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192
Flocking for MultiAgent Dynamic Systems: Algorithms and Theory
, 2006
"... In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in freespace and presence of multiple obstacles are considered. We present three flocking algorithms: two for freeflocking and one for constrained flocking. A compre ..."
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Cited by 436 (2 self)
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In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in freespace and presence of multiple obstacles are considered. We present three flocking algorithms: two for freeflocking and one for constrained flocking. A comprehensive analysis of the first two algorithms is provided. We demonstrate the first algorithm embodies all three rules of Reynolds. This is a formal approach to extraction of interaction rules that lead to the emergence of collective behavior. We show that the first algorithm generically leads to regular fragmentation, whereas the second and third algorithms both lead to flocking. A systematic method is provided for construction of cost functions (or collective potentials) for flocking. These collective potentials penalize deviation from a class of latticeshape objects called αlattices. We use a multispecies framework for construction of collective potentials that consist of flockmembers, or αagents, and virtual agents associated with αagents called β and γagents. We show that migration of flocks can be performed using a peertopeer network of agents, i.e. “flocks need no leaders.” A “universal” definition of flocking for particle systems with similarities to Lyapunov stability is given. Several simulation results are provided that demonstrate performing 2D and 3D flocking, split/rejoin maneuver, and squeezing maneuver for hundreds of agents using the proposed algorithms.
Distributed consensus algorithms in sensor networks with communication channel noise and random link failures
 in Proc. 41st Asilomar Conf. Signals, Systems, Computers
, 2007
"... Abstract—The paper studies average consensus with random topologies (intermittent links) and noisy channels. Consensus with noise in the network links leads to the biasvariance dilemma—running consensus for long reduces the bias of the final average estimate but increases its variance. We present t ..."
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Cited by 149 (21 self)
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Abstract—The paper studies average consensus with random topologies (intermittent links) and noisy channels. Consensus with noise in the network links leads to the biasvariance dilemma—running consensus for long reduces the bias of the final average estimate but increases its variance. We present two different compromises to this tradeoff: the algorithm modifies conventional consensus by forcing the weights to satisfy a persistence condition (slowly decaying to zero;) and the algorithm where the weights are constant but consensus is run for a fixed number of iterations, then it is restarted and rerun for a total of runs, and at the end averages the final states of the runs (Monte Carlo averaging). We use controlled Markov processes and stochastic approximation arguments to prove almost sure convergence of to a finite consensus limit and compute explicitly the mean square error (mse) (variance) of the consensus limit. We show that represents the best of both worlds—zero bias and low variance—at the cost of a slow convergence rate; rescaling the weights balances the variance versus the rate of bias reduction (convergence rate). In contrast, , because of its constant weights, converges fast but presents a different biasvariance tradeoff. For the same number of iterations, shorter runs (smaller) lead to high bias but smaller variance (larger number of runs to average over.) For a static nonrandom network with Gaussian noise, we compute the optimal gain for to reach in the shortest number of iterations, with high probability (1), ()consensus ( residual bias). Our results hold under fairly general assumptions on the random link failures and communication noise. Index Terms—Additive noise, consensus, sensor networks, stochastic approximation, random topology. I.
Distributed Connectivity Control of Mobile Networks
, 2007
"... Control of mobile networks raises fundamental and novel problems in controlling the structure of the resulting dynamic graphs. In particular, in applications involving mobile sensor networks and multiagent systems, a great new challenge is the development of distributed motion algorithms that guara ..."
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Cited by 75 (10 self)
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Control of mobile networks raises fundamental and novel problems in controlling the structure of the resulting dynamic graphs. In particular, in applications involving mobile sensor networks and multiagent systems, a great new challenge is the development of distributed motion algorithms that guarantee connectivity of the overall network. In this paper, we address this challenge using a novel control decomposition. First, motion control is performed in the continuous state space, where nearest neighbor potential fields are used to maintain existing links in the network. Second, distributed coordination protocols in the discrete graph space ensure connectivity of the switching network topology. Coordination is based on locally updated estimates of the abstract network topology by every agent as well as distributed auctions that enable tie breaking whenever simultaneous link deletions may violate connectivity. Integration of the overall system results in a distributed, multiagent, hybrid system for which we show that, under certain secondary objectives on the agents and the assumption that the initial network is connected, the resulting motion always satisfies connectivity of the network. Our approach can also account for communication time delays in the network as well as collision avoidance, while its efficiency is illustrated in nontrivial computer simulations.
