Abstract — This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or circular motion of all particles with fixed relative phases. The stabilizing feedbacks derive from Lyapunov functions that prove exponential stability and suggest almost global convergence properties. The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higherlevel tasks at the group level. Index Terms — Cooperative control, geometric control, multiagent systems, stabilization.

Abstract—This paper proposes a design methodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel motion of all particles with fixed relative spacing or to circular motion of all particles around the same circle. Particles exchange relative information according to a communication graph that can be undirected or directed and time-invariant or timevarying. The emphasis of this paper is to show how previous results assuming all-to-all communication can be extended to a general communication framework. Index Terms—Cooperative control, geometric control, multiagent systems, stabilization. I.

This paper proposes a formal model for a network of robotic agents that move and communicate. Building on concepts from distributed computation, robotics and control theory, we define notions of robotic network, control and communication law, coordination task, and time and communication complexity. We illustrate our model and compute the proposed complexity measures in the example of a network of locally connected agents on a circle that agree upon a direction of motion and pursue their immediate neighbors. I.

and the optimum value of max[P (0)] was max[P (0)] = 00:40844 < 0 which indicates that this system has no robustly unobservable states. For the optimal value of given above, a plot of max[P (t)] as a function of t is shown in Fig. 6.

This paper analyzes a number of basic coordination algorithms running on synchronous robotic networks. We provide upper and lower bounds on the time complexity of the move-toward average and circumcenter laws, both achieving rendezvous, and of the centroid law, achieving deployment over a region of interest. The results are derived via novel analysis methods, including a set of results on the convergence rates of linear dynamical systems defined by tridiagonal Toeplitz and circulant matrices. I.

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Abstract — We study minimalism in sensing and control by considering a multi-agent system in which each agent moves like a Dubins car and has a limited sensor that reports only the presence of another agent within some sector of its windshield. Using a very simple quantized control law with three values, each agent tracks another agent assigned to it by maintaining that agent within this windshield sector. We use Lyapunov analysis to show that by acting autonomously in this way, the agents will achieve rendezvous if the initial assignment graph is connected. A distinguishing feature of our approach is that it does not involve any estimation procedure aimed at reconstructing coordinate information. Our scenario thus appears to be the first example in which an interesting task is performed with extremely coarse sensing and control, and without state estimation. The system was implemented in computer simulation, accessible through the Web, of which the results are presented in the paper. (a) (b)

In this article we study the convergence of the positions of a multi-agent system in a cyclic pursuit under asynchronism and time delays. Each agent is assumed to operate on an infinite sequence of behaviors modeled by a finite state machine, which is represented by a discrete asynchronous mathematical model on a higher-level. The results on the convergence of the synchronous model is used in the proof of convergence of the asynchronous system. Numerical simulations are also performed to verify the theoretical results. 1

Abstract. In this paper, we analyze the problem of finding a periodic schedule for the wake-up times of a set of nodes in a Wireless Sensor Network that optimizes the coverage of the region the nodes are deployed on. An exact solution of the problem entails the solution of an Integer Linear Program and is hardly viable on low power nodes. Giusti et. al. [6] have recently proposed an efficient decentralized approach that produces a generally good suboptimal solution. In this paper, we study the convergence of this algorithm by casting the problem into one of asymptotic stability for a particular class of linear switching systems. For general topologies of the WSN, we offer local stability results. In some specific special cases, we are also able to prove global stability properties. 1

Abstract — Motivated by the problem of formation control for vehicles moving at unit speed in three-dimensional space, we are led to models of gyroscopically interacting particles, which require the machinery of curves and frames to describe and analyze. A Lie group formulation arises naturally, and we discuss the general problem of determining (relative) equilibria for arbitrary G-invariant controls (where G = SE(3) is a symmetry group for the control law). We then present global convergence (and non-collision) results for specific two-vehicle interaction laws in three dimensions, which lead to specific formations (i.e., relative equilibria). Generalizations of the interaction laws to n vehicles is also discussed, and simulation results presented. I.