NONLINEAR DYNAMIC MOTION OPTIMIZATION AND CONTROL OF MULTIBODY SYSTEMS

This paper suggests a general numerical method for control and off-lin e motion optimization of rigid multibody systems, using nonlinear dyna mic models. The models are numerically derived as ordinary differentia l equations for a minimal set of generalized coordinates. The dynamic equations and the solution trajectory are discretized in small interva ls (nodes), where robot motion is assumed to occur with constant gener alized coordinate acceleration. The algorithm is applied for adaptive control of many degree of freedom mechanical systems. The mathematical description of the problem for optimal motion planning is presented a s a nonlinear programming problem. The characteristics of motion and d iscretized generalized forces in every node are parameters of the opti mization problem. Since they are numerically defined, an arbitrary res ponse function can be evaluated numerically. Linearized motion functio ns and dynamic equations are treated as equality constraints for the p rogramming problem. Restrictions imposed on force and motion character istics, or on any functional dependence among them, are treated as ine quality constraints. The gradient of the response function, most often implicitly defined for the parameters, is computed by solving a linea r equation system obtained from partial derivatives of the equality co nstraints. The convergence of the algorithm is tested using a five deg ree of freedom redundant robot, achieving point-to-point time optimal motion.