New repulsive potential functions with angle distributions for local path planning

This paper presents new repulsive potential functions (RPFs) for point robot path planning. In this scheme, the RPF for path planning has a different magnitude at each direction of a RPF based on the angle between a goal and an obstacle, unlike a conventional RPF in which the same magnitude at each direction is obtained. In doing so, the RPF attempts to overcome some of the typical problems that may arise with the conventional RPF In particular, this paper presents a set of analyses for designing potential functions to avoid local minima for a number of representative scenarios. Specifically, the following cases are addressed: (i) a non-reachable goal problem (a case in which the potential of the goal is overwhelmed by the potential of an obstacle), (ii) an obstacle collision problem (a case in which the potential of the obstacle is overwhelmed by the potential of the goal) and (iii) a narrow passage problem (a case in which the potential of the goal is overwhelmed by the potential of two obstacles). The proposed RPF scheme eliminates the non-feasible area for the three cases by the help of an angle-varying magnitude between a goal and an obstacle. The example results show that the proposed RPF scheme can effectively construct a path-planning system with the capability of reaching a goal and avoiding obstacles despite possible local minima.