Energy efficient control for mechanical systems based on inherent dynamical structures

Many optimal control problems for mechanical systems include the computation of control policies that are optimal with respect to the energetic effort. In this contribution, we will demonstrate how to exploit inherent dynamical properties of the dynamical system to build up a motion planning framework that can in particular be used to compute good initial guesses for energy efficient solutions. This method is based on a motion planning library consisting of three types of trajectories: (1.) motions induced by the system´s symmetry, (2.) trajectories on (un)stable manifolds of the natural dynamics, and (3.) controlled maneuvers to sequence the so called motion primitives. We demonstrate our proposed optimal control method on the example of a double spherical pendulum.