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

Even if a manipulator does not have to follow a prespecified path (i.e., a time history of position and velocity) due to the complexity and nonlinearity of the manipulator dynamics, control of manipulators has been conventionally divided into two subproblems, namely path planning and path tracking, which are then separately and independently solved. This may result in mathematically tractable solutions but cannot 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 has a simple structure allowing for on-line implementation with inexpensive mini- or microcomputers, and offers a near minimum time-fuel (NMTF) solution, thus enabling manipulators to perform nearly up to their maximum capability and efficiency. As a demonstrative example, we have simulated the proposed control method with a dynamic model of the Unimation PUMA 600 series manipulator on a DEC VAX-11/780. The simulation results agree with the expected high performance nature of the control method.