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36
Oscillator models and collective motion: Splay state stabilization of selfpropelled particles
 in Proc. 44th IEEE Conference on Decision and Control
, 2005
"... Abstract — This paper presents a Lyapunov design for the stabilization of collective motion in a planar kinematic model of N particles moving at constant speed. We derive a control law that achieves asymptotic stability of the splay state formation, characterized by uniform rotation of N evenly spac ..."
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Cited by 26 (10 self)
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Abstract — This paper presents a Lyapunov design for the stabilization of collective motion in a planar kinematic model of N particles moving at constant speed. We derive a control law that achieves asymptotic stability of the splay state formation, characterized by uniform rotation of N evenly spaced particles on a circle. In designing the control law, the particle headings are treated as a system of coupled phase oscillators. The coupling function which exponentially stabilizes the splay state of particle phases is combined with a decentralized beacon control law that stabilizes circular motion of the particles in the splay state formation around the center of mass of the group. I.
COORDINATED PATHFOLLOWING IN THE PRESENCE OF COMMUNICATION LOSSES AND TIME DELAYS ∗
"... Abstract. This paper addresses the problem of steering a group of vehicles along given paths while holding a desired formation pattern. The solution to this problem, henceforth referred to as the Coordinated PathFollowing problem, unfolds in two basic steps. First, a pathfollowing control law is u ..."
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Cited by 19 (9 self)
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Abstract. This paper addresses the problem of steering a group of vehicles along given paths while holding a desired formation pattern. The solution to this problem, henceforth referred to as the Coordinated PathFollowing problem, unfolds in two basic steps. First, a pathfollowing control law is used that drives each vehicle to its assigned path regardless of the temporal speed profile adopted. This is done by making each vehicle approach a conveniently defined virtual target that moves along the path. In the second step, the speeds of the vehicles are adjusted so as to synchronize the positions of the corresponding virtual targets (also called coordination states) thus achieving coordination along the paths. In the problem formulation, it is explicitly considered that each vehicle transmits its coordination state to only a subset of the other vehicles, as determined by the communications topology adopted. It is shown that the system that is obtained by putting together the path following and coordination strategies can be naturally viewed as a feedback interconnected system. Using this result and recent results from nonlinear system and graph theory, conditions are derived under which the path following and the coordination errors are driven to a neighborhood of zero in the presence of communication failures and time delays. Two different situations are considered. The first captures the case where the communication graph is alternately connected and disconnected (brief connectivity losses). The second reflects an operating scenario where the union of the communication graphs over uniform intervals of time remains connected (uniformly connected in mean). To better ground the paper on a nontrivial design example, a coordinated pathfollowing algorithm is derived for multiple underactuated Autonomous Underwater Vehicles (AUVs). Simulation results are presented and discussed. Key words. Coordination control, communication losses and time delays, pathfollowing, autonomous underwater vehicle AMS subject classifications. 1. Introduction. Increasingly
Stability of leaderless multiagent systems. Extension of a result by Moreau
, 2008
"... The paper presents a result which relates connectedness of the interaction graphs in a multiagent systems with the capability for global convergence to a common equilibrium of the system. In particular we extend a previously known result by Moreau by including the possibility of arbitrary bounded t ..."
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Cited by 16 (0 self)
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The paper presents a result which relates connectedness of the interaction graphs in a multiagent systems with the capability for global convergence to a common equilibrium of the system. In particular we extend a previously known result by Moreau by including the possibility of arbitrary bounded timedelays in the communication channels and relaxing the convexity of the allowed regions for the state transition map of each agent.
Collective motion of ringcoupled planar particles
 in Proc. 44th IEEE Conf. Decision Control
, 2005
"... Abstract — We study stabilization of collective motion of N constantspeed, planar particles with less than alltoall coupling. Our interest is in circular motions of the particles around the fixed center of mass of the group, as has been studied previously with alltoall coupling. We focus on cou ..."
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Cited by 13 (3 self)
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Abstract — We study stabilization of collective motion of N constantspeed, planar particles with less than alltoall coupling. Our interest is in circular motions of the particles around the fixed center of mass of the group, as has been studied previously with alltoall coupling. We focus on coupling defined by a ring, i.e., each particle communicates with exactly two other particles. The Kuramoto model of coupled oscillators, restricted to “ring ” coupling, serves as our model for controlling the relative headings of the particles. Each phase oscillator represents the heading of a particle. We prove convergence to a set of solutions that correspond to symmetric patterns of the phases about the unit circle. The exponentially stable patterns are generalized regular polygons, determined by the sign of the coupling gain K. I.
MultiAUV control and adaptive sampling
 in Monterey Bay. In: Autonomous Underwater Vehicles, 2004 IEEE/OES
, 2004
"... Abstract — MultiAUV operations have much to offer a variety of underwater applications. With sensors to measure the environment and coordination that is appropriate to critical spatial and temporal scales, the group can perform important tasks such as adaptive ocean sampling. We describe a methodol ..."
