Hostname: page-component-74656f9884-g96k6 Total loading time: 0 Render date: 2026-11-09T20:13:06.447Z Has data issue: false hasContentIssue false
  • English
  • Français

A computationally efficient algorithm to find time-optimal trajectory of redundantly actuated robots moving on a specified path

Published online by Cambridge University Press:  29 August 2018

Saeed Mansouri ,
Mohammad Jafar Sadigh  and
Masoud Fazeli
Saeed Mansouri*
Affiliation:
School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
Mohammad Jafar Sadigh
Affiliation:
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran. E-mail: mjsadigh@ut.ac.ir
Masoud Fazeli
Affiliation:
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran. E-mail: mas.fazeli2001@gmail.com
*
*Corresponding author. E-mail: s_mansouri@mech.sharif.edu
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

A time-optimal problem for redundantly actuated robots moving on a specified path is a challenging problem. Although the problem is well explored and there are proposed solutions based on phase plane analysis, there are still several unresolved issues regarding calculation of solution curves. In this paper, we explore the characteristics of the maximum velocity curve and propose an efficient algorithm to establish the solution curve. Then we propose a straightforward method to calculate the maximum or minimum possible acceleration on the path based on the pattern of saturated actuators, which substantially reduces the computational cost. Two numerical examples are provided to illustrate the issues and the solutions.

Keywords

Time-optimalRedundantly actuated robotsRobot control

Information

Type
Articles
Information
Robotica , Volume 37 , Issue 1 , January 2019 , pp. 62 - 79
Copyright
Copyright © Cambridge University Press 2018 

References

1. Bobrow, J., Dubowsky, S. and Gibson, J., “Time-optimal control of robotic manipulators along specified paths,” Int. J. Robot. Res. 4 (3), 3–17 (1985).Google Scholar
2. Pham, Q.-C., “A general, fast, and robust implementation of the time-optimal path parameterization algorithm,” IEEE Trans. Robot. 30 (6), 1533–1540 (2014).Google Scholar
3. Pfeiffer, F. and Johanni, R., “A concept for manipulator trajectory planning,” IEEE J. Robot. Autom. 3 (2), 115–123 (1987).Google Scholar
4. Zlajpah, L., “On Time Optimal Path Control of Manipulators with Bounded Joint vVelocities and Torques,” Proceedings of IEEE International Conference on Robotics and Automation (1996) pp. 1572–1577.Google Scholar
5. Kunz, T. and Stilman, M., “Time-Optimal Trajectory Generation for Path Following with Bounded Acceleration and Velocity,” Robotics: Science and Systems VIII (2012) pp. 1–8.Google Scholar
6. Nguyen, H. and Pham, Q.-C., “Time-optimal path parameterization of rigid-body motions: Applications to spacecraft reorientation,” J. Guid., Control, Dyn. 39 (7), 1667–1671 (2016).Google Scholar
7. Shen, P., Zhang, X. and Fang, Y., “Essential properties of numerical integration for time-optimal path-constrained trajectory planning,” IEEE Robot. Autom. 2 (2), 888–895 (2017).Google Scholar
8. Behzadipour, S. and Khajepour, A., “Time-optimal trajectory planning in cable-based manipulators,” IEEE Trans. Robot. 22 (3), 559–563 (2006).Google Scholar
9. Moon, S. and Ahmad, S., “Time Optimal Trajectories for Cooperative Multi-Robot Systems,” Proceedings of the 29th IEEE Conference on Decision and Control (1990) pp. 1126–1127.Google Scholar
10. Bobrow, J., McCarthy, J. and Chu, V., “Minimum-Time Trajectories for Two Robots Holding the Same Workpiece,” Proceedings of the 29th IEEE Conference on Decision and Control (1990) pp. 3102–3107.Google Scholar
11. Moon, S. and Ahmad, S., “Time scaling of cooperative multirobot trajectories,” IEEE Trans. Syst., Man, Cybern. 21 (4), 900–908 (1991).Google Scholar
12. Moon, S. and Ahmad, S., “Time-optimal trajectories for cooperative multi-manipulator systems,” IEEE Trans., Man Cybern., Part B (Cybernetics) 27 (2), 343–353 (1997).Google Scholar
13. McCarthy, J. and Bobrow, J., “The number of saturated actuators and constraint forces during time-optimal movement of a general robotic system,” IEEE Trans. Robot. Autom. 8 (3), 407–409 (1992).Google Scholar
14. Ghasemi, M. H. and Sadigh, M. J., “A direct algorithm to compute the switching curve for time-optimal motion of cooperative multi-manipulators,” Adv. Robot. 22 (5), 493–506 (2008).Google Scholar
15. Sadigh, M. J. and Mansouri, S., “Application of phase-plane method in generating minimum time solution for stable walking of biped robot with specified pattern of motion,” Robotica 31 (6), 837–851 (2013).Google Scholar
16. Pham, Q.-C. and Nakamura, Y., “Time-Optimal Path Parameterization for Critically Dynamic Motions of Humanoid Robots,” Proceedings of the 12th IEEE-RAS International Conference on Humanoid Robots (2012) pp. 165–170.Google Scholar
17. Caron, S. and Pham, Q.-C., “When to Make a Step? Tackling the Timing Problem in Multi-Contact Locomotion by TOPP-MPC,” Proceedings of the 17th IEEE-RAS International Conference on Humanoid Robots (2017) pp. 522–528.Google Scholar
18. 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. Control 54 (10), 2318–2327 (2009).Google Scholar
19. Zhang, Q., Li, S., Guo, J. and Gao, X., “Time-optimal path tracking for robots under dynamics constraints based on convex optimization,” Robotica 34 (9), 2116–2139 (2016).Google Scholar
20. Zhao, M.-Y., Gao, X.-S. and Zhang, Q., “An efficient stochastic approach for robust time-optimal trajectory planning of robotic manipulators under limited actuation,” Robotica 35 (12), 2400–2417 (2017).Google Scholar
21. Hauser, K., “Fast interpolation and time-optimization with contact,” Int. J. Robot. Res. 33 (9), 1231–1250 (2014s).Google Scholar
22. Pham, Q.-C. and Stasse, O., “Time-optimal path parameterization for redundantly actuated robots: A numerical integration approach,” IEEE/ASME Trans. Mechatron. 20 (6), 3257–3263 (2015).Google Scholar
23. Shiller, Z. and Lu, H.-H., “Computation of path constrained time optimal motions with dynamic singularities,” J. Dyn. Syst., Meas., Control 114 (1), 34–40 (1992).Google Scholar
24. Armstrong, B., Khatib, O. and Burdick, J., “The Explicit Dynamic Model and Inertial Parameters of the PUMA 560 Arm,” Proceedings of IEEE International Conference on Robotics and Automation (1986) pp. 510–518.Google Scholar
25. Liu, C., Atkeson, C. G. and Su, J., “Biped walking control using a trajectory library,” Robotica 31 (02), 311–322 (2013).Google Scholar