We present a two-lane path planning of autonomous vehicles in two-and-a-half-dimensional (2.5D) environments. Our method builds on collision-free two-dimensional (2D) path-planning techniques from our previous work, and extends these techniques to 2.5D by mapping a 2D path in the parameter space onto a terrain graph surface, as a curve on the surface in the object space. Based on this path on the terrain surface, we propose a novel method of designing cross slopes in high curvature regions of the path, such that vehicles need not slow down in these regions. Furthermore, we apply time-optimal control techniques developed in robotics to compute the minimal-time speed control along the specified path. Examples are provided to demonstrate the effectiveness of the proposed algorithm.
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