Simplification of robot dynamic model based on system performance

The dynamic performance of a robot manipulator is directly dependent on the efficiency of the controller and the dynamic model of the robot. This paper addresses the fundamental issue of how much manipulator dynamics information should be included in the manipulator dynamic model for control such that the manipulator will achieve the desired system performance under a proportional-plus-derivatlve control scheme. An efficient minimax simplification scheme has been developed which automatically generates simplified closed-form manipulator motion equations in symbolic form while maintaining the desired manipulator system performance under a proportional-plus-derivative controller. The scheme involves the identification and selection of basis functions that represent the dynamic coefficients in the dynamic model. These basis functions consist of a linear combination of the product terms of sinusoidal and polynomial functions of the generalized coordinates and form a Chebyshev set on the workspace of the manipulator. A multi-layered decision scheme is developed for selecting significant basis terms in each layer for each dynamic coefficient. The linear combination of these significant basis terms is then utilized to construct each simplified dynamic coefficient based on the minimax approximation technique. A verification of the proposed scheme on a Stanford robot arm is included for discussion.