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Cited by 12 (5 self)
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Abstract — MultiAUV operations have much to offer a variety of underwater applications. With sensors to measure the environment and coordination that is appropriate to critical spatial and temporal scales, the group can perform important tasks such as adaptive ocean sampling. We describe a methodology for cooperative control of multiple vehicles based on virtual bodies and artificial potentials (VBAP). This methodology allows for adaptable formation control and can be used for missions such as gradient climbing and feature tracking in an uncertain environment. We discuss our implementation on a fleet of autonomous underwater gliders and present results from sea trials in Monterey Bay in August 2003. These atsea demonstrations were performed as part of the Autonomous Ocean Sampling Network (AOSN) II project.
Discrete Time Kuramoto Models with Delay
"... Summary. Motivated by the needs of multiagent systems in the presence of sensing and communication that is delayed, intermittent and asynchronous, we present here a discretetime Kuramoto oscillator model that incorporates delays. Analytical results are derived for certain cases of stability of sync ..."
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Cited by 12 (4 self)
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Summary. Motivated by the needs of multiagent systems in the presence of sensing and communication that is delayed, intermittent and asynchronous, we present here a discretetime Kuramoto oscillator model that incorporates delays. Analytical results are derived for certain cases of stability of synchronized and balanced equilibrium sets both when delay is not present and when it is. In all cases, oscillators are assumed to be identical and fully connected, with constant and equal network delays. For complex cases, the analysis is supplemented with Monte Carlo simulations, and all results are verified in simulation. 1
Convergence speed of unsteady distributed consensus: decay estimate along the settling spanningtrees
, 2008
"... Results for estimating the convergence rate of nonstationary distributed consensus algorithms are provided, on the basis of qualitative (mainly topological) as well as basic quantitative information (lowerbounds on the matrix entries). The results appear to be tight in a number of instances and ar ..."
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Cited by 12 (1 self)
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Results for estimating the convergence rate of nonstationary distributed consensus algorithms are provided, on the basis of qualitative (mainly topological) as well as basic quantitative information (lowerbounds on the matrix entries). The results appear to be tight in a number of instances and are illustrated through simple as well as more sophisticated examples. The main idea is to follow propagation of information along certain spanning trees which arise in the communication graph.
Synchronization on the circle
, 2009
"... The goal of the present paper is to highlight the fundamental differences of socalled synchronization or consensus algorithms when the agents to synchronize evolve on a compact homogeneous manifold (like the circle, sphere or the group of rotation matrices), instead of a vector space. For the benef ..."
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Cited by 3 (1 self)
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The goal of the present paper is to highlight the fundamental differences of socalled synchronization or consensus algorithms when the agents to synchronize evolve on a compact homogeneous manifold (like the circle, sphere or the group of rotation matrices), instead of a vector space. For the benefit of understanding, the discussion is restricted to the circle. First, a fundamental consensus algorithm on R n is reviewed, from which continuous and discretetime synchronization algorithms on the circle are deduced by analogy. It is shown how they are connected to Kuramoto and Vicsek models from the literature. Their convergence properties are similar to vector spaces only for specific graphs or if the agents are all located within a semicircle. Examples are proposed to illustrate several other possible behaviors. Finally, new algorithms are proposed to recover (almost)global synchronization properties. 1
TuB03.5 Natural frames and interacting particles in three dimensions
"... 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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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.
TimeCoordinated Path Following of Multiple UAVs Over TimeVarying Networks using L1 Adaptation." AIAA Guidance, Navigation and Control Conference and Exhibit, August 18, 2008  August 21 American Institute of Aeronautics and Astronautics Inc, 2008 http:/
"... Motivated by challenging mission scenarios, this paper tackles the problem of multiUnmanned Aerial Vehicle (UAV) cooperative control in the presence of timevarying communication networks. Specifically, we address the problem of steering a fleet of UAVs along given paths (path following) so as to ..."
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Cited by 1 (0 self)
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Motivated by challenging mission scenarios, this paper tackles the problem of multiUnmanned Aerial Vehicle (UAV) cooperative control in the presence of timevarying communication networks. Specifically, we address the problem of steering a fleet of UAVs along given paths (path following) so as to meet spatial and/or temporal constraints. One possible scenario is the situation where a fleet of vehicles is tasked to execute collisionfree maneuvers under strict spatial constraints and arrive at their final destinations at exactly the same time. The paper builds on previous work by the authors on coordinated path following and extends it to allow for timevarying communication topologies. Path following control in 3D builds on a nonlinear control strategy that is first derived at the kinematic level (outerloop control). This is followed by the design of an L1 adaptive output feedback control law that effectively augments an existing autopilot and yields an innerouter loop control structure with guaranteed performance. Multiple vehicle timecritical coordination is achieved by enforcing temporal constraints on the speed profiles of the vehicles along their paths in response to information exchanged over a dynamic communication network. We address explicitly the situation where each vehicle transmits