Optimal motion synthesis -: Dynamic modelling and numerical solving aspects

A general approach for generating optimal movements of actuated multi-jointed systems is presented. The method is based on the implementation of the Pontryagin Maximum Principle (PMP) used as a mathematical optimization tool. It applies to mechanical systems with kinematic tree-like topology such as serial robots, walking machines, and articulated biosystems. Emphasis is put on the choice of an appropriate dynamic model of the multibody system, together with the choice of relevant performance criteria to be minimized for generating the optimal motion. It is shown that the Hamiltonian formalism is perfectly suitable to deal with the optimization problem using the PMP. On the other hand, prominence is given to performance criteria ensuring soft and efficient functioning of the articulated systems. Two computing techniques for solving the optimization problem are presented. Three numerical simulations demonstrate the applicability of the method.