This paper proposes a neural network solution to path planning by two degree-of-freedom (DOF) robots. The proposed network is a two-dimensional sheet of neurons forming a distributed representation of the robot's workspace. Lateral interconnections between neurons are “cooperative,” so that the field exhibits oscillatory behavior. This paper shows how that oscillatory behavior can be used to solve the path-planning problem. The results reported show that the proposed neural network finds the variational solution of Bellman's dynamic programming equation.