Time-Subminimal Trajectory Planning for Discrete Non-linear Systems

While several time-optimal trajectory planning techniques have been developed for continuous non-linear systems, there has been little discussion on the subject for discrete non-linear systems. This paper, therefore, presents a technique to search for the time sub-optimal trajectory for general discrete non-linear systems. In this technique, the control inputs with respect to time are partitioned into piecewise constant functions. The piecewise constant functions and the time step interval, which are used in the discretisation of the system, are then searched by a general-purpose non-linear programming optimization method. The example of a time sub-optimal trajectory planning of a SCARA-type manipulator presented in this paper indicates that the proposed technique has the same ability as the existing time sub-optimal trajectory planning techniques for continuous systems. The second numerical example of a non-differentiable car backing-up system shows that the proposed technique also works well for general discrete systems.

[1]  Bernard Roth,et al.  The Near-Minimum-Time Control Of Open-Loop Articulated Kinematic Chains , 1971 .

[2]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[3]  Hajime Akashi,et al.  Minimum time controllers of linear discrete-time systems , 1981 .

[4]  R. Paul.  Robot manipulators : mathematics, programming, and control : the computer control of robot manipulators , 1981 .

[5]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[6]  Alexander H. G. Rinnooy Kan,et al.  Stochastic methods for global optimization , 1984 .

[7]  Gene F. Franklin,et al.  Feedback Control of Dynamic Systems , 1986 .

[8]  Francis L. Merat,et al.  Introduction to robotics: Mechanics and control , 1987, IEEE J. Robotics Autom..

[9]  Panos M. Pardalos,et al.  Constrained Global Optimization: Algorithms and Applications , 1987, Lecture Notes in Computer Science.

[10]  C. Goh,et al.  A simple computational procedure for optimization problems with functional inequality constraints , 1987 .

[11]  E. Gilbert,et al.  Computation of minimum-time feedback control laws for discrete-time systems with state-control constraints , 1987 .

[12]  Ek Peng Chew,et al.  ON MINIMUM TIME OPTIMAL CONTROL OF BATCH CRYSTALLIZATION OF SUGAR , 1989 .

[13]  C. Goh,et al.  Nonlinearly constrained discrete-time optimal-control problems , 1990 .

[14]  C.-H. Wang,et al.  Constrained minimum-time path planning for robot manipulators via virtual knots of the cubic B-spline functions , 1990 .

[15]  C. J. Goh,et al.  Time-optimal Trajectories for Robot Manipulators , 1991, Robotica.

[16]  Kok Lay Teo,et al.  A Unified Computational Approach to Optimal Control Problems , 1991 .

[17]  Tomonari Furukawa,et al.  A Method for Sub-Minimal-Time Trajectory Planning of Redundant Dual manipulator Systems , 1995 .

[18]  Panos Y. Papalambros,et al.  A Deterministic Global Design Optimization Method for Nonconvex Generalized Polynomial Problems , 1996 .

[19]  K. Teo,et al.  Control parametrization enhancing technique for time optimal control problems , 1997 .

[20]  M. W. M. G. Dissanayake,et al.  NUMERICAL SOLUTION FOR A NEAR-MINIMUM-TIME TRAJECTORY FOR TWO COORDINATED MANIPULATORS , 1998 .

[21]  L. S. Jennings,et al.  A Survey of the Control Parametrization and Control Parametrization Enhancing Methods for Constrained Optimal Control Problems , 1999 .