Optimal Control of Underactuated Mechanical Systems: A Geometric Approach

Details Optimal Control of Underactuated Mechanical Systems: A Geometric Approach Optimal Control of Underactuated Mechanical Systems: A Geometric Approach

2009-12-10

arxiv.org/abs/0912.2033v1

Physics

Mathematical Physics

20 pages, 2 figures

Scientific paper

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.

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