We present a novel method that constructs and navigates a network of local minima of potential fields defined over multidimensional spaces. Though motivated by problems of motion planning for robotic manipulators, similar techniques have been proposed for use in other domains such as molecular chemistry and drug design. The method is based on building a roadmap of paths connecting local minima of a potential function. The novel approach consists of an up-hill search strategy used to climb out of local minima and find new nearby local minima, without doubling back on previous local minima. With this up-hill search strategy, one can find local minima otherwise difficult to encounter, and one can focus the search to specific local minima and specific directions from those local minima. The construction of the roadmap can be done in parallel with very little communication. We present extensive simulation results.