A global optimization approach to trajectory planning for industrial robots

A deterministic global optimization approach is proposed for the optimal trajectory planning of D-joint industrial robots. After mapping Cartesian knots into joint knots, by inverse kinematics, they are interpolated with spline functions under constraints on joint accelerations and jerks. An interval algorithm, a procedure based on interval analysis techniques, is presented to determine an optimal piecewise trajectory which globally minimizes the total travelling time. With arbitrarily sharp precision, this procedure solves the nonlinearly constrained optimization problem which is obtained using the branch-and-bound principle where the branching is performed by uniform subdivision and the bounding via interval inclusion functions. The interval algorithm, implemented in C++ with the PROFIL/BIAS libraries, has been applied to the optimal four-spline planning of a 6-joint arm, and computational results are included.

[1]  Jon G. Rokne,et al.  New computer methods for global optimization , 1988 .

[2]  Renfrey B. Potts,et al.  Minimum time trajectory planner for the discrete dynamic robot model with dynamic constraints , 1988, IEEE J. Robotics Autom..

[3]  Dan Simon.  The application of neural networks to optimal robot trajectory planning , 1993, Robotics Auton. Syst..

[4]  Ramon E. Moore.  Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[5]  Jon G. Rokne,et al.  Computer Methods for the Range of Functions , 1984 .

[6]  Aurelio Piazzi,et al.  Robust stability using interval analysis , 1996, Int. J. Syst. Sci..

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

[8]  Steven Dubowsky,et al.  Robot Path Planning with Obstacles, Actuator, Gripper, and Payload Constraints , 1989, Int. J. Robotics Res..

[9]  Ronald R. Willis,et al.  New Computer Methods for Global Optimization , 1990 .

[10]  E. Walter,et al.  Guaranteed characterization of stability domains via set inversion , 1994, IEEE Trans. Autom. Control..

[11]  Chia-Ju Wu,et al.  A numerical approach for time-optimal path-planning of kinematically redundant manipulators , 1994, Robotica.

[12]  Eric Walter,et al.  Guaranteed tuning, with application to robust control and motion planning , 1996, Autom..

[13]  N. McKay,et al.  A dynamic programming approach to trajectory planning of robotic manipulators , 1986 .

[14]  James E. Bobrow,et al.  Optimal robot plant planning using the minimum-time criterion , 1988, IEEE J. Robotics Autom..