Path Planning Using the Newtonian Potential

Potential functions are used to represent the topological structure of free space in solving path planning problems because of the simplicity in the free space representation and the guidance provided by the negative gradient of the potential field in the form of repulsive force. In this paper, Newtonian potential function is used to represent polygonal objects and obstacles. The closedform expression of this potential field as well as some other gradient-related quantities are derived. Such results not only eliminate the problems associated with the discretization of the object and obstacles in evaluating the risk of collision but also make the search for the optimal object configurations efficient. The object skeleton, a shape description of the moving object, is introduced to guide the moving object through narrow regions while the above search is done at different stages. The free space can then be divided by the narrow regions where the above path planning takes place a very simple free space decomposition scheme. Successful global strategies are developed to connect the above local plans into a safe and smooth global path.