Optimal control of constrained mechanical systems in redundant coordinates: Formulation and structure-preserving discretization

This work deals with optimal control problems for constrained mechanical systems whose motion is governed by differential algebraic equations (DAEs). Both index-3 DAEs and stabilized index-2 DAEs are considered. Two alternative formulations of the optimal control problem are compared to each other. It is shown that symmetries of the optimal control problem lead to the conservation of generalized momentum maps. These generalized momentum maps are related to quadratic invariants of the optimal control problem. A direct discretization approach is newly proposed which is (i) capable to conserve the quadratic invariants, and (ii) equivalent to the indirect approach to the optimal control problem. Numerical examples are presented to access the properties of the newly developed schemes.