This paper presents a novel feedback motion planning method for mobile robot navigation in 3D uneven terrains. We take advantage of the \textit{supervoxel} representation of point clouds, which enables a compact connectivity graph of traversable regions on the point cloud maps. Given this graph of traversable areas, our approach navigates the robot to any reachable goal pose using a control Lyapunov function (cLf) and a navigation function. The cLf ensures the kinodynamic feasibility and target convergence of the generated motion plans, while the navigation function optimizes the resulting feedback motion plans. We carried out navigation experiments in real and simulated 3D uneven terrains. In all circumstances, the experimental findings show that our approach performs superior to the baselines, proving the approach's efficiency and adaptability to navigate a robot in challenging uneven 3D terrains. The proposed method can also navigate a robot with a particular objective, e.g., shortest-distance or least-inclined plan. We compared our approach to well-established sampling-based motion planners in which our method outperformed all other planners in terms of execution time and resulting path length. Finally, we provide an open-source implementation of the proposed method to benefit the robotics community.

翻译：摘要：本文提出一种新颖的反馈运动规划方法，用于移动机器人在三维非平坦地形中的导航。我们利用点云的**超体素**表示，在点云地图上的可通行区域中构建紧凑的连通图。基于该可通行区域图，我们的方法通过控制李雅普诺夫函数（cLf）和导航函数将机器人导航至任何可达目标位姿。cLf确保所生成运动规划的动力学可行性与目标收敛性，而导航函数则优化最终的反馈运动规划结果。我们在真实与仿真的三维非平坦地形中开展了导航实验。实验结果表明，在所有场景下，我们的方法均优于基线方法，证明了该方法在复杂非平坦三维地形中导航机器人的高效性与适应性。所提方法还能根据特定目标（如最短路径或最小倾斜路径）进行导航。我们将方法与成熟的基于采样的运动规划器进行对比，结果表明本方法在执行时间和路径长度上均优于所有其他规划器。最后，我们开源了所提方法的实现代码，以惠及机器人社区。