Nonlinear Dynamic Motion Optimization and Control of Multibody Systems∗

Abstract

Abstract This paper suggests a general numerical method for control and off-line motion optimization of rigid multibody systems, using nonlinear dynamic models. The models are numerically derived as ordinary differential equations for a minimal set of generalized coordinates. The dynamic equations and the solution trajectory are discretized in small intervals (nodes), where robot motion is assumed to occur with constant generalized 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 as a nonlinear programming problem. The characteristics of motion and discretized generalized forces in every node are parameters of the optimization problem. Since they are numerically defined, an arbitrary response function can be evaluated numerically. Linearized motion functions and dynamic equations are treated as equality constraints for the programming problem. Restrictions imposed on force and motion characteristics, or on any functional dependence among them, are treated as inequality constraints. The gradient of the response function, most often implicitly defined for the parameters, is computed by solving a linear equation system obtained from partial derivatives of the equality constraints. The convergence of the algorithm is tested using a five degree of freedom redundant robot, achieving point-to-point time optimal motion