A comparative study of geometric path planning methods for a mobile robot: Potential field and voronoi diagrams

In this paper, two real-time path-planning algorithms that provide an optimal path for autonomous robots with static obstacles avoidance are studied and compared. The proposed planning algorithms compute a path based on geometric strategies and visual identification of the environment. Is well known that traditional geometric strategies have convergence problems, local minima and definition of non-optimal paths. We propose strategies that modify the original algorithms, resulting in new strategies free of convergence problems and with optimal paths. The first algorithm corresponds to the artificial potential field method modified by using dummy loads. We propose a radar strategy, with this concept we simulated dummy loads. These dummy loads are similar to the robot load, at specific points of the environment. These points are determined iteratively by the robot´s position and the target position, and are responsible for describing the navigation path. The second proposed algorithm corresponds to the Voronoi diagrams, but including Delaunay triangulation to avoid routes that could block the robot. This strategy performs a mesh that determines the Voronoi diagram of the environment, and Delaunay triangulation is applied to determine the midpoints, and the best options of mobile navigation. Some experiments with differential drive robots and several simulations are conducted to show the effectiveness and performance of both strategies.