Distance optimal target assignment in robotic networks under communication and sensing constraints
We study the problem of minimizing the total distance incurred in assigning a group of mobile robots to an equal number of static targets. Assuming that the robots have limited, range-based communication and target-sensing capabilities, we present a necessary and sufficient condition for ensuring distance optimality when robots and targets are uniformly randomly distributed. We then provide an explicit, non-asymptotic formula for computing the number of robots needed for guaranteeing optimality in terms of the robots' sensing and communication capabilities with arbitrarily high probabilities. The bound given in the formula is also asymptotically tight. Due to the large number of robots needed for high-probability optimality guarantee, we continue to investigate strategies for cases in which the number of robots cannot be freely chosen. We show that a properly designed strategy can be asymptotically optimal or suboptimal with constant approximation ratios.
© 2014 IEEE. Date of Conference: 31 May-7 June 2014. Date Added to IEEE Xplore: 29 September 2014. This work was supported in part by AFOSR grant FA95501210193 and NSF grant IIS-1253758. This paper is intended as an early dissemination of results of an extended draft  which contains more complete proofs and significant generalizations. We thank the reviewers for their constructive comments.