Avoiding local minima in the potential field method using input-to-state stability

Supported by a novel field definition and recent control theory results, a new method to avoid local minima is proposed. It is formally shown that the system has an attracting equilibrium at the target point, repelling equilibriums in the obstacle centers and saddle points on the borders. Those unstable equilibriums are avoided capitalizing on the established Input-to-State Stability (ISS) property of this multistable system. The proposed modification of the PF method is shown to be effective by simulation for a two variable integrator and then applied to a unicycle-like wheeled mobile robots which is subject to additive input disturbances.