A Monte-Carlo algorithm for path planning with many degrees of freedom

A stochastic technique is described for planning collision-free paths of robots with many degrees of freedom (DOFs). The algorithm incrementally builds a graph connecting the local minima of a potential function defined in the robot´s configuration space and concurrently searches the graph until a goal configuration is attained. A local minimum is connected to another one by executing a random motion that escapes the well of the first minimum, succeeded by a gradient motion that follows the negated gradient of the potential function. All the motions are executed in a grid shown through the robot´s configuration space. The random motions are implemented as random walks which are known to converge toward Brownian motions when the steps of the walks tend toward zero. The local minima graph is searched using a depth-first strategy with random backtracking. In the technique, the planner does not explicitly represent the local-minima graph. The path-planning algorithm has been fully implemented and has run successfully on a variety of problems involving robots with many degrees of freedom