Efficient Algorithm for Time-Optimal Control of a Two-Link Manipulator

A class of optimization problems of interest in the field of robotics is one that seeks to minimize the time required to force a manipulator to travel a specified distance. Robots employ multiple, bounded control inputs. This work describes a new, very fast algorithm for determining minimum-time trajectories for such systems. We have modified the steepest descent method of optimal programming to find time-optimal switch times for bang-bang control systems. The Switch Time Optimization (STO) program has been applied to a two-link manipulator with two control inputs. To find the minimum time for a robot end-effector to travel between two points in its workspace, one must establish the optimal position of the robot with respect to the work station. The algorithm accomplishes this by allowing optimal initial states to be determined along with the time history of the controls. Exact control switch times and optimal initial conditions have been found for minimum-time repositioning maneuvers in which the robot was required to travel a specified distance. The STO algorithm is not limited to use with manipulators; it is applicable to any bang-bang system.

[1]  Bong Wie,et al.  Minimum-time pointing control of a two-link manipulator , 1988 .

[2]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[3]  A. Bryson,et al.  Optimal control of systems with hard control bounds , 1985 .

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

[5]  Steven Dubowsky,et al.  On computing the global time-optimal motions of robotic manipulators in the presence of obstacles , 1991, IEEE Trans. Robotics Autom..

[6]  J. Y. S. Luh,et al.  An anatomy of industrial robots and their controls , 1983 .

[7]  D. M. Monro,et al.  A computational technique for finding time optimal controls of nonlinear time-varying systems , 1969 .

[8]  Gerald Cook,et al.  Path planning for robotic manipulators with redundant degrees of freedom , 1991 .

[9]  I. Fluegge-Lotz,et al.  Minimum-fuel Attitude Control of a Rigid Body in Orbit by an Extended Method of Steepest-descent , 1966 .

[10]  Bernard Roth,et al.  On the Optimal Selection and Placement of Manipulators , 1985 .

[11]  David M. Auslander,et al.  Optimal Control of a Robot with Obstacles , 1984 .

[12]  Eduardo D. Sontag,et al.  Time-optimal control of manipulators , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[13]  Elke-Barbara Meier,et al.  An efficient algorithm for bang-bang control systems applied to a two-link manipulator , 1987 .

[14]  Allan Y. Lee.  Solving constrained minimum-time robot problems using the sequential gradient restoration algorithm , 1992 .

[15]  Yaobin Chen,et al.  A proof of the structure of the minimum-time control law of robotic manipulators using a Hamiltonian formulation , 1990, IEEE Trans. Robotics Autom..

[16]  Phillip J. McKerrow,et al.  Introduction to robotics , 1991 .

[17]  John M. Hollerbach,et al.  Planning a minimum-time trajectories for robot arms , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[18]  Kang G. Shin,et al.  Minimum-time control of robotic manipulators with geometric path constraints , 1985 .

[19]  V. T. Rajan.  Minimum time trajectory planning , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[20]  Eduardo Sontag,et al.  Remarks on the time-optimal control of two-link manipulators , 1985, 1985 24th IEEE Conference on Decision and Control.

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

[22]  Lino Guzzella,et al.  Time-optimal motions of robots in assembly tasks , 1985, 1985 24th IEEE Conference on Decision and Control.

[23]  S. Dubowsky,et al.  On the Optimal Control of Robotic Manipulators with Actuator Constraints , 1983, 1983 American Control Conference.

[24]  Y. Chen,et al.  On the structure of the minimum-time control law for multiple robot arms handling a common object , 1991 .

[25]  George M. Siouris,et al.  Applied Optimal Control: Optimization, Estimation, and Control , 1979, IEEE Transactions on Systems, Man, and Cybernetics.