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This paper introduces a method based on trajectory analysis and waiting strategy for robot manipulators in changing environments. In order to avoid collision with moving obstacles, devious trajectories appear in most path planning problems in changing environments. For complicated environments some methods even don not work. In this paper, on the premise that whether an obstacle has automatic avoidance ability is known in advance, obstacles are categorized into four groups by analyzing their trajectories. First A* algorithm is employed to find the shortest path, ignoring obstacles. If only a small group of obstacles which slightly disturb robot manipulator obstruct the frontal part of the path, waiting strategy will be adopted, i.e., robot manipulator will wait for their departure. Otherwise, A* algorithm will be arranged again to search for a feasible path. Although A* algorithm would be employed twice in some situations, the advantage it brings can make up it. In plentiful comparison experiments, our method shows good performance.