Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-22T14:15:34.532Z Has data issue: false hasContentIssue false
  • English
  • Français

A numerical approach for time-optimal path-planning of kinematically redundant manipulators*

Published online by Cambridge University Press:  09 March 2009

Chia-Ju Wu
Chia-Ju Wu
Affiliation:
Department of Electrical Engineering, National Yunlin Institute of Technology, Touliu, Yunlin 640(Taiwan, R.O.C.)
Get access Rights & Permissions [Opens in a new window]

Summary

In this paper, a numerical approach is proposed to solve the time-optimal path-planning (TOPP) problem of kinematically redundant manipulators between two end-points. The first step is to transform the TOPP problem into a nonlinear programming problem by an iterative procedure. Then an approach to find the initial feasible solutions of the problem is proposed. Since initial feasible solutions can be found easily, the optimization process of the nonlinear programming problem can be started from different points to find the global minimum. A planar three-link robotic manipulator is used to illustrate the validity of the proposed approach.

Keywords

Time-optimal path-planningRedundant manipulators; Nonlinear programmingNumerical methods
Type
Article
Information
Robotica , Volume 12 , Issue 5 , September 1994 , pp. 401 - 410
Copyright
Copyright © Cambridge University Press 1994

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

1.Kahn, M.E. and Roth, B., “The near-minimum-time control of open-loop articulated kinematic chains” ASME J. Dyn. Sys., Meas. Control 93, 164–172 (1971).CrossRefGoogle Scholar
2.Pontryagin, L.S. et al. , The Mathematical Theory of Optimal Process (Wiley, New York, 1962).Google Scholar
3.Dubowsky, S.M., Norris, M.A. and Shiller, Z., “Timeoptimal trajectory planning for robotic manipulator” Proc. IEEE Int. Conf. on Robotics and Automation(1986) pp. 1906–1912.Google Scholar
4.Sahar, B. and Hollerbach, J.M., “Planning of minimum time trajectory for robot arms” Int. J. Robotic Research 5, 90–100 (1986).CrossRefGoogle Scholar
5.Flash, T. and Potts, R.B., “Discrete trajectory planning” Int. J. Robotics Research 7, 48–57 (1988).Google Scholar
6.Bobrow, J.E., “Optimal robot path planning using the minimum-time criterion” IEEE J. Robotics and Automation 4, 443–450 (1988).Google Scholar
7.Bobrow, J.E., Dubowsky, S. and Gibson, J.S., “Timeoptimal control for robotic manipulators along specified paths” Int. J. Robotics Research 4, 3–17 (1985).Google Scholar
8.Chen, Y. and Desrochers, A.A., “Structure of minimumtime control law for robotic manipulators with constrained paths” Proc. IEEE Int. Conf. on Robotics and Automation(1989) pp. 759–764.Google Scholar
9.Hollerbach, J.M., “Dynamics scaling of manipulator trajectories” ASME J. Dyn. Sys. Meas., Control 106, 102–106 (1984).Google Scholar
10.Tan, H.H. and Potts, R.B., “Minimum time trajectory planner for the discrete dynamics robot model with dynamic constraints” IEEE J. Robotics and Automation 4, 174–185 (1988).Google Scholar
11.Tan, H.H. and Potts, R.B., “A discrete trajectory planner for robotic arms with six degrees of freedom” IEEE Trans, on Robotics and Automation 5, 681–690 (1989).CrossRefGoogle Scholar
12.Whitney, D.E., “Resolved motion rate control of manipulators and human prostheses” IEEE Trans. Man-Machine Syst. 10, 47–53 (1969).Google Scholar
13.Liegeois, A., “Automatic supervisory control of the configuration and behavior of multibody mechanisms” IEEE Trans. Systems, Man, Cybern. 7, 868–871 (1977).Google Scholar
14.Yoshikawa, T., “Manipulability and redundancy control of robotic mechanisms” Proc. IEEE Int. Conf. on Robotics and Automation(1985) pp. 1004–1009.Google Scholar
15.Baillieul, J., Hollerbach, J.M. and Brockett, R., “Programming and control of kinematically redundant manipulators” Proc. 23rd IEEE Conf. on Decision and Control(1984) pp. 768–774.Google Scholar
16.Walker, I.D. and Marcus, S.I., “An approach to the control of kinematically redundant robot manipulators” Proc. American Control Conf.(1986) pp. 1907–1912.Google Scholar
17.Klein, C.A. and Huang, C.H., “Review of pseudoinverse control for use with kinematically redundant manipulators” IEEE Trans. Systems, Man, Cybern. 13, 245–250 (1983).Google Scholar
18.Oh, S.Y., Orin, D. and Bach, M., “An inverse kinematic solution for kinematically redundant robot manipulators” J. Robotic Systems 1, 235–249 (1984).CrossRefGoogle Scholar
19.Khatib, O., “A unified approach for motion and force control of robot manipulators: The operational space formulation” IEEE J. Robotics and Automation 3, 43–53 (1987).Google Scholar
20.Maciejewsky, A.A. and Klein, C.A., “Obstacle avoidance for kinematically redundant manipulators in dynamically varying environments” Int. J. Robotics Research 4, 109–117 (1985).Google Scholar
21.Baker, D.R. and Wampler, C.W., “Some facts concerning the inverse kinematics of redundant manipulators” Proc. IEEE Int. Conf. on Robotics and Automation(1987) pp. 604–609.Google Scholar
22.Hollerbach, J.M. and Suh, K.C., “Redundancy resolution of manipulators through torque optimization” Proc. IEEE Conf. on Robotics and Automation(1985) pp. 1016–1021.Google Scholar
23.Egeland, O., “Cartesian control of a hydraulic redundant manipulator” Proc. IEEE Int. Conf. on Robotics and Automation(1987) pp. 2081–2086.Google Scholar
24.Hsu, P., Hauser, J. and Sastry, S., “Dynamic control of redundant manipulators” Proc. IEEE Int. Conf. on Robotics and Automation(1988) pp. 183–187.Google Scholar
25.Dubey, R.V., Euler, J.A. and Babcock, S.M., “An efficient gradient projection optimization scheme for a 7-dof redundant robot with spherical wrist” Proc. IEEE Int. Conf. on Robotics and Automation(1988) pp. 28–36.Google Scholar
26.Chung, T.S. and Wu, C.J., “A computationally efficient numerical algorithm for the minimum-time control problem of continuous systems” Automatica 28, 841–847 (1992).Google Scholar
27.Craig, J.J., Introduction to Robotics: Mechanics and Control, 2nd edition, (Addison-Wesley, Reading, MA, 1989).Google Scholar
28.Polak, E., Computational Methods in Optimization: A Unified Approach (Academic Press, New York, 1971).Google Scholar
29.Luenberger, D.G., Linear and Nonlinear Programming (Addison-Wesley, Reading, MA, 1973).Google Scholar
30.Lasdon, L.S. and Waren, A.D., GRG2 USER'S GUIDE (Dept. of General Business, University of Texas at Austin, Austin, Texas, 1986).Google Scholar