Efficient solution method based on inverse dynamics for optimal control problems of rigid body systems

TL;DR

This paper introduces an efficient inverse dynamics-based method for solving optimal control problems in rigid-body systems, significantly reducing computational costs and improving robustness compared to forward dynamics approaches.

Contribution

The paper presents a novel inverse dynamics approach combined with multiple-shooting and condensing techniques, enhancing efficiency and robustness in optimal control computations for rigid-body systems.

Findings

Reduces computational cost using recursive Newton-Euler algorithm

Increases sparsity of the Hessian, lowering Riccati recursion costs

Outperforms forward dynamics methods in speed and robustness

Abstract

We propose an efficient way of solving optimal control problems for rigid-body systems on the basis of inverse dynamics and the multiple-shooting method. We treat all variables, including the state, acceleration, and control input torques, as optimization variables and treat the inverse dynamics as an equality constraint. We eliminate the update of the control input torques from the linear equation of Newton's method by applying condensing for inverse dynamics. The size of the resultant linear equation is the same as that of the multiple-shooting method based on forward dynamics except for the variables related to the passive joints and contacts. Compared with the conventional methods based on forward dynamics, the proposed method reduces the computational cost of the dynamics and their sensitivities by utilizing the recursive Newton-Euler algorithm (RNEA) and its partial derivatives. In addition, it increases the sparsity of the Hessian of the Karush-Kuhn-Tucker conditions, which reduces the computational cost, e.g., of Riccati recursion. Numerical experiments show that the proposed method outperforms state-of-the-art implementations of differential dynamic programming based on forward dynamics in terms of computational time and numerical robustness.