “A unified approach to the inverse kinematic solution for a redundant manipulator” Robotica 11, Part 2, 159–165 (1993).CrossRefGoogle Scholar
2.Whitney, D.E., “Resolved motion rate control of manipulator and human prostheses” IEEE Trans, on Man-Machine Systems 10, 47–53 (1969).CrossRefGoogle Scholar
3.Baillieul, J., “Kinematic programming alternatives for redundant manipulators” Proc. of IEEE Int. Conf. on Robotics and Automation,St. Louis, Missouri(1985) pp. 722–728.Google Scholar
4.Baillieul, J., “Avoiding obstacles and resolving kinematic redundancy” Proc. IEEE Int. Conf. on Robotics and Automation,San Francisco, California(1986) pp. 1698–1704.Google Scholar
5.Chang, P.H., “A closed-form solution for inverse kinematics of robot manipulators with redundancy” IEEE J. Robotics and Automation 3, 393–403 (1987).CrossRefGoogle Scholar
6.Baker, D.R. and Wampler, C.W. II, “On the inverse kinematics of redundant manipulators” Int. J. Robotics Research 7, 2–21 (1988).CrossRefGoogle Scholar
7.Angeles, J. and Mathur, S., “Resolved-rate control of redundant manipulators with elimination of non-conservative effects” Proc. 5th Int. Symposium of Robotics Research(1989) pp.209–216.Google Scholar
8.Burdick, J.W., “On the inverse kinematics of redundant manipulators: characterization of the self-motion manifolds” Proc. IEEE Int. Conf. on Robotics and Automation,Scottsdale, Arizona(1989) pp. 264–270.Google Scholar
9.Cho, D.K., Choi, B.W., Won, J.H. and Chung, M.J., “Singularity-free condition of optimal solution for kinematical control of redundant manipulators” Proc. IEEE/RSJ Int. Workshop on Intelligent Robots and Systems,Raleigh, North Carolina, USA(1992) pp. 1753–1760.Google Scholar
10.Choi, B.W., Won, J.H. and Chung, M.J., “Performance evaluation of dexterity measures using measure constraint locus” Proc. IEEE/RSJ Int. Workshop on Intelligent Robots and Systems,Raleigh, North Carolina, USA(1992) pp. 1943–1950.Google Scholar
11.Klein, C., Chu-jenq, C. & Ahmed, S., “Use of an extended Jacobian method to map algorithmic singularities” Proc. IEEE Int. Conf. on Robotics and Automation,Atlanta, Georgia(1993) pp. 632–637.Google Scholar
12.Yoshikawa, T., “Analysis and control of robot manipulators with redundancy” In: Robotics Research: the First Int. Symp. (eds., Brady, and Paul, ) (MIT Press, Cambridge. Mass., 1984) pp. 735–737.Google Scholar