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arXiv · 0912.2033

Optimal Control of Underactuated Mechanical Systems: A Geometric Approach

L. Colombo·D. Martin de Diego·M. Zuccalli
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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.

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L. Colombo, D. Martin de Diego, M. Zuccalli. 2009-12-10. Optimal Control of Underactuated Mechanical Systems: A Geometric Approach. https://doi.org/10.1063/1.3456158

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