On the Optimal Control of Robotic Manipulators with Actuator Constraints

High speed motions and increased productivity are linked in the industrial applications of many robotic manipulators, yet the speeds which can be achieved by a manipulator during a given task are limited by a number of factors. The dynamic properties of a manipulator and its actuator limitations and characteristics are probably the most important factors. This paper presents an optimal control policy which results in minimum-time motion for a robotic manipulator along any predetermined path in three dimensional space. The technique permits the manipulator user to specify completely the path of the arm; therefore the method does not interfere with the manipulator´s industrial utility. The method accounts for the nonlinear dynamics of articulated manipulators with rigid links and limitations on the actuators. These limitations may be arbitrary functions of the manipulator joint positions and velocities. The algorithm developed for obtaining the optimal control is computationally simple, and it does not require the extensive iterations often found in optimal control strategies. Examples are presented of the method´s application.