Optimal Motion Synthesis – Dynamic Modelling and Numerical Solving Aspects

A general approach for generating optimal movements of actuatedmulti-jointed systems is presented. The method is based on theimplementation of the Pontryagin Maximum Principle (PMP) used as amathematical optimization tool. It applies to mechanical systems withkinematic tree-like topology such as serial robots, walking machines,and articulated biosystems. Emphasis is put on the choice of anappropriate dynamic model of the multibody system, together with thechoice of relevant performance criteria to be minimized for generatingthe optimal motion. It is shown that the Hamiltonian formalism isperfectly suitable to deal with the optimization problem using the PMP.On the other hand, prominence is given to performance criteria ensuringsoft and efficient functioning of the articulated systems. Two computingtechniques for solving the optimization problem are presented. Threenumerical simulations demonstrate the applicability of the method.