Adjoint method for optimal control of multibody systems in the Hamiltonian setting

Abstract

This paper presents an efficient adjoint-based technique to numerically solve optimal control problems arising in holonomically-constrained multibody systems found in e.g. many robotic applications. A multibody system is described in terms of Hamilton’s canonical equations. A modification of the standard adjoint method, which introduces a set of augmented costate variables, is proposed to improve the quality of numerical solutions. A step-by-step algorithm is shown in the paper and the problem of computational efficiency is addressed shortly. Three numerical test cases are investigated and the applicability and validity of the proposed optimal control technique is demonstrated for open- and closed-loop kinematic chains including under- and overactuated systems. The collected results serve to show the potential of the proposed algorithm in solving optimal control problems.