Forward and Inverse Optimal Control of Bipedal Running

This paper discusses forward and inverse optimal control problems for bipedal human-like running, with a focus on inverse optimal control. The (forward) optimal control problem looks for the optimal solution for a problem formulation, i.e. given objective function and given dynamic constraints. The inverse optimal control problem is more challenging and consists in determining the objective function and potentially unknown parts in the dynamic model that best reproduce a solution that is known from measurements. Periodic running motions are modeled as hybrid dynamic models with multiple phases and discontinuities, based on a three-dimensional multibody system model with 25 degrees of freedom.We investigate a recorded running motion on a treadmill at 10 km/h running speed and identify the best possible objective function based on some hypotheses for potential contributions to this objective function. For this, we apply a previously developed inverse optimal control technique which uses a combination of a direct multiple shooting method and a derivative-free optimization technique, and we demonstrate here that it also works for problems of the given complexity.