Multiagent Flocking Under General Communication Rule

In this paper, we consider a multiagent system consisting of mobile agents with second-order dynamics. The communication network is determined by a general interaction rule based on the distance between agents. The goal of this paper is to determine practical conditions ensuring that the agents asymptotically agree on a common velocity, i.e., a flocking behavior is achieved. Unlike previous studies on the topic, our results simultaneously satisfy the three following features: 1) our conditions apply to a model, which does not require long distance communication; 2) they only depend on the initial positions and velocities of the agents; and 3) most importantly, our results allow for the disconnection of communication links which are not necessary for flocking. To circumvent the difficulty arising from the state dependent dynamics, a suitable bounding process is used. We apply our result to two cases, where communication takes place either within deterministic or stochastic distance radiuses. Our result is illustrated through simulations.

[1]  Irinel-Constantin Morarescu,et al.  Set theory based condition in LMI form for network topology preservation for decentralized control , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[2]  Behrouz Touri,et al.  On Ergodicity, Infinite Flow, and Consensus in Random Models , 2010, IEEE Transactions on Automatic Control.

[3]  Giorgio Picci,et al.  Almost sure convergence of random gossip algorithms , 2007, 2007 46th IEEE Conference on Decision and Control.

[4]  Alireza Tahbaz-Salehi,et al.  On consensus over random networks , 2006 .

[5]  John S. Baras,et al.  Convergence Results for the Linear Consensus Problem under Markovian Random Graphs , 2013, SIAM J. Control. Optim..

[6]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[7]  Alireza Tahbaz-Salehi,et al.  Consensus Over Ergodic Stationary Graph Processes , 2010, IEEE Transactions on Automatic Control.

[8]  F. Cucker,et al.  Flocking in noisy environments , 2007, 0706.3343.

[9]  Maurizio Porfiri,et al.  Consensus Seeking Over Random Weighted Directed Graphs , 2007, IEEE Transactions on Automatic Control.

[10]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[11]  Alireza Tahbaz-Salehi,et al.  A Necessary and Sufficient Condition for Consensus Over Random Networks , 2008, IEEE Transactions on Automatic Control.

[12]  Craig W. Reynolds.  Flocks, herds, and schools: a distributed behavioral model , 1987, SIGGRAPH.

[13]  George J. Pappas,et al.  Flocking in Fixed and Switching Networks , 2007, IEEE Transactions on Automatic Control.

[14]  Mehran Mesbahi,et al.  Agreement over random networks , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[15]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[16]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[17]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[18]  Bernard Chazelle,et al.  The Convergence of Bird Flocking , 2009, JACM.

[19]  Soummya Kar,et al.  Sensor Networks With Random Links: Topology Design for Distributed Consensus , 2007, IEEE Transactions on Signal Processing.

[20]  A. Ozdaglar,et al.  Discrete Opinion Dynamics with Stubborn Agents , 2011 .

[21]  John N. Tsitsiklis,et al.  Distributed Asynchronous Deterministic and Stochastic Gradient Optimization Algorithms , 1984, 1984 American Control Conference.

[22]  Asuman E. Ozdaglar,et al.  Spread of (Mis)Information in Social Networks , 2009, Games Econ. Behav..

[23]  Chai Wah Wu,et al.  Synchronization and convergence of linear dynamics in random directed networks , 2006, IEEE Transactions on Automatic Control.

[24]  George J. Pappas,et al.  Hybrid Control for Connectivity Preserving Flocking , 2009, IEEE Transactions on Automatic Control.

[25]  J. Dall,et al.  Random geometric graphs. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  ScienceDirect,et al.  Deep sea research. Part II, Topical studies in oceanography , 1993 .

[27]  James G. Bellingham,et al.  Progress toward autonomous ocean sampling networks , 2009 .

[28]  Sandro Zampieri,et al.  Randomized consensus algorithms over large scale networks , 2007, 2007 Information Theory and Applications Workshop.

[29]  Antoine Girard,et al.  Sufficient conditions for flocking via graph robustness analysis , 2010, 49th IEEE Conference on Decision and Control (CDC).

[30]  Stephen B. Wicker,et al.  Connectivity of Finite Wireless Networks with Random Communication Range Nodes , 2009, 2009 IEEE International Conference on Communications.

[31]  Samuel Martin,et al.  Multi-agent flocking under topological interactions , 2013, Syst. Control. Lett..

[32]  A. Rollett,et al.  The Monte Carlo Method , 2004 .

[33]  J.N. Tsitsiklis,et al.  Convergence in Multiagent Coordination, Consensus, and Flocking , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[34]  R. Merris.  Laplacian matrices of graphs: a survey , 1994 .

[35]  Antoine Girard,et al.  Multi-agent flocking with random communication radius , 2012, 2012 American Control Conference (ACC).

[36]  Samuel Martin.  Coordination et robustesse des systèmes dynamiques multi-agents , 2012 .

[37]  Sonia Martínez,et al.  Coverage control for mobile sensing networks , 2002, IEEE Transactions on Robotics and Automation.

[38]  Ernesto Mordecki,et al.  Cucker-Smale Flocking Under Hierarchical Leadership and Random Interactions , 2009, SIAM J. Appl. Math..

[39]  Felipe Cucker,et al.  Emergent Behavior in Flocks , 2007, IEEE Transactions on Automatic Control.