Oscillatory Neural Fields for Globally Optimal Path Planning

A neural network solution is proposed for solving path planning problems faced by mobile 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 network exhibits oscillatory behaviour. These oscillations are used to generate solutions of Bellman's dynamic programming equation in the context of path planning. Simulation experiments imply that these networks locate global optimal paths even in the presence of substantial levels of circuit nOlse. 1 Dynamic Programming and Path Planning Consider a 2-DOF robot moving about in a 2-dimensional world. A robot's location is denoted by the real vector, p. The collection of all locations forms a set called the workspace. An admissible point in the workspace is any location which the robot may occupy. The set of all admissible points is called the free workspace. The free workspace's complement represents a collection of obstacles. The robot moves through the workspace along a path which is denoted by the parameterized curve, p(t). An admissible path is one which lies wholly in the robot's free workspace. Assume that there is an initial robot position, Po, and a desired final position, p J. The robot path planning problem is to find an admissible path with Po and p J as endpoints such that some "optimality" criterion is satisfied. The path planning problem may be stated more precisely from an optimal control 539