A Geometric Assignment Problem for Robotic Networks

In this chapter we look at a geometric target assignment problem consisting of an equal number of mobile robotic agents and distinct target locations. Each agent has a fixed communication range, a maximum speed, and knowledge of every target’s position. The problem is to devise a distributed algorithm that allows the agents to divide the target locations among themselves and, simultaneously, leads each agent to its unique target. We summarize two algorithms for this problem; one designed for “sparse” environments, in which communication between robots is sparse, and one for “dense” environments, where communication is more prevalent. We characterize the asymptotic performance of these algorithms as the number of agents increases and the environment grows to accommodate them.