Optimal Control of Underactuated Mechanical Systems: A Geometric Approach

Abstract

In this paper, we consider a geometric formalism for optimal control of underactuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order constraints. We study a regular case where it is possible to establish a symplectic framework and, as a consequence, to obtain a unique vector field determining the dynamics of the optimal control problem. These developments will allow us to develop a new class of geometric integrators based on discrete variational calculus.

20 pages, 2 figures

References in corpus (3)

• Multisymplectic geometry, variational integrators, and nonlinear PDEs
• Geometric Approach to Pontryagin's Maximum Principle
• Skinner-Rusk Unified Formalism for Optimal Control Systems and Applications

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• Regularity properties of fiber derivatives associated with higher-order mechanical systems
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• Skinner-Rusk formalism for k-contact systems