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NUMERICAL TRAJECTORY OPTIMIZATION FOR STOCHASTIC MECHANICAL SYSTEMS
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DOI：10.1137/17M116272X.png)
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Abstract
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In this paper we develop a novel optimal control framework for uncertain mechanical systems. Our work extends differential dynamic programming and handles uncertainty through generalized polynomial chaos (gPC) theory. The obtained scheme is able to influence the probabilistic evolution of nonlinear systems with stochastic model parameters. Its scalable, fast-converging nature plays a key role when dealing with gPC expansions of high-dimensional problems. Based on Lagrangian principles, we also prove that variational integrators can be designed to properly propagate and linearize gPC representations in discrete time. This observation allows us to further improve the efficiency of our trajectory-optimization methodology. Numerical simulations support the aforementioned arguments, while demonstrating the benefits of our approach over standard optimization methods. Last but not least, a complete analysis is provided that studies the properties of the proposed algorithm.
Keywords:
trajectory optimization
polynomial chaos
differential dynamic programming
discrete mechanics
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