Optimal dynamics of actuated kinematic chains. Part 2: Problem statements and computational aspects

A general method for generating optimal motions of actuated multibody systems is presented. A dynamics-based optimization technique is developed using the Pontryagin Maximum Principle. For the reasons stated in Part 1 of the paper, this powerful mathematical tool is associated with a Hamiltonian dynamic model for the mechanical system. In the present Part 2 of the paper, a unified approach is designed for dealing with unconstrained as well as constrained mechanical systems. In the latter case, kinematic loops are cut at appropriate joints or mechanical contacts in order to deal with open tree-like kinematic structures. Pontryaginʹs Maximum Principle makes it possible to account for related closure constraints together with interaction efforts at cut joints in a quite general and efficient way in stating and solving the dynamic optimization problem. The salient features of the method lies in considering interaction forces at cut joints as additional control variables, and dealing with closure (holonomic) constraints using a penalty method. A new solving strategy was developed for the final problem, making easier the search for guess solutions. Three numerical simulations demonstrate the effectiveness of the method.