Suboptimal control of industrial manipulators with a weighted minimum time-fuel criterion

Abstract

Even if a manipulator does not have to follow a prespecified path (i.e. a geometric path and a velocity schedule), due to the complexity and nonlinearity of the manipulator dynamics, control of manipulators has been conventionally divided into two sub-problems, namely path planning and path tracking, which are then separately and independently solved. This may result in mathematically tractable solutions but can not offer a solution that utilizes manipulators' maximum capabilities (e.g. operating them at their maximum speed). To combat this problem, we have developed a suboptimal method for controlling manipulators that provides improved performance in both their operating speed and use of energy. The nonlinearity and the joint couplings in the manipulator dynamics-- a major hurdle in the design of robot control--are handled by a new concept of averaging the dynamics at each sampling interval. With the averaged dynamics, we have derived a feedback controller which (i) has a simple structure allowing for on-line implementation with inexpensive microprocessors, and (ii) offers a near minimum time-fuel(NMTF) solution, thus enabling manipulators to perform nearly up to their maximum capacity and efficiency. As a demonstrative example, we have applied the method to control the Unimation PUMA 600 series manipulator and simulated its performance on a DEC VAX-11/780. The simulation results agree with the expected high performance nature of the control method.