Computation and Implementation of Digital Time-Optimal Feedback Controllers for an Industrial X-Y Robot subjected to Path, Torque, and Velocity Constraints

Abstract

For an industrial X-Y robot, in which the links are subjected to torque and velocity constraints, the time-optimal control prob lem is solved where the robot motion is constrained to follow an arbitrary path. A numerical procedure to compute the solu tion is presented and demonstrated. The solution consists of a continuous-time state trajectory and open-loop control. Because the X-Y robot is controlled by a digital computer, a recently developed numerical procedure to compute optimal tracking digital controllers is applied to the solution to arrive at an implementable digital time-optimal feedback controller that accounts for modeling errors as well. Experimental results ob tained after implementation of the digital time-optimal feedback controllers are presented for two paths. The robot dynamics include both viscous and Coulomb friction. The extension of the solution and numerical procedures to general rigid ma nipulators, including both viscous and Coulomb friction, is straightforward.