Motion Planning Algorithm for Homogeneous Combinatorial Robots in Time-Varying Environment

This paper introduces the concept of homogeneous combinatorial robots, specifying their properties and algorithms needed to solve the problems in motion-planning. In this paper, "homogeneous combinatorial robots" are a set of robots that can be combined and separated freely in motion. The complexity and obstacles of motion planning are explained in terms of the principle of optimality. To plan the optimal paths in time-varying environment for those robots, a dynamic programming algorithm is developed and proposed in the paper. Suppose η is the maximum number of vertices of the time-varying graph,
n
is the number of robots, and k is the number of steps of the motion plan. The time complexity of this problem is
O(η^2nk)
.