A Hierarchical Path Planner Based on Even-order Hyperelliptic Orbital Limit-Cycles

This paper proposes a Hierarchical Path Planner (HPP) based on Even-order Hyperelliptic Orbital Limit-Cycles (EHOLC). Traditional Elliptic Orbital Limit-Cycles (EOLC) have been widely studied. However, in structured rectangular obstacle environments, ellipses have a higher porosity when enveloping rectangles, resulting in lower environmental adaptability. Therefore, EHOLC is introduced, and the hyperelliptic equation order of obstacles is determined based on a set porosity. Then, the differential equation of the EHOLC is established, and the trajectory is solved. Finally, a hierarchical path planner is proposed, which selects obstacle avoidance controllers and target reaching controllers according to the environment map to solve the entire path. Simulation experiments show that compared with traditional EOLC, the EHOLC-based HPP has higher map space utilization, shorter path planning length, and maintains flexibility, smoothness, and safety.