Optimal Control on Stable Manifolds for a Double Pendulum

Optimal control problems for mechanical systems often arise in technical applications, e.g. in the computation of energy efficient or time optimal steering maneuvers between operation points. In this contribution, we propose a control strategy for mechanical systems that includes uncontrolled trajectories on (un)stable manifolds in a sequence together with short control maneuvers to design a feedforward control. In particular, we present optimal swing-up solutions for a double pendulum that are based on trajectories on the stable manifold of the pendulum's upper equilibrium. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)