Safe navigation in cluttered environments is an important challenge for autonomous systems. Robots navigating through obstacle ridden scenarios need to be able to navigate safely in the presence of obstacles, goals, and ego objects of varying geometries. In this work, reachable set representations of the robot's real-time capabilities in the state space can be utilized to capture safe navigation requirements. While neural radiance fields (NeRFs) are utilized to compute, store, and manipulate the volumetric representations of the obstacles, or ego vehicle, as needed. Constrained optimal control is employed to represent the resulting path planning problem, involving linear matrix inequality constraints. We present simulation results for path planning in the presence of numerous obstacles in two different scenarios. Safe navigation is demonstrated through using reachable sets in the corresponding constrained optimal control problems.

翻译：在杂乱环境中安全导航是自主系统面临的重要挑战。在布满障碍物的场景中穿梭的机器人需要能够针对不同几何形状的障碍物、目标及自车对象实现安全导航。本研究利用状态空间中机器人实时能力的可达集表示来捕捉安全导航需求，同时采用神经辐射场（NeRF）按需计算、存储和处理障碍物或自车车辆的体素表示。通过约束最优控制构建路径规划问题，该问题涉及线性矩阵不等式约束。我们在两种不同场景下展示了存在大量障碍物时的路径规划仿真结果，并通过在相应约束最优控制问题中应用可达集证明了安全导航的可行性。