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

Abstract

A path planning method is presented based on non-autonomous dynamicmodeling of open-loops in articulated systems. It is assumed that one part ofthe mechanical system is submitted to specified motions laws, while movements ofthe complementary part are free. Thus, motion optimization is related to freejoint movements but it is achieved on the basis of the dynamic model of thewhole mechanical system. This approach introduces a non-autonomous stateequation of a special type in the sense that it can not only depend on therunning time but also on the unknown travelling time. The cost function to beminimized involves the travelling time and the actuating inputs. Optimization isachieved by applying the Pontryagin Maximum Principle which yields a newoptimality condition concerning the travelling time dependency of the statedproblem. Two simulation examples are presented. The first one shows how thedeveloped technique makes possible both the reducing and mastering the dynamiccomplexity of a four degrees of freedom-vertical manipulator. Set at fourdegrees of freedom, the second one deals with a redundant planar manipulatorcharacterized by a mobile base that is submitted to a specified drivingmotion.