Optimal path planning of manipulatory systems subjected tonon-autonomous motion laws

A path planning method is presented based on non-autonomous dynamic modeling of open-loops in articulated systems. It is assumed that one part of the mechanical system is submitted to specified motions laws, while movements of the complementary part are free. Thus, motion optimization is related to free joint movements but it is achieved on the basis of the dynamic model of the whole mechanical system. This approach introduces a non-autonomous state equation of a special type in the sense that it can not only depend on the running time but also on the unknown travelling time. The cost function to be minimized involves the travelling time and the actuating inputs. Optimization is achieved by applying the Pontryagin Maximum Principle which yields a new optimality condition concerning the travelling time dependency of the stated problem. Two simulation examples are presented. The first one shows how the developed technique makes possible both the reducing and mastering the dynamic complexity of a four degrees of freedom-vertical manipulator. Set at four degrees of freedom, the second one deals with a redundant planar manipulator characterized by a mobile base that is submitted to a specified driving motion.