This paper focuses on spatial time-optimal motion planning, a generalization of the exact time-optimal path following problem that allows the system to plan within a predefined space. In contrast to state-of-the-art methods, we drop the assumption that a collision-free geometric reference is given. Instead, we present a two-stage motion planning method that solely relies on a goal location and a geometric representation of the environment to compute a time-optimal trajectory that is compliant with system dynamics and constraints. To do so, the proposed scheme first computes an obstacle-free Pythagorean Hodograph parametric spline, and second solves a spatially reformulated minimum-time optimization problem. The spline obtained in the first stage is not a geometric reference, but an extension of the environment representation, and thus, time-optimality of the solution is guaranteed. The efficacy of the proposed approach is benchmarked by a known planar example and validated in a more complex spatial system, illustrating its versatility and applicability.

翻译：本文聚焦于空间时间最优运动规划，这是精确时间最优路径跟踪问题的一种泛化形式，允许系统在预定义空间内进行规划。与现有先进方法不同，我们摒弃了存在无碰撞几何参考路径的假设，转而提出一种两阶段运动规划方法，该方法仅依赖目标位置和环境的几何表示，即可计算出满足系统动力学与约束的时间最优轨迹。为此，所提出的方案首先计算一条无碰撞的Pythagorean Hodograph参数样条曲线，随后求解一个空间重表述的最小时间优化问题。第一阶段获得的样条曲线并非几何参考路径，而是环境表示的扩展，从而保证了解的时间最优性。通过一个已知的二维平面算例验证该方法的有效性，并在更复杂的空间系统中进行测试，充分展示了其通用性与适用性。