On the optimality of Dubins paths across heterogeneous terrain

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URL:

https://hybrid.soe.ucsc.edu/files/preprints/23.pdf

Keywords:

hybrid systems

Abstract:

We derive optimality conditions for the paths of Dubins vehicle when the state space is given by the union of two patches with different vehicle constant forward velocity. We recast this problem as a hybrid optimal control problem and solve it using recent optimality principles for hybrid systems. Among the optimality conditions, we derive a ``refraction" law at the boundary of the patches which generalizes the so-called Snell's law of refraction in optics to the case of paths with bounded maximum curvature.

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