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Optimal trigonometric robot joint trajectories

Published online by Cambridge University Press:  09 March 2009

Dan Simon  and
Can Isik
Dan Simon
Affiliation:
121 Link Hall, Department of Electrical Engineering, Syracuse University, Syracuse, NY 13244-1240 (USA)
Can Isik
Affiliation:
121 Link Hall, Department of Electrical Engineering, Syracuse University, Syracuse, NY 13244-1240 (USA)
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Summary

Interpolation of a robot joint trajectory is realized using trigonometric splines. This original application has several advantages over existing methods (e.g. those using algebraic splines). For example, the computational expense is lower, more constraints can be imposed on the trajectory, obstacle avoidance can be implemented in real time, and smoother trajectories are obtained. Some of the spline parameters can be chosen to minimize an objective function (e.g. minimum jerk or minimum energy). If jerk is minimized, the optimization has a closed form solution. This paper introduces a trajectory interpolation algorithm, discusses a method for path optimization, and includes examples.

Keywords

Robot path planningTrigonometric splinesOptimizationJoint trajectories

Information

Type
Article
Information
Robotica , Volume 9 , Issue 4 , December 1991 , pp. 379 - 386
Copyright
Copyright © Cambridge University Press 1991

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References

1.Shin, L. and McKay, N., “Minimum-Time Control of Robotic Manipulators with Geometric Path Constraints” IEEE Transactions on Automatic Control AC-30, 531–541 (1985).CrossRefGoogle Scholar
2.Shiller, Z. and Dubowsky, S., “Robot Path Planning with Obstacles, Actuator, Gripper, and Payload Constraints” Int. J. Robotics Research 8, 3–18 (12., 1989).CrossRefGoogle Scholar
3.Lin, C., Chang, P. and Luh, J., “Formulation and Optimization of Cubic Polynomial Joint Trajectories for Industrial Robots” IEEE Transactions on Automatic Control AC-28, 1066–1073 (12., 1983).CrossRefGoogle Scholar
4.Thompson, S. and Patel, R., “Formulation of Joint Trajectories for Industrial Robots using B-Splines” IEEE Transactions on Industrial Electronics IE-34, 192–199 (05, 1987).CrossRefGoogle Scholar
5.Yamamoto, M. et al. , “Planning of Manipulator Joint Trajectories by an Iterative Method” Robotica 6, 101–105 (1988).CrossRefGoogle Scholar
6.Chang, Y., Lee, T. and Liu, C., “On-Line Cartesian Path Trajectory Planning for Robot Manipulators” IEEE International Conference on Robotics and Automation1, 62–67 (1988).Google Scholar
7.Chand, S. and Doty, K., “On-Line Polynomial Trajectories for Robot Manipulators” Int. J. Robotics Research 4, 38–48 (Summer, 1985).CrossRefGoogle Scholar
8.Mujtaba, M., “Discussion of Trajectory Calculation Methods” In: Exploratory Study of Computer Integrated Assembly Systems (Binford, T. et al. , eds) (Artificial Intelligence Lab, Stanford University, Palo Alto, CA, Report AIM 285.4, 1977).Google Scholar
9.Schoenberg, I., “On Trigonometric Spline Interpolation” J. Mathematics and Mechanics 13, 795–825 (1964).Google Scholar
10.Lyche, T. and Winther, R., “A Stable Recurrence Relation for Trigonometric B-Splines” J. Approximation Theory 25, 266–279 (03, 1979).CrossRefGoogle Scholar
11.Koch, P., “Error Bounds for Interpolation by Fourth Order Trigonometric Splines” In: Approximation Theory and Spline Functions (Singh, , Burry, , and Watson, , eds.) (D. Reidel Publishing Company, Dordrecht Holland, 1984) pp. 349–360.CrossRefGoogle Scholar
12.Koch, P. and Lyche, T., “Bounds for the Error in Trigonometric Hermite Interpolation” In: Quantitative Approximation (Devore, and Scherer, , eds.) (Academic Press, New York, 1980) pp. 185–196.CrossRefGoogle Scholar
13.Ruoff, C., “Fast Trigonometric Functions for Robot Control” Robotics Age 12–20 (11., 1981).Google Scholar
14.Chen, Y. and Vidyasagar, M., “Optimal Control of Robotic Manipulators in the Presence of Obstacles” J. Robotic Systems 7, 721–740 (1990).CrossRefGoogle Scholar
15.Yen, V. and Nagurka, M., “Fourier-Based Optimal Control Approach for Structural Systems” J. Guidance, Control and Dynamics 13, 265–276 (03, 1990).CrossRefGoogle Scholar