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

This paper presents a novel solution to a motion planning problem of heterogeneous combinatorial point robots in a time-varying environment, involving some properties and an algorithm. These combinatorial point robots can be combined and separated freely during moving. The problem that is proven to be compliant to the principle of optimality in a time-varying environment can be solved using dynamic programming algorithms. Assume that y denotes the number of kinds of heterogeneous combinatorial point robots, eta_f represents the maximum number of vertices of the time-varying graph, k denotes the number of steps, n denotes the total number of all robots, and c_f denotes the number of f^th kind of heterogeneous combinatorial point robots in the motion plan. The time complexity of this problem is proven to be O (^ypi_f=1eta_f ^2kn), where n=^ySigma_f=1c_fldr