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This article provides a comprehensive view of the novel fast marching (FM) methods we developed for robot path planning. We recall some of the methods developed in recent years and present two improvements upon them: the saturated FM square (FM2) and an heuristic optimization called the FM2 star (FM2*) method. The saturated variation of the existing saturated FM2 provides safe paths that avoid unnecessarily long trajectories (like those computed using the Voronoi diagram). FM2* considerably reduces the computation time. As a result, these methods provide not only a trajectory but also an associated control speed for the robot at each point of the trajectory. The proposed methods are complete; if there is a valid trajectory, it will always be found and will always be optimal in estimated completion time.