A convergence proof of a fusion algorithm of global and local path-planning for multiple mobile robots

First of all, a global path-planning algorithm. synchronously selects shortest paths of multiple mobile robots. Therefore, it is time consuming because of hard combination search. On the other hand, a local path-planning algorithm independently selects a shorter path of each mobile robot. Therefore, it is not time consuming because of non-combination search. However, we must consider the following two problems: (1) Several types of collisions of two or more robots should be solved. (2) Convergence of all robots to their destinations, should be theoretically ensured. To solve these problems, we design a fusion algorithm by mixing global and local path-planning algorithms, and then we give a proof such that all robots arrive at their destinations in this paper.