Time Complexity of Motion Planning Algorithm for Homogeneous Combinatorial Robots

Some properties and an algorithm of the motion planning problem of homogeneous combinatorial robots are presented. Homogeneous combinatorial robots can be combined and separated freely in the process of moving. The motion planning problem of homogeneous combinatorial robots in a static discrete environment is proven to be compliant to the principle of optimality. A backward dynamic motion planning algorithm is used to find the optimal motion plans. Suppose that |V| is the number of all vertices in the graph, n is the number of robots, and k is the number of stages robots passing the graph. The time complexity without considering the limitation function of this problem is O(|V|^2nk ). Furthermore, the time complexity with the limitation function of the problem is presented