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An algebraic approach to collision-avoidance trajectory planning for dual-robot systems: Formulation and optimization

Published online by Cambridge University Press:  09 March 2009

Suk-Hwan Suh  and
Myung-Soo Kim
Suk-Hwan Suh
Affiliation:
Department of Industrial Engineering, POSTECH, P.O. Box 125, Pohang (Korea) 790–600
Myung-Soo Kim
Affiliation:
Department of Computer Science, POSTECH, P.O. Box 125, Pohang (Korea) 790–600
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Summary

Collision-Avoidance is a key issue in planning trajectories for dual robots whose workspaces overlap. In this paper, we develop a new trajectory planning method by proposing a traffic control schemes. The traffic controller determines the next positions for each robot based on the motion priority and path direction subject to the collision-avoidance conditions and the robots' physical limits. The problem of determining the next positions is formulated and optimized. Algebraic expressions for collision avoidance between every-pair of links – one from the first robot and the other from the second robot – are derived in configuration space. These algebraic expressions are then used to solve the problem of determining “optimal” (in the sense of path direction and motion priority) robots' trajectories. A solution procedure is developed using a nonlinear programming (NLP) solver. The main advantage of our approach is that the two robots' trajectories can be determined simultaneously without requiring any a priori path information. Several numerical examples are presented to demonstrate the validity and effectiveness of the proposed approach.

Keywords

Dual Robot SystemsTrajectory PlanningNonlinear ProgrammingConfiguration Space

Information

Type
Article
Information
Robotica , Volume 10 , Issue 2 , March 1992 , pp. 173 - 182
Copyright
Copyright © Cambridge University Press 1992

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References

1.Freund, E., and Hoyer, H., “Pathfinding in multi-robot systems: Solution and applications” Proc. Int. Conf. on Robot. Automat.103–111 (1986).Google Scholar
2.Tournassoud, P., “A strategy for obstacle avoidance and its application to multi-robot systems” Proc. Int. Conf. on Robot. Automat.1224–1229 (1986).Google Scholar
3.Lee, B.H. and Lee, C.S.G., “Collision-Free motion planning of two robots” IEEE Trans, on Syst., Man, and Cybern. SMC-17, No. 1, 21–32 (01/02, 1987).Google Scholar
4.Chong, N.Y., Choi, D.H. and Suh, I.H., “Collision-Free trajectory planning for dual robot arms” Proc. Conf. on Automat. Contr.951–957 (1988).Google Scholar
5.Tarn, T.J., Bejczy, A.K. and Yun, X., “Design of dynamic control of two cooperating robot arms: Closed chain formulation” Proc. Int. Conf. on Robot. Automat.7–13 (1987).Google Scholar
6.Zheng, Y.F. and Luh, J.Y.S., “Joint torques for control of two coordinated moving robots” Proc. Int. Conf. on Robot. Automat.1375–1380 (1986).Google Scholar
7.Lim, J.H. and Chyung, D.H., “On a control scheme for two cooperating robot arms” Proc. Int. Conf. on Robot. Automat.334–337 (1985).Google Scholar
8.Suh, S.H., “A study on the trajectory planning for multi-robot systems” Proc. Joint Conf. of Korean Management Science and Korean Industrial Engineering18–25 (1989).Google Scholar
9.Gilbert, E.G., Johnson, D.T. and Keerthi, S.S., “A fast procedure for computing the distance between complex objects in three-dimensional space” IEEE Trans, on Robot. Automat. 4, No. 2, 193–203 (04, 1988).Google Scholar
10.Thorpe, C.E., “Path relaxation: Path planning for a mobile robot” Carnegie Mellon Univ., Pittsburgh, PA, Tech. Rep. CMU-RI-TR-84–5 (1984)Google Scholar
11.Brooke, A., Kendrick, D. and Meeraus, A., GAMS: A User's Guide (The Scientific Press, Redwood City, CA, USA, 1988).Google Scholar
12.Liebman, J., Lasdon, L., Schrage, L. and Waren, A., Modeling and Optimization with GINO (The Scientific Press, Palo Alto, CA, USA, 1986).Google Scholar
13.Tarjan, R.E. and Van Wyk, C.J., “An O (n log log n)-Time Algorithm for Triangulating Simple Polygons” SIAM J. on Computing 17, No. 1, 143–178 (1988).CrossRefGoogle Scholar
14.Halmos, P.R., Finite-Dimensional Vector Spaces (Springer-Verlag, New York, USA, 1958).Google Scholar
15.Asada, H. and Slotine, J.E., Robot Analysis and Control (John Wiley and Sons, New York, USA, 1986).Google Scholar