Local path planning using a new artificial potential function composition and its analytical design guidelines

This paper presents a new framework for path planning based on artificial potential functions (APFs). In this scheme, the APFs for path planning have a multiplicative and additive composition between APFs for goal destination and APFs for obstacle avoidance, unlike conventional composition where the APF for obstacle avoidance is added to the APF for goal destination. In particular, this paper presents a set of analytical guidelines for designing potential functions to avoid local minima for a number of representative scenarios based on the proposed framework for path planning. 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 example results for each case show that the proposed scheme can effectively construct a path-planning system with the capability of reaching a goal and avoiding obstacles despite possible local minima.