This paper presents an approach for learning motion planners that are accompanied with probabilistic guarantees of success on new environments that hold uniformly for any disturbance to the robot's dynamics within an admissible set. We achieve this by bringing together tools from generalization theory and robust control. First, we curate a library of motion primitives where the robustness of each primitive is characterized by an over-approximation of the forward reachable set, i.e., a "funnel". Then, we optimize probably approximately correct (PAC)-Bayes generalization bounds for training our planner to compose these primitives such that the entire funnels respect the problem specification. We demonstrate the ability of our approach to provide strong guarantees on two simulated examples: (i) navigation of an autonomous vehicle under external disturbances on a five-lane highway with multiple vehicles, and (ii) navigation of a drone across an obstacle field in the presence of wind disturbances.

翻译：本文为学习运动规划者提供了一种方法,在学习运动规划者的同时,还提供了在新环境中取得成功的概率保障,这些新环境在任何干扰机器人的动态时都统一存在一个可受理的一组。我们通过汇集一般化理论和强力控制的工具来实现这一点。首先,我们建立一个运动原始体图书馆,其中每个原始体的强力特征是过度接近前方可达标集,即“漏网 ” 。然后,我们可能优化了大致正确的(PAC)-Bayes一般化界限,以训练我们的规划者组成这些原始体,使整个漏斗都尊重问题规范。我们展示了我们的方法能够在两个模拟例子上提供强有力的保证:(一) 在多辆汽车的五线高速公路上,在外部动乱下驾驶一部自主车辆,以及(二) 在风扰动时驾驶无人驾驶无人驾驶无人驾驶飞机穿越障碍场。