Monotonic Target Assignment for Robotic Networks

Abstract

Abstract-Consider an equal number of mobile robotic agents and distinct target locations dispersed in an environment. Each agent has a limited communication range and either: 1) knowledge of every target position or 2) a finite-range sensor capable of acquiring target positions and no a priori knowledge of target positions. In this paper we study the following target assignment problem: design a distributed algorithm with which the agents divide the targets among themselves and, simultaneously, move to their unique target. We evaluate an algorithm's performance by characterizing its worst-case asymptotic time to complete the target assignment; that is the task completion time as the number of agents (and targets) increases, and the size of the environment scales to accommodate them. We introduce the intuitive class of monotonic algorithms, and give a lower bound on its worst-case completion time. We design and analyze two algorithms within this class: the ETSP ASSGMT algorithm which works under assumption 1), and the GRID ASSGMT algorithm which works under either assumption 1) or 2). In "sparse environments," where communication is infrequent, the ETSP ASSGMT algorithm is within a constant factor of the optimal monotonic algorithm for worst-case initial conditions. In "dense environments," where communication is more prevalent, the GRID ASSGMT algorithm is within a constant factor of the optimal monotonic algorithm for worst-case initial conditions. In addition we characterize the performance of the GRID ASSGMT algorithm for uniformly distributed targets and agents, and for the case when there are more agents than targets.

Stochastic and Dynamic Routing Problems for Multiple Uninhabited Aerial Vehicles

“…A related problem has been investigated as the Weapon-Target Assignment (WTA) problem, in which vehicles are allowed to team up in order to enhance the probability of a favorable outcome in a target engagement. 33,34 Other related works address UAV taskassignment: [35][36][37][38] in this setup, targets locations are known and an assignment strategy is sought that maximizes a global performance metric such as success rate. Some other works, like this paper, address coverage and sensing tasks with only prior statistics on the operating environment.…”

UAV Routing and Coordination in Stochastic, Dynamic Environments

“…In the recent past, considerable efforts have been devoted to the problem of how to cooperatively assign and schedule tasks that are defined over an extended geographical area (Alighanbari and How, 2008;Arslan et al, 2007;Beard et al, 2002;Moore and Passino, 2007;Smith and Bullo, 2009). In these papers, the main focus is in developing distributed algorithms that operate with knowledge about the task locations and with limited communication between robots.…”

Multi-Level Partitioning and Distribution of the Assignment Problem for Large-Scale Multi-Robot Task Allocation

“…By manipulating ρ the quality/efficiency trade-off may be tuned to suit user needs; we believe this to be more representative of our physical robots than directly relating task sparsity to some fixed range (e.g., based on communication radius, although cf. [15] for such a treatment).…”

“…The similar underlying combinatorial task-assignment problems have also been tackled from a hybrid systems perspective (e.g., role assignment with preemption [13], and potential-field hybrid controllers with relaxed mutual exclusion constraints [14]). An important recent result is that of [15], who studied a class of problems in which assigned robots must remain at targets indefinitely, but for which important performance bounds under different environmental models could be identified.…”