Flocking while preserving network connectivity

Coordinated motion of multiple agents raises fundamental and novel problems in control theory and robotics. In particular, in applications such as consensus seeking or flocking by a group of mobile agents, a great new challenge is the development of robust distributed motion algorithms that can always achieve the desired coordination. In this paper, we address this challenge by embedding the requirement for connectivity of the underlying communication network in the controller specifications. We employ double integrator models for the agents and design nearest neighbor control laws, based on potential fields, that serve a twofold objective. First, they contribute to velocity alignment in the system and second, they regulate switching among different network topologies so that the connectivity requirement is always met. Collision avoidance among neighboring agents is also ensured and under the assumption that the initial network is connected, the overall system is shown to asymptotically flock for all initial conditions. In particular, it is shown that flocking is achieved even in sparse communication networks where connectivity is more prone to failure. We conclude by illustrating a class of interesting problems that can be achieved while preserving connectivity.

[1]  Petter Ögren,et al.  A control Lyapunov function approach to multi-agent coordination , 2001 .

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

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

[4]  Meng Ji,et al.  Distributed Formation Control While Preserving Connectedness , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[5]  Dimos V. Dimarogonas,et al.  A feedback stabilization and collