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58
Spatiallydistributed coverage optimization and control with limitedrange interactions
 ESAIM Control, Optimisation Calculus Variations
, 2005
"... Abstract. This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing/communication radius. Based on the geometry of Voronoi partitions and proximity grap ..."
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Cited by 74 (34 self)
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Abstract. This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing/communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed with respect to appropriate proximity graphs. Numerical simulations illustrate the results.
Stabilization of planar collective motion: alltoall communication
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2007
"... This paper proposes a design methodology to stabilize isolated relative equilibria in a model of alltoall 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 motio ..."
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Cited by 45 (19 self)
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This paper proposes a design methodology to stabilize isolated relative equilibria in a model of alltoall 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 loworder parametric family of stabilizable collectives that offer a set of primitives for the design of higherlevel tasks at the group level.
Stabilization of planar collective motion with limited communication
 IEEE Trans. Automat. Contr
"... 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 particle ..."
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Cited by 41 (21 self)
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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 timeinvariant or timevarying. The emphasis of this paper is to show how previous results assuming alltoall communication can be extended to a general communication framework. Index Terms—Cooperative control, geometric control, multiagent systems, stabilization. I.
On synchronous robotic networks Part I: models, tasks, and complexity notions
 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference (CDCECC ’05
, 2005
"... 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. ..."
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Cited by 24 (13 self)
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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.
Natural frames and interacting particles in three dimensions
, 2005
"... Abstract — Motivated by the problem of formation control for vehicles moving at unit speed in threedimensional 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 ..."
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Cited by 19 (10 self)
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Abstract — Motivated by the problem of formation control for vehicles moving at unit speed in threedimensional 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 Ginvariant controls (where G = SE(3) is a symmetry group for the control law). We then present global convergence (and noncollision) results for specific twovehicle 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.
On synchronous robotic networks – Part II: Time complexity of rendezvous and deployment algorithms
 IEEE Transactions on Automatic Control, Apr
"... 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 movetoward average and circumcenter laws, both achieving rendezvous, and of the centroid law, achieving deployment over a region of ..."
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Cited by 16 (6 self)
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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 movetoward 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.
Stable flocking of multiple inertial agents on balanced graphs
 Computer Science, The University of Newcastle
, 2006
"... 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. ..."
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Cited by 16 (3 self)
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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.
Distributed intelligence: Overview of the field and its application in multirobot systems
 Journal of Physical Agents
, 2008
"... Abstract—This article overviews the concepts of distributed intelligence, outlining the motivations for studying this field of research. First, common systems of distributed intelligence are classified based upon the types of interactions exhibited, since the type of interaction has relevance to the ..."
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Cited by 13 (1 self)
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Abstract—This article overviews the concepts of distributed intelligence, outlining the motivations for studying this field of research. First, common systems of distributed intelligence are classified based upon the types of interactions exhibited, since the type of interaction has relevance to the solution paradigm to be used. We outline three common paradigms for distributed intelligence — the bioinspired paradigm, the organizational and social paradigm, and the knowledgebased, ontological paradigm — and give examples of how these paradigms can be used in multirobot systems. We then look at a common problem in multirobot systems — that of task allocation — and show how the solution approach to this problem is very different depending upon the paradigm chosen for abstracting the problem. Our conclusion is that the paradigms are not interchangeable, but rather the selection of the appropriate paradigm is dependent
Multiagent coordination by decentralized estimation and control
 IEEE Transactions on Automatic Control
, 2008
"... Abstract — We describe a framework for the design of collective behaviors for groups of identical mobile agents. The approach is based on decentralized simultaneous estimation and control, where each agent communicates with neighbors and estimates the global performance properties of the swarm neede ..."
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Cited by 12 (0 self)
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Abstract — We describe a framework for the design of collective behaviors for groups of identical mobile agents. The approach is based on decentralized simultaneous estimation and control, where each agent communicates with neighbors and estimates the global performance properties of the swarm needed to make a local control decision. Challenges of the approach include designing a control law with desired convergence properties, assuming each agent has perfect global knowledge; designing an estimator that allows each agent to make correct estimates of the global properties needed to implement the controller; and possibly modifying the controller to recover desired convergence properties when using the estimates of global performance. We apply this framework to two different problems: (1) controlling the moment statistics describing the location and shape of a swarm, and (2) cooperative target localization. For the swarm formation control problem, we derive smallgain conditions which, if satisfied, guarantee that the formation statistics are driven to desired values, even in the presence of a changing network topology and the addition and deletion of robots. Index Terms — Multiagent systems, decentralized control, distributed control, dynamic average consensus estimation, formation control. I.
2007] Curve shortening and the rendezvous problem for mobile autonomous robots
 IEEE Transactions on Automatic Control
"... If a smooth, closed, and embedded curve is deformed along its normal vector field at a rate proportional to its curvature, it shrinks to a circular point. This curve evolution is called Euclidean curve shortening and the result is known as the GageHamiltonGrayson Theorem. Motivated by the rendezvo ..."
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Cited by 11 (0 self)
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If a smooth, closed, and embedded curve is deformed along its normal vector field at a rate proportional to its curvature, it shrinks to a circular point. This curve evolution is called Euclidean curve shortening and the result is known as the GageHamiltonGrayson Theorem. Motivated by the rendezvous problem for mobile autonomous robots, we address the problem of creating a polygon shortening flow. A linear scheme is proposed that exhibits several analogues to Euclidean curve shortening: The polygon shrinks to an elliptical point, convex polygons remain convex, and the perimeter of the polygon is monotonically decreasing. I.