Weyl fractional potential in path planning
Pierre Melchior, B. Orsoni, A. Oustaloup · 2001
In path planning design, potential fields can introduce force constraints to ensure curvature continuity of trajectories to facilitate path tracking design. The parametric thrift of fractional potentials permits continuous variation without modification of the geometric distribution of charge. We define here a normalized Weyl fractional potential field which allows continuous passage between these two charge distributions. The Coulombian potential of an isolated charge and an infinite segment are included in Weyl's formalism. Variation of the fractional order generates smooth variation of potential, without requiring design of geometric charge distribution. An A* algorithm is defined using fractional potentials in its evaluation function. A weighting factor permits smooth passage from minimum-length to minimum-energy trajectories.