Near Time Optimal Path Control of Kinematically Redundant Manipulators with Bounded Joint Velocities and Torques

Abstract:

here, a time optimal control scheme for trajectory planning of kinematically manipulators subjects to actuator torque limits is proposed by using the phase plane analysis and linear programming technique. In addition, the limit on joint velocities is considered. In order to affect the constraint of joint velocities, this constraint is converted to constraint on joint acceleration and it is affected linear programming problem as an additional constraint. Also, an explicit algorithm for finding the switching points is presented. To this end, some simulations are given to demonstrate the efficiency of proposed trajectory planning algorithm.

• Periodical: Applied Mechanics and Materials (Volumes 110-116)
• Pages: 1547-1555
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.110-116.1547
• Online since: October 2011
• Authors: Mohammad Hassan Ghasemi, Navvab Kashiri, Morteza Dardel, Mohammad Hadi Pashaei
• Keywords: Joint Velocity Constraint, Phase Plane Analysis, Redundant Manipulators, Specified Path, Time-Optimal

References

[1] J. E. Bobrow, S. Dubowsky, and J. S. Gibson, Time-optimal control of robotic manipulators along specified paths, The International Journal of Robotics Research, vol. 4 no. 3, pp.3-17, September 1985, doi: 10. 1177/027836498500400301.

DOI: 10.1177/027836498500400301

[2] K. G. Shin and N. D. McKay, Minimum-time control of robotic manipulators with geometric path-constraints, IEEE Transactions on Automatic Control, vol. 30, no. 6, p.531–541, Jun 1985, doi: 10. 1109/TAC. 1985. 1104009.

DOI: 10.1109/tac.1985.1104009

[3] Pfeiffer and R. Johanni, A concept for manipulator trajectory planning, IEEE Journal of Robotics and Automation, vol. 3, no. 2 , p.115–123, April 1987, doi: 10. 1109/JRA. 1987. 1087090.

DOI: 10.1109/jra.1987.1087090

[4] Y. Chen and A. A. Desrochers, Structure of minimum time control law for robotic manipulators with constrained paths, Proc. IEEE International Conference on Robotics and Automation, IEEE Press, May 1989, pp.970-975.

DOI: 10.1109/robot.1989.100107

[5] L. Zlajpah, on time optimal path control of manipulators with bounded joint velocities and torques, Proc. IEEE International Conference on Robotics and Automation, IEEE Press, Apr. 1996, p.1572–1577, doi: 10. 1109/ROBOT. 1996. 506928.

DOI: 10.1109/robot.1996.506928

[6] S. D. Timar, R. T. Farouki, and T. S. Smith, C. L. Boyadjieff, Algorithms for time-optimal control of CNC machines along curved tool paths, Robotics and Computer-Integrated Manufacturing, vol. 21, no. 1, Feb. 2005, p.37.

DOI: 10.1016/j.rcim.2004.05.004

[7] J. Mattmüller and D. Gisler, Calculating a near time-optimal jerk-constrained trajectory along a specified smooth path, International Journal of Advanced Manufacturing Technology, vol. 45 no. 9-10, p.1007.

DOI: 10.1007/s00170-009-2032-9

[8] M. J. Sadigh and M. H. Ghasemi, A Direct Algorithm to Compute the Switching Curve for Time-Optimal Motion of Cooperative Multi-Manipulators Moving on a Specified Path, Advanced Robotics, vol. 22, no. 5, pp.493-506.

DOI: 10.1163/156855308x294851

[9] S. Ma and M. Watanabe, Minimum time path-tracking control of redundant manipulators, Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, IEEE Press, Nov. 2000, vol. 1, p.27–32 doi: 10. 1109/IROS. 2000. 894577.

DOI: 10.1109/iros.2000.894577

[10] S. Ma and M. Watanabe, Time optimal path-tracking control of kinematically redundant manipulators, JSME Int. J. C. Mech. Syst. Mach. Elem. Manuf. Vol. 47, no. 2, p.582–590, 2004, doi: 10. 1299/jsmec. 47. 582.

DOI: 10.1299/jsmec.47.582

[11] S. Ma and M. Watanabe, Minimum-time control of coupled tendon-driven manipulators, Advanced Robotics, vol. 15, no. 4, pp.409-427, 2001, doi: 10. 1163/156855301750398338.

DOI: 10.1163/156855301750398338

[12] S. Ma and M. Watanabe, Time-optimal control of kinematically redundant manipulators with limit heat characteristics of actuators, Advanced Robotics, vol. 16, no. 8, pp.735-749, 2002, doi: 10. 1163/15685530260425729.

DOI: 10.1163/15685530260425729

[13] M. Galicki, Time-optimal controls of kinematically redundant manipulators with geometric constraints, IEEE Transactions on Robotics and Automation, vol. 16, no. 1, p.89–93, Feb. 2000, doi: 10. 1109/70. 833194.

DOI: 10.1109/70.833194