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.