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On the Optimality of Dubins Paths across Heterogeneous Terrain

机译:跨非均质地形的杜宾斯路径的最优性

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摘要

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.
机译:当状态空间被分成两个具有不同车辆前进速度的斑块时,我们推导了杜宾斯车辆路径的最优条件。我们将此问题重塑为混合最优控制问题,并使用混合系统的最优性原理对其进行求解。在最佳条件中,我们在斑块的边界处得出“折射”定律,将“光学斯涅尔折射定律”推广到最大曲率有界的情况。

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