Path planning: an approach based on connecting all the minimizers and maximizers of a potential function

An improved potential-based method for robot path planning is developed by connecting all the local minima and local maxima of the potential function defined in the configuration space of the robot. The authors construct an adjacency graph of the local minima and maxima of the potential function. An edge connecting a local minimum and a local maximum has an associated pair of perturbations which gives a way of moving between them. The method is based on the stability theory of dynamical systems. The usefulness of the method was demonstrated on a two-dimensional piano mover´s problem with three degrees of freedom