Near-Minimum-Time Motion Planning of Manipulators along Specified Path

Document Type: Original Article

Authors

1 Babol University of Technology

2 Isfahan University of Technology

Abstract

The large amount of computation necessary for obtaining time optimal solution for moving a manipulator on specified path has made it impossible to introduce an on line time optimal control algorithm. Most of this computational burden is due to calculation of switching points. In this paper a learning algorithm is proposed for finding the switching points. The method, which can be used for both serial and parallel manipulators, is based on a two-switch algorithm with three segments of moving with maximum acceleration, constant velocity and maximum deceleration along the path. The learning algorithm is aimed at decreasing the length of constant velocity segment in each step of learning process. The algorithm is applied to find the near minimum time solution of a parallel manipulator along a specified path. The results prove versatility of the algorithm both in tracking accuracy and short training process.

Keywords


Bobrow, J. E., Dubowsky, S. and Gibson, J.S.: Timeoptimal control of robotic manipulators along specified paths, Int. J. Robotics Res., 1985, vol.4, no.3, pp.3-17.

Pfeiffer, F. and Johanni, R.: A Concept for Manipulator Trajectory Planning, IEEE Journal of Robotics and Automation, vol.RA-3, 1987, no.2, pp.115-123.

Zlajpah, L.: On Time Optimal Path Control of Manipulators with Bounded Joint Velocities and Torques, In Proc of IEEE Int. Conf. on Robotics and Automation, Minneapolis, 1996, pp.1572 - 1577.

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 ComputerIntegrated Manufacturing, 2005, 21, 37–53.

Sadigh, M. J. and Ghasemi, M.H.: A Fast Algo rithm for Time Optimal Control of a Cooperative Multi Manipulator System on Specified Path, in proc of 5th Vienna symposium on mathematical modeling, modeling for/and control, 2006, vol.2, pp.1-7.

McCarthy, J. M. and Bobrow, J. E.: The Number of saturated Actuators and Constraint Forces During TimeOptimal Movement of a General Robotic System, IEEE Transaction on Robotics and Automation, 1992, vol.8, no.3, pp.407-409, June.

Moon, S. B. and Ahmad, S.: Time-Optimal Trajectories for Cooperative Multi-Manipulator System, IEEE Transaction on system, Man and cybernetics, 1997, vol.27, no.2, pp.343-353.

Ghasemi, M. H. and Sadigh, M. J.: A Direct Algorithm to Compute Switching Curve for Time Optimal Motion of Cooperative Multi-Manipulators Moving on Specified Path, International Journal of Advanced Robotics, 2008, vol.22, no.5, pp.493-506.

S. Ma and M. Watanabe, Time-optimal control of kinematically redundant manipulators with limit heat charac teristics of actuators, Advanced Robotics, 2002, vol.16, no.8, pp.735 – 749

M. Galicki, Control of kinematically redundant manipulator with actuator constraints, Robot Motion and Control,in proc of the Fifth International Workshop (RoMoCo '05), 2005, pp.123- 130.

J. Mattmüller and D. Gisler, Calculating a near timeoptimal jerk-constrained trajectory along a specified smooth path, International Journal of Advanced Manufacturing Technology, 2009, 45, 1007–1016.

D. Constantinescu and E. A. Croft, Smooth and time optimal trajectory planning for industrial manipulators along specified paths, Journal of Robotic Systems, 2000, 17, 233-249.

Bianco, C. G. L. and Piazzi, A. Minimum-time trajectory planning of mechanical manipulators under dynamic constraints, International Journal of Control, 2002, 75(13), 967-980.

H. Osumi, S.Kamiya, H. Kato, K. Umeda, R. Ueda, and T. Arai, Time optimal control for quadruped walking robots, in Proc. IEEE International Conference on Robotics and Automation, 2006, Orlando, pp. 1050-4729.

F. Y. Yi, K. CH. Nan, L. T. Li, and W. CH. Ju, A Nonlinear Programming Method for Time-Optimal Control of an Omni-Directional Mobile Robot. Journal of Vibration and Control, 2008, 14, 1729-1747.