Transformation of Output Constraints in Optimal Control Applied to a Double Pendulum on a Cart

This paper describes a constraint transformation technique for optimal control problems (OCP) with nonlinear single-input single-output (SISO) systems subject to output constraints. An input-output transformation and saturation functions are used to transform the system dynamics into a new unconstrained representation. This method allows to reformulate the original OCP into an unconstrained counterpart. The transformation technique is applied to a double pendulum on a cart in order to compute optimal trajectories for a multi-stage transition scenario. Simulation as well as experimental results with an additional feedback control demonstrate the applicability of the presented method.