A Note on the Consensus Protocol with Some Applications to Agent Orbit Pattern Generation

We propose an extension to the standard feedback control for consensus problems for multi-agent systems in the plane. The proposed extension allows for a richer class of trajectories including periodic and quasi-periodic solutions, as well as agreement to consensus states outside the convex hull of the initial positions of the agents. We investigate in great detail the special case of three agents, which results in non-trivial geometric patterns described by ellipsoidal, epitrochoidal and hypotrochoidal curves. 1 A Generalized Consensus Protocol Consensus problems have been originally used in distributed computing and management science and, most recently, have found extensive application in multi-agent, mobile network problems [12, 16]. In this paper we propose a generalization of the standard consensus algorithm which has been used extensively in the literature [13, 3, 11]. The proposed extension of the standard consensus protocol leads to the following advantages: first, it can be used to achieve consensus at points that do not necessarily belong to the convex hull of the initial conditions. This may be beneficial in case of obstacle avoidance or as part of deception strategies. Second, as shown in the second part of the paper, it can be utilized to generate intricate geometrical patterns of the agent paths. These paths can be useful for coordinated, distributed surveillance and monitoring applications. Coordinated algorithms for network formations have appeared previously, for example, in [14, 15, 7] as well as in the work of Leonard and Sepulchre [9, 17, 18]. Therein the authors make use of geometric information to achieve specific formation Panagiotis Tsiotras School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0105, USA Tel: +1-404-894-9526, Fax: +1-404-894-2760, e-mail: [email protected] Luis I. Reyes Castro School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0105, USA, e-mail: nacho [email protected]