Abstract：A centralized motion planning method has been presented in this paper, it realizes the collision avoidance in a multi-robot system by adjusting the velocity of robots. The basic idea of this method is:the paths of robots are segmented to several sub-paths first, and then the restrictions to the time of robot passing through these sub-paths can be established according to the request of collision avoidance. So, the question has been converted to an optimal question in a linear-space and it can be resolved by a group of linear equations in closed form. Because this method has a high complexity, several ways have been developed to reduce the burden of calculation. The basic idea of this method, some related theorem and their proving, the method of predigestion are presented in this paper, the simulation results and a short discussion are also given in the last session of this paper.
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