Abstract: This paper presents coordination algorithms for networks of mobile autonomous agents. The objective of the proposed algorithms is to achieve rendezvous, that is, agreement over the location of the agents in the network. We provide analysis and design results for multi-agent networks in arbitrary dimensions under weak requirements on the switching and failing communication topology. The correctness proof relies on proximity graphs and their properties and on a LaSalle Invariance Principle for nondeterministic discrete-time systems. Copyright c ○ 2005 IFAC

Abstract — This paper presents a control strategy that allows a group of mobile robots to position themselves to optimize the measurement of sensory information in the environment. The robots use sensed information to estimate a function indicating the relative importance of different areas in the environment. Their estimate is then used to drive the network to a desirable placement configuration using a computationally simple decentralized control law. We formulate the problem, provide a practical control solution, and present the results of numerical simulations. We then discuss experiments carried out on a swarm of mobile robots. I.

A decentralized, adaptive control law is presented to drive a network of mobile robots to an optimal sensing configuration. The control law is adaptive in that it uses sensor measurements to learn an approximation of the distribution of sensory information in the environment. It is decentralized in that it requires only information local to each robot. The controller is then improved upon by implementing a consensus algorithm in parallel with the learning algorithm, greatly increasing parameter convergence rates. Convergence and consensus of parameters is proven. Finally, several variations on the learning algorithm are explored with a discussion of their stability in closed loop. The controller with and without parameter consensus is demonstrated in numerical simulations. These techniques are suggestive of broader applications of adaptive control methodologies to decentralized control problems in unknown dynamical environments. 1

Abstract — A decentralized, adaptive control law is presented to drive a network of mobile robots to a near-optimal sensing configuration. The control law is adaptive in that it integrates sensor measurements to provide a converging estimate of the distribution of sensory information in the environment. It is decentralized in that it requires only information local to each robot. A Lyapunov-type proof is used to show that the control law causes the network to converge to a near-optimal sensing configuration, and the controller is demonstrated in numerical simulations. This technique suggests a broader application of adaptive control methodologies to decentralized control problems in unknown dynamical environments. I.

Centroidal Voronoi tessellation (CVT) is a fundamental geometric structure that finds many applications in

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.

This paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function. Extending recent results on nonsmooth stability analysis, we characterize their asymptotic convergence properties and identify conditions that guarantee finite-time convergence. We discuss the application of the results to the design of multi-agent coordination algorithms, paying special attention to their scalability properties. Finally, we consider network consensus problems and show how the proposed nonsmooth gradient flows achieve the desired coordination task in finite time.

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This paper surveys recently-developed theoretical tools for the analysis and design of coordination algorithms for networks of mobile autonomous agents. First, various motion coordination tasks are encoded into aggregate cost functions from Geometric Optimization. Second, the limited communication capabilities of the mobile agents are modeled via the notions of proximity graphs from Computational Geometry and of spatially distributed maps. Finally, we illustrate how to apply these tools to design and analyze scalable cooperative strategies in a variety of motion coordination problems such as deployment, rendezvous, and flocking.