Computing kinodynamically feasible motion plans and repairing them on-the-fly as the environment changes is a challenging, yet relevant problem in robot-navigation. We propose a novel online single-query sampling-based motion re-planning algorithm - PiP-X, using finite-time invariant sets - funnels. We combine concepts from sampling-based methods, nonlinear systems analysis and control theory to create a single framework that enables feedback motion re-planning for any general nonlinear dynamical system in dynamic workspaces. A volumetric funnel-graph is constructed using sampling-based methods, and an optimal funnel-path from robot configuration to a desired goal region is then determined by computing the shortest-path subtree in it. Analysing and formally quantifying the stability of trajectories using Lyapunov level-set theory ensures kinodynamic feasibility and guaranteed set-invariance of the solution-paths. The use of incremental search techniques and a pre-computed library of motion-primitives ensure that our method can be used for quick online rewiring of controllable motion plans in densely cluttered and dynamic environments. We represent traversability and sequencibility of trajectories together in the form of an augmented directed-graph, helping us leverage discrete graph-based replanning algorithms to efficiently recompute feasible and controllable motion plans that are volumetric in nature. We validate our approach on a simulated 6DOF quadrotor platform in a variety of scenarios within a maze and random forest environment. From repeated experiments, we analyse the performance in terms of algorithm-success and length of traversed-trajectory.

翻译：计算机动态可行运动规划并在环境变化时实时修复该规划是机器人导航中一个具有挑战性且实际意义重大的问题。我们提出一种新颖的在线单查询采样运动重规划算法——PiP-X，该方法采用有限时间不变集（漏斗）。我们融合了基于采样的方法、非线性系统分析与控制理论等概念，构建了一个统一框架，能够为动态工作空间中的任意一般非线性动力学系统实现反馈运动重规划。通过基于采样的方法构建体积漏斗图，并计算其中的最短路径子树，从而确定从机器人构型到期望目标区域的最优漏斗路径。利用李雅普诺夫水平集理论对轨迹的稳定性进行分析与形式化量化，可确保解的动力学可行性与集合不变性。增量搜索技术与预计算运动基元库的应用，使得该方法能够在密集杂乱且动态的环境中快速实现可控运动规划的在线重连。我们将轨迹的可穿越性与可序列性共同表示为增广有向图的形式，从而利用基于离散图的重规划算法高效地重新计算可行的、可控的且具有体积属性的运动规划。我们在一个模拟的6自由度四旋翼平台上，于迷宫与随机森林环境中的多种场景下验证了该方法。通过重复实验，我们从算法成功率和穿越轨迹长度两方面对其性能进行了分析。