Path planning by fractional differentiation

Abstract

In path planning design, potential fields can introduce force constraints to ensure curvature continuity of trajectories and thus facilitate path-tracking design. The parametric thrift of fractional potentials permits smooth variations of the potential in function of the distance to obstacles without requiring design of geometric charge distribution. In the approach we use, the fractional order of differentiation is the risk coefficient associated to obstacles. A convex danger map towards a target and a convex geodesic distance map are defined. Real-time computation can also lead to the shortest minimum danger trajectory, or to the least dangerous of minimum length trajectories.