Efficient Solution Method Based on Inverse Dynamics of Optimal Control Problems for Fixed-Based Rigid-Body Systems

Abstract

We propose an efficient solution method of finite horizon optimal control problems (FHOCPs) for fixed-based rigid-body systems based on inverse dynamics. Our method can reduce the computational cost compared with the conventional FHOCP based on forward dynamics. We reformulate the FHOCP for the rigid-body systems by utilizing the generalized acceleration as the decision variables and inverse dynamics as the equality constraint. We derive the necessary conditions of the optimal control, namely, the optimality conditions, and formulate a two-point boundary-value problem that can be solved efficiently by using the recursive Newton Euler algorithm (RNEA) and the partial derivatives of RNEA. The results of the several numerical experiments on nonlinear model predictive control using the proposed formulation demonstrate the effectiveness of our approach.