Decentralized Centroid Estimation for Multi-Agent Systems in Absence of any Common Reference Frame Mauro Franceschelli † and Andrea Gasparri ⋆ † Electrical and Electronic Engineering ⋆ Computer Science and Automation University of Cagliari University of “Roma Tre” 09123 Cagliari, Italy 00146 Roma Italy mauro.franceschelli@diee.unica.it gasparri@dia.uniroma3.it Abstract— In this paper, a novel distributed algorithm to deal with the problem of estimating the network centroid in a multi-agent system is proposed. In this scenario, agents are assumed to be lacking any global reference frame or absolute position information. The proposed algorithm can be thought as a general tool to retrieve information about the centroid of a network of agents. Indeed, this allows to release several simplifying assumptions for a significant family of algorithms dealing with decentralized motion coordination. The convergence properties of the algorithm are carefully investigated in the case of a fully connected network for which a proof of convergence is provided. Successively, simulations to show the effectiveness of the algorithm also for arbitrary undirected connected graphs are given. I. I NTRODUCTION In recent years multi agent systems have drawn the atten- tion of a huge amount of researchers, for a representative example see [1], [2], [3], [4]. In this framework Laplacian based controllers [5], [6], [7], [8] have been studied in many forms and applications, for instance rendezvous [9], leader following [10], attitude control [11] and many others [12], [13], [14]. The majority of these algorithms, dealing with decentralized motion coordination problems, assume that the agents have access to absolute position information (GPS) and thus have a common global reference that makes it easy to interpret the information passed by other agents. Even when in multi agent systems the agents are not supposed to know their absolute position, many times they are assumed to have a common attitude reference to exchange information that can be achieved by using a compass, gyroscopes and oc- casionally gravity as common reference for their coordinate system. For space applications another technological solution is to use a frame of fixed stars to have a common reference. In all these instances several technological countermeasures have to be undertaken for the implementation of coordination algorithms increasing the total costs of the single agents. Many coordination algorithms rely on local information taken by the neighbors in the sensing radius of the agents and some general information about the swarm of mobile units, for instance its centroid. In this paper we are interested in developing an asynchronous and decentralized algorithm to estimate the location of the centroid of the network of agents that does not require any common attitude reference nor any absolute position information. We believe that removing such hidden assumption could significantly advance the technological feasibility of mobile swarm of agents, reducing their dependence on the global positioning system in the low level control loops. Furthermore in many space applications, where networks of mobile robots are envisioned in the so not distant future, the absence of the need for absolute position information or a common coordinate system could prove to be an essential robust feature. The rest of the paper is organized as follows. In Section I-A the scenario along with simplifying assumptions is introduced. In Section II a more formal description of the problem formulation is given. In Section III the proposed algorithm is described and the proof of its convergence in case a fully connected graph is given. In Section IV, the performance of the algorithm for several network topologies is discussed. Finally, in Section V conclusions are drawn and future work is discussed. A. Paper content In this paper, a decentralized asynchronous algorithm to estimate the centroid of a network of agents is proposed. It allows to release several simplifying assumption for a large family of algorithms proposed in literature dealing with decentralized motion coordination. In particular, the following assumptions are made: • The network of agents can be described by a connected undirected graph. • Each agent can only communicate with agents directly connected to it. • Communications are asynchronous, i.e. communication failures or delays do not affect the network. • Each agent is able to sense the distance between itself and its neighbors. • Each agent is able to sense the direction in which it sees its neighbors with respect to its local reference frame, arbitrary fixed on it. Objective of the proposed algorithm is to make available to each agent an estimate of where the network centroid is with respect to the local agents reference frame. The convergence properties of the algorithm are carefully investigated in the 2009 American Control Conference Hyatt Regency Riverfront, St. Louis, MO, USA June 10-12, 2009 WeA16.4 978-1-4244-4524-0/09/$25.00 ©2009 AACC 512