Mobile device path planning basing on the fractional potential

Abstract

The aim of the paper is to develop new quick and safe algorithms used for mobile device path planning [1,2,6,7,8,10,13,19]. The path should lead the device to some predefined target without striking the obstacles. In the proposed algorithms, applying fractional-calculus [12,14-18,22] where the frac- . tional-order differences [17,18] are defined one evaluates the generalised fractional potential [3,5,11,20,21] defining the level of an obstacle danger. Autonomous mobile devices equipped with safe paths creation abilities are valuable in different real-life situations. One can mention catastrophe areas with different types of obstacles of different obstacle danger. Applying the fractional calculus with mentioned earlier integrals of any, fractional orders one can create 3D space with better indication of the danger zones. Next one defines an optimal, safe path.[...]