Resolved-acceleration control of mechanical manipulators

Abstract

Position control of a manipulator involves the practical problem of solving for the correct input torques to apply to the joints for a set of specified positions, velocities, and accelerations. Since the manipulator is a nonlinear system whose joints are highly coupled, it is very difficult to control. This paper presents a technique which adopts the idea of "inverse problem" and extends the results of "resolved-motion-rate" controls. The method deals directly with the position and orientation of the hand. It differs from others in that accelerations are specified and that all the feedback control is done at the hand level. The control algorithm is shown to be asymptotically convergent. A PDP 11/45 computer is used as part of a controller which computes the input torques/forces at each sampling period for the control system using the Newton-Euler formulation of equations of motion. The program is written in floating point assembly language, and has an average execution time of less than 11.5 ms for a Stanford manipulator. This makes a sampling frequency of 87 Hz possible. The controller is verified by an example which includes a simulated manipulator.