Skip to main content Accessibility help

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

  • Ming-Yong Zhao (a1) (a2), Xiao-Shan Gao (a1) and Qiang Zhang (a1)


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.


Corresponding author

*Corresponding author. E-mail:


Hide All
1. Constantinescu, D. and Croft, E. A., “Smooth and time optimal trajectory planning for industrial manipulators along specified paths,” J. Robot. Syst. 17 (5), 233249 (2002).
2. Bobrow, J. E., Dubowsky, S. and Gibson, J., “Time-optimal control of robotic manipulators along specified paths,” Int. J. Robot. Res. 4, 317 (1985).
3. Shin, K. and McKay, N., “Minimum-time control of robotic manipulators with geometric path constraints,” IEEE Trans. Autom. Cont. 30, 531541 (1985).
4. Pham, Q. C., “A general, fast, and robust implementation of the time-optimal path parameterization algorithm,” IEEE Trans. Robot. 30 (6), 15331540 (2014).
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. 971976.
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), 23182327 (2009).
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), 14851495 (2013).
8. Kröger, T. and Wahl, F. M., “Online trajectory generation: Basic concepts for instantaneous reactions to unforeseen events,” IEEE Trans. Robot., 26 (1), 94111 (2010).
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. 133155.
10. Shin, K. G. and Mckay, N. D., “Robust trajectory planning for robotic manipulators under payload uncertainties,” IEEE Trans. Autom. Cont. 32 (12), 10441054 (1987).
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), 880890 (1997).
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), 123135 (2015).
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), 2836 (2015).
14. Frigerio, N. and Matta, A., “Energy-efficient control strategies for machine tools with stochastic arrivals,” IEEE Trans. Autom. Sci. Eng. 12 (1), 5061 (2015).
15. Marti, K. and Aurnhammer, A., “Robust optimal trajectory planning for robots by stochastic optimization,” Math. Comput. Modelling Dyn. Syst. 8 (1), 75116 (2002).
16. Pfeiffer, F. and Johanni, R., “A concept for manipulator trajectory planning,” IEEE J. Robot. Autom. 3 (2), 115123 (1987).
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), 16851697 (2013).
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), 836870 (2013).
19. LaValle, S. M., Planning Algorithms (Cambridge University Press, Cambridge, UK, 2006).
20. Peter, K. and Stein, W., Stochastic Programming (Wiley, Chichester, 1995).
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, 353362 (2005).
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), 379390 (2006).
23. Piegl, L. and Tiller, W., The NURBS Book, 2nd ed. (Springer-Verlag, Berlin, 1997).
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. 371377.
25. Robbins, H. and Monro, S., “A stochastic approximation method,” Ann. Math. Stat. 22 (3), 400407 (1951).
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), 21162139 (2016).


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

  • Ming-Yong Zhao (a1) (a2), Xiao-Shan Gao (a1) and Qiang Zhang (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed