Numerical methods for the optimal control of constrained mechanical systems

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Optimal control problems have many interesting applications in the field of multibody dynamics ranging from the energy efficient control of lightweight robots to the biomechanics of human motion. Provided that minimal coordinates can be found for the description of the multibody system, the equations of motion assume the form of ordinary differential equations which play the role of state equations in the optimal control problem. For this case well-established numerical methods can be applied to solve the optimal control problem. However, the use of minimal coordinates is confined to comparatively simple multibody systems with tree structure. The general approach to multibody dynamics relies on the use of redundant coordinates. Correspondingly, the state equations of the optimal control problem now assume the form of differential-algebraic equations. For this class of problems there is still great need for research, since the common approach does not guarantee that the correct necessary optimality conditions are solved. The goal of the present proposal is the development of new methods which resolve this shortcoming of existing methods.