Target assignment for robotic networks: asymptotic performance under limited communication

TL;DR

This paper presents a distributed target assignment algorithm for robotic networks with limited communication, ensuring asymptotic optimality and efficiency without requiring continuous connectivity.

Contribution

The paper introduces a novel distributed assignment algorithm that is asymptotically optimal and does not require persistent network connectivity.

Findings

Algorithm guarantees correct target assignment

Achieves asymptotic optimality among similar algorithms

Provides bounds on assignment completion time

Abstract

We are given an equal number of mobile robotic agents, and distinct target locations. Each agent has simple integrator dynamics, a limited communication range, and knowledge of the position of every target. We address the problem of designing a distributed algorithm that allows the group of agents to divide the targets among themselves and, simultaneously, leads each agent to reach its unique target. We do not require connectivity of the communication graph at any time. We introduce a novel assignment-based algorithm with the following features: initial assignments and robot motions follow a greedy rule, and distributed refinements of the assignment exploit an implicit circular ordering of the targets. We prove correctness of the algorithm, and give worst-case asymptotic bounds on the time to complete the assignment as the environment grows with the number of agents. We show that among a certain class of distributed algorithms, our algorithm is asymptotically optimal. The analysis utilizes results on the Euclidean traveling salesperson problem.