Decentralized control of vehicle formations
, 2005
"... This paper investigates a method for decentralized stabilization of vehicle formations using techniques from algebraic graph theory. The vehicles exchange information according to a prespecified communication digraph, G. A feedback control is designed using relative information between a vehicle an ..."
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Cited by 68 (0 self)
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This paper investigates a method for decentralized stabilization of vehicle formations using techniques from algebraic graph theory. The vehicles exchange information according to a prespecified communication digraph, G. A feedback control is designed using relative information between a vehicle and its inneighbors in G. We prove that a necessary and sufficient condition for an appropriate decentralized linear stabilizing feedback to exist is that G has a rooted directed spanning tree. We show the direct relationship between the rate of convergence to formation and the eigenvalues of the (directed) Laplacian of G. Various special situations are discussed, including symmetric communication graphs and formations with leaders. Several numerical simulations are used to illustrate the results.
On consensus algorithms for doubleintegrator dynamics
"... Abstract — This paper extends some existing results in consensus algorithms for doubleintegrator dynamics. We propose consensus algorithms for doubleintegrator dynamics in four cases: (i) with a bounded control input, (ii) without relative velocity measurement, (iii) without relative velocity me ..."
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Cited by 68 (6 self)
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Abstract — This paper extends some existing results in consensus algorithms for doubleintegrator dynamics. We propose consensus algorithms for doubleintegrator dynamics in four cases: (i) with a bounded control input, (ii) without relative velocity measurement, (iii) without relative velocity measurement in the presence of a group reference velocity, and (iv) with a bounded control input and with partial access to a group reference state. We show that consensus is reached asymptotically for the first two cases if the undirected interaction graph is connected. We further show that consensus is reached asymptotically for the third case if the directed interaction graph has a directed spanning tree and the gain for velocity matching with the group reference velocity is above a certain bound. We also show that consensus is reached asymptotically for the fourth case if and only if the group reference state flows directly or indirectly to all of the vehicles in the team. I.
Finitetime convergent gradient flows with applications to network consensus
 Automatica
"... 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 finitetime convergence. We d ..."
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Cited by 66 (5 self)
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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 finitetime convergence. We discuss the application of the results to the design of multiagent 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.
Decentralized, Adaptive Coverage Control for Networked Robots
, 2007
"... 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 ..."
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Cited by 44 (7 self)
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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
Distributed control of robotic networks: a mathematical approach to motion coordination algorithms
, 2009
"... (i) You are allowed to freely download, share, print, or photocopy this document. (ii) You are not allowed to modify, sell, or claim authorship of any part of this document. (iii) We thank you for any feedback information, including errors, suggestions, evaluations, and teaching or research uses. 2 ..."
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Cited by 41 (1 self)
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(i) You are allowed to freely download, share, print, or photocopy this document. (ii) You are not allowed to modify, sell, or claim authorship of any part of this document. (iii) We thank you for any feedback information, including errors, suggestions, evaluations, and teaching or research uses. 2 “Distributed Control of Robotic Networks ” by F. Bullo, J. Cortés and S. Martínez
Dynamic assignment in distributed motion planning with local information
 IEEE TRANSACTIONS ON ROBOTICS
, 2008
"... Distributed motion planning of multiple agents raises fundamental and novel problems in control theory and robotics. In particular, in applications such as coverage by mobile sensor networks or multiple target tracking, a great new challenge is the development of motion planning algorithms that dyna ..."
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Cited by 40 (4 self)
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Distributed motion planning of multiple agents raises fundamental and novel problems in control theory and robotics. In particular, in applications such as coverage by mobile sensor networks or multiple target tracking, a great new challenge is the development of motion planning algorithms that dynamically assign targets or destinations to multiple homogeneous agents, not relying on any aprioriassignment of agents to destinations. In this paper, we address this challenge using two novel ideas. First, distributed multidestination potential fields are developed that are able to drive every agent to any available destination. Second, nearest neighbor coordination protocols are developed ensuring that distinct agents are assigned to distinct destinations. Integration of the overall system results in a distributed, multiagent, hybrid system for which we show that the mutual exclusion property of the final assignment is guaranteed for almost all initial conditions. Furthermore, we show that our dynamic assignment algorithm will converge after exploring at most a polynomial number of assignments, dramatically reducing the combinatorial nature of purely discrete assignment problems. Our scalable approach is illustrated with nontrivial computer simulations.