Motion planning using Maxwell´s equations

This paper presents a new formulation of the artificial potential approach to the motion planning problem for a mobile robot in a global environment. To model the potential (magnetic) field by Maxwell\´s Equations that completely eliminate the local minima problem, which is exhibited in most artificial potential methods, such as Harmonic functions based methods. However, the proposed model is superior to the Harmonic one because it is easily extendable to 3D, the time dimension is modeled by default which means it is a suitable model for time-varying environments, computations are less and hence faster, and most important it eliminates the "flat-regions" problem. In this work, electrical currents are assumed to be floating in a cluttered environment with obstacles. The obstacles are assigned zero conductivity whereas the goal point is assigned the highest electrical conductivity. The magnetic field induced by the electric currents is used to find a free path between the start and goal points. Simulation results reflects the validity and the potential of the proposed model.