Marden-Based Homotopic Enclosed Safe Motion Corridor Generation for UAV Navigation in Complex Environments

This paper proposes a novel hierarchical methodology to planning safe UAV trajectories in complex environments. We start by improving a canonical hybrid A* in relation to high memory requirements, performance degradation, and the low efficiency customarily observed in the initial global trajectory suggested by the planner. Then, the Marden theorem is applied -for the first time in local path planning -to generate continuous, non-intersecting, enclosed, and safe flight corridors, termed homotopic enclosed safe motion corridors (HESMCs) hereafter. This is efficiently realized through a series of unique ellipsoids along the initial route. Meanwhile, the optimized motion trajectory along the corridors is built by considering two waypoints and prescribed performance functions. The resolved path is safe and complete, with a comprehensive Lyapunov stability analysis included to ensure accurate and efficient trajectory tracking. The simulation and physical tests demonstrate the superiority of our proposed planner over existing state-of-the-art methods, with consistent and significant improvements in processing time and guaranteed completeness. Note to Practitioners-The authors perceived the contribution of the manuscript of particular relevance to users of UAVs seeking advanced safety in their guidance and navigational solutions, offering a blend of theoretical innovation and practical applicability. The work introduces a distinct hierarchical motion planner specifically designed to enhance safety and reliability in UAV navigation. Key to this is the development of an improved hybrid A* algorithm for global planning, which effectively tackles practical issues such as high memory consumption and performance degradation. A significant theoretical contribution is the application of the Marden theorem in local optimization. This facilitates the generation of homotopic enclosed motion corridors using unique safe boundary ellipsoids, thus reducing navigation complexity and the risk of failure during task execution. Additionally, the proposed scheme emphasizes the generation of motion trajectories considering position errors and prescribed performance functions, supplemented by a thorough Lyapunov stability analysis. Looking ahead, we aim to extend the proposed scheme in the context of UAV swarms for more efficient navigation in complex environments.