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An efficient stochastic approach for robust time-optimal trajectory planning of robotic manipulators under limited actuation

Published online by Cambridge University Press:  03 April 2017

Ming-Yong Zhao ,
Xiao-Shan Gao  and
Qiang Zhang
Ming-Yong Zhao
Affiliation:
KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China. E-mails: [email protected], [email protected] BKLPUMEC, Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China
Xiao-Shan Gao*
Affiliation:
KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China. E-mails: [email protected], [email protected]
Qiang Zhang
Affiliation:
KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China. E-mails: [email protected], [email protected]
*
*Corresponding author. E-mail: [email protected]
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Summary

This paper focuses on the problem of robust time-optimal trajectory planning of robotic manipulators to track a given path under a probabilistic limited actuation, that is, the probability for the actuation to be limited is no less than a given bound κ. We give a general and practical method to reduce the probabilistic constraints to a set of deterministic constraints and show that the deterministic constraints are equivalent to a set of linear constraints under certain conditions. As a result, the original problem is reduced to a linear optimal control problem which can be solved with linear programming in polynomial time. In the case of κ = 1, the original problem is proved to be equivalent to the linear optimal control problem. Overall, a very general, practical, and efficient algorithm is given to solve the above problem and numerical simulation results are used to show the effectiveness of the method.

Keywords

Robust trajectory planningRobotic manipulatorsStochastic optimizationProbability constraintLinear programming
Type
Articles
Information
Robotica , Volume 35 , Issue 12 , December 2017 , pp. 2400 - 2417
Copyright
Copyright © Cambridge University Press 2017 

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References

1. Constantinescu, D. and Croft, E. A., “Smooth and time optimal trajectory planning for industrial manipulators along specified paths,” J. Robot. Syst. 17 (5), 233–249 (2002).3.0.CO;2-Y>CrossRefGoogle Scholar
2. Bobrow, J. E., Dubowsky, S. and Gibson, J., “Time-optimal control of robotic manipulators along specified paths,” Int. J. Robot. Res. 4, 3–17 (1985).CrossRefGoogle Scholar
3. Shin, K. and McKay, N., “Minimum-time control of robotic manipulators with geometric path constraints,” IEEE Trans. Autom. Cont. 30, 531–541 (1985).CrossRefGoogle Scholar
4. Pham, Q. C., “A general, fast, and robust implementation of the time-optimal path parameterization algorithm,” IEEE Trans. Robot. 30 (6), 1533–1540 (2014).CrossRefGoogle Scholar
5. Chen, Y. and Desrochers, A. A., “Structure of Minimum-Time Control Law for Robotic Manipulators with Constrained Paths,” Proceedings of the IEEE International Conference on Robot and Automation, Scottsdale, USA (1989) pp. 971–976.Google Scholar
6. Verscheure, D., Demeulenaere, B., Swevers, J., De Schutter, J. and Diehl, M., “Time-optimal path tracking for robots: A convex optimization approach,” IEEE Trans. Autom. Cont. 54 (10), 2318–2327 (2009).CrossRefGoogle Scholar
7. Debrouwere, F., Van Loock, W., Pipeleers, G., Dinh, Q. T., Diehl, M., De Schutter, J. and Swevers, J., “Time-optimal path following for robots with convex-concave constraints using sequential convex programming,” IEEE Trans. Robot. 29 (6), 1485–1495 (2013).CrossRefGoogle Scholar
8. Kröger, T. and Wahl, F. M., “Online trajectory generation: Basic concepts for instantaneous reactions to unforeseen events,” IEEE Trans. Robot., 26 (1), 94–111 (2010).CrossRefGoogle Scholar
9. Aurnhammer, A. and Marti, K., “Real-time robust optimal trajectory planning for industrial robots,” In: Dynamic Stochastic Optimization (Marti, K., Ermoliev, Y. and Pflug, G., eds) (Springer-Verlag, Berlin, 2004), pp. 133–155.CrossRefGoogle Scholar
10. Shin, K. G. and Mckay, N. D., “Robust trajectory planning for robotic manipulators under payload uncertainties,” IEEE Trans. Autom. Cont. 32 (12), 1044–1054 (1987).CrossRefGoogle Scholar
11. Kieffer, J., Cahill, A. J. and James, M. R., “Robust and accurate time-optimal path-tracking control for robot manipulators,” IEEE Trans. Robot. Autom. 13 (6), 880–890 (1997).CrossRefGoogle Scholar
12. Zhang, Q., Guo, J. X., Gao, X. S. and Li, S., “Tractable algorithm for robust time-optimal trajectory planning of robotic manipulators under confined torque,” Int. J. Comput. Commun. 10 (1), 123–135 (2015).CrossRefGoogle Scholar
13. Wilson, A. J., Schultz, J. A. and Murphey, T. D., “Trajectory optimization for well-conditioned parameter estimation,” IEEE Trans. Autom. Sci. Eng. 12 (1), 28–36 (2015).CrossRefGoogle Scholar
14. Frigerio, N. and Matta, A., “Energy-efficient control strategies for machine tools with stochastic arrivals,” IEEE Trans. Autom. Sci. Eng. 12 (1), 50–61 (2015).CrossRefGoogle Scholar
15. Marti, K. and Aurnhammer, A., “Robust optimal trajectory planning for robots by stochastic optimization,” Math. Comput. Modelling Dyn. Syst. 8 (1), 75–116 (2002).Google Scholar
16. Pfeiffer, F. and Johanni, R., “A concept for manipulator trajectory planning,” IEEE J. Robot. Autom. 3 (2), 115–123 (1987).CrossRefGoogle Scholar
17. Zhang, K., Yuan, C. M. and Gao, X. S., “Efficient algorithm for feedrate planning and smoothing with confined chord error and acceleration for each axis,” Int. J. Adv. Manuf. Technol. 66 (9), 1685–1697 (2013).CrossRefGoogle Scholar
18. Yuan, C., Zhang, K. and Fan, W., “Time-optimal interpolation for CNC machining along curved tool pathes with confined chord error,” J. Syst. Sci. Complex 26 (5), 836–870 (2013).CrossRefGoogle Scholar
19. LaValle, S. M., Planning Algorithms (Cambridge University Press, Cambridge, UK, 2006).CrossRefGoogle Scholar
20. Peter, K. and Stein, W., Stochastic Programming (Wiley, Chichester, 1995).Google Scholar
21. Chen, T. W. C. and Vassiliadis, V. S., “Inequality path constraints in optimal control: A finite iteration ϵ-convergent scheme based on pointwise discretization,” J. Process Control 15, 353–362 (2005).CrossRefGoogle Scholar
22. Dong, J. and Stori, J. A., “A generalized time-optimal bidirectional scan algorithm for constrained feed-rate optimization,” J. Dyn. Syst. Meas. Control 128 (2), 379–390 (2006).CrossRefGoogle Scholar
23. Piegl, L. and Tiller, W., The NURBS Book, 2nd ed. (Springer-Verlag, Berlin, 1997).CrossRefGoogle Scholar
24. Reynoso-Mora, P., Chen, W. and Tomizuka, M., “On the Time-Optimal Trajectory Planning and Control of Robotic,” Proceedings of the American Control Conference, Washington (June 17–19, 2013), pp. 371–377.Google Scholar
25. Robbins, H. and Monro, S., “A stochastic approximation method,” Ann. Math. Stat. 22 (3), 400–407 (1951).CrossRefGoogle Scholar
26. Zhang, Q., Li, S., Guo, J. and Gao, X. S., “Efficient trajectory optimization for minimum time motion of robotic manipulators with confined dynamics constraints,” Robotica 34 (09), 2116–2139 (2016).CrossRefGoogle Scholar