We consider time-optimal motion planning for dynamical systems that are translation-invariant, a property that holds for many mobile robots, such as differential-drives, cars, airplanes, and multirotors. Our key insight is that we can extend graph-search algorithms to the continuous case when used symbiotically with optimization. For the graph search, we introduce discontinuity-bounded A* (db-A*), a generalization of the A* algorithm that uses concepts and data structures from sampling-based planners. Db-A* reuses short trajectories, so-called motion primitives, as edges and allows a maximum user-specified discontinuity at the vertices. These trajectories are locally repaired with trajectory optimization, which also provides new improved motion primitives. Our novel kinodynamic motion planner, kMP-db-A*, has almost surely asymptotic optimal behavior and computes near-optimal solutions quickly. For our empirical validation, we provide the first benchmark that compares search-, sampling-, and optimization-based time-optimal motion planning on multiple dynamical systems in different settings. Compared to the baselines, kMP-db-A* consistently solves more problem instances, finds lower-cost initial solutions, and converges more quickly.
翻译:我们考虑对具有翻译变量的动态系统进行时间最佳运动规划,这是许多移动机器人(如差异驱动器、汽车、飞机和多色机器人)所持有的属性。我们的关键洞察力是,我们可以将图形搜索算法扩展至使用共生优化时的连续情况。在图形搜索中,我们引入了受不连续限制的 A* (db-A*),一种使用基于抽样的规划者的概念和数据结构的A* 算法的概括化。Db-A* 重新利用短轨,即所谓的运动原始,作为边缘,并允许在顶部最大限度地保持用户指定的不连续状态。这些轨迹是用轨迹优化在当地修复的,也提供了新的改良运动原始体。我们的新动动动动力运动规划器, kMP- db-A* 几乎可以肯定地使用不严谨的最佳行为,并快速地对近最佳的解决方案进行计算。对于我们的经验验证,我们提供了第一个基准,将搜索、抽样和优化的原始原始原始, 优化的基点和最优化的基点定位的基点 — 更稳定的基点的基点比的基点的基点,在不同的基点上找到更低的基点上, 的基点的基点和基点的基点的基点的基点的基点。