Path optimization for terrestrial robots using Homotopy Path Planning Method

The path planning method is an important element in the architecture of all mobile robots with certain degree of autonomy. An appropriate path planning method provides the robot the ability to move in a previously known environment while avoiding collisions with obstacles along the way. Additionally, this method should generate optimal trajectories from one point to another. In this work the optimal path is defined as the shortest one. Path planning is not an easy task, some algorithms and methods have been developed for solving this problem, however, its success is not guaranteed. On the other hand, Homotopy Path Planning Method (HPPM) is a new tool used to find collision-free paths, this takes the properties of the Homotopy Continuation Methods (HCM) to find a successful path. However, the path found by this method is not the optimal. In this work, a path planning method for a terrestrial mobile robot based on HPPM and Spherical Algorithm (SA) is presented. Furthermore, a new strategy able to obtain the optimal path is proposed. Finally, simulation results for several environment maps with hundreds of circular obstacles are shown.