Optimal trajectory planning for industrial robots

An analysis of the results of an algorithm for optimal trajectory planning of robot manipulators is described in this paper. The objective function to be minimized is a weighted sum of the integral squared jerk and the execution time. Two possible primitives for building the trajectory are considered: cubic splines or fifth-order B-splines. The proposed technique allows to set constraints on the robot motion, expressed as upper bounds on the absolute values of velocity, acceleration and jerk. The described method is then applied to a 6-d.o.f. robot (a Cartesian gantry manipulator with a spherical wrist); the results obtained using the two different primitives are presented and discussed.

[1]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[2]  A. Piazzi,et al.  An interval algorithm for minimum-jerk trajectory planning of robot manipulators , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[3]  A. Gasparetto,et al.  A new method for smooth trajectory planning of robot manipulators , 2007 .

[4]  Yury Stepanenko,et al.  Iterative dynamic programming: an approach to minimum energy trajectory planning for robotic manipulators , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[5]  Valder Steffen,et al.  OPTIMIZATION OF THE TRAJECTORY PLANNING OF ROBOT MANIPULATORS TAKING INTO ACCOUNT THE DYNAMICS OF THE SYSTEM , 1998 .

[6]  Dan Simon,et al.  A trigonometric trajectory generator for robotic arms , 1993 .

[7]  O. V. Stryk,et al.  Optimal control of the industrial robot Manutec r3 , 1994 .

[8]  E. Wagner.  International Series of Numerical Mathematics , 1963 .

[9]  Aurelio Piazzi,et al.  Global minimum-jerk trajectory planning of robot manipulators , 2000, IEEE Trans. Ind. Electron..

[10]  Subchan Subchan,et al.  Computational Optimal Control , 2009 .

[11]  E. Croft,et al.  Smooth and time-optimal trajectory planning for industrial manipulators along specified paths , 2000 .

[12]  A. Piazzi,et al.  Global minimum-time trajectory planning of mechanical manipulators using interval analysis , 1998 .

[13]  C. Lin,et al.  Formulation and optimization of cubic polynomial joint trajectories for industrial robots , 1983 .

[14]  Kostas J. Kyriakopoulos,et al.  Minimum jerk path generation , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[15]  A. Gasparetto,et al.  A technique for time-jerk optimal planning of robot trajectories , 2008 .

[16]  S. F. P. Saramago,et al.  OPTIMAL TRAJECTORY PLANNING OF ROBOT MANIPULATORS IN THE PRESENCE OF MOVING OBSTACLES , 2000 .