An ISS based solution to avoid local minima in the Potential Field method

This work solves the obstacle avoidance problem extending the Potential Field (PF) method for a mobile robot. The usual definition of the PF has been modified to have a field which is continuous everywhere. It is shown that the system has an attracting equilibrium at the target point, repelling equilibriums in the centers of the obstacles and saddle points on the borders. Those unstable equilibriums are avoided capitalizing on the established Input-to-State Stability (ISS) property of this multi-stable system. To escape a local minima this work makes the most of ISS property that is not lost for perturbations. And for small properly designed disturbances the global attractivity of the target point is proved. The proposed modification of the PF method is shown to be effective by simulation and then applied for unicycle-like mobile robots with additive input disturbances.