Discrete Optimal Control of Interconnected Mechanical Systems

TL;DR

This paper develops variational integrators and formulates a discrete optimal control problem for interconnected underactuated mechanical systems, providing a systematic way to compute optimal trajectories with numerical validation.

Contribution

It introduces a novel variational integrator-based framework for discrete optimal control of interconnected underactuated mechanical systems.

Findings

Successful application to benchmark systems

Derivation of necessary optimality conditions

Numerical simulations validate the approach

Abstract

This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and subsequently solved using variational principles again, to obtain necessary conditions that characterize optimal trajectories. The proposed approach is demonstrated on benchmark underactuated systems and accompanied by numerical simulations.