Abstract
We derive optimality conditions for the paths of a Dubins vehicle when the state space is partitioned into two patches with different vehicle’s forward velocity. We recast this problem as a hybrid optimal control problem and solve it using 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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Sanfelice, R.G., Frazzoli, E. (2008). On the Optimality of Dubins Paths across Heterogeneous Terrain. In: Egerstedt, M., Mishra, B. (eds) Hybrid Systems: Computation and Control. HSCC 2008. Lecture Notes in Computer Science, vol 4981. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78929-1_33
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DOI: https://doi.org/10.1007/978-3-540-78929-1_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78928-4
Online ISBN: 978-3-540-78929-1
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