Discrete Optimal Control of Interconnected Mechanical Systems

This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. A discrete optimal control problem is then formulated for this class of system on the phase spaces of the actuated and unactuated subsystems separately. Exploiting the left-trivialization of the cotangent bundle, and assuming the time-step of discrete evolution is small enough to exploit the diffeomorphism feature of the exponential map in a neighbourhood of the identity of the Lie group, that enables a mapping of the group variables to the Lie algebra, a variational approach is adopted to obtain the first order necessary conditions that characterise optimal trajectories. The proposed approach is then demonstrated on two benchmark underactuated systems through numerical experiments. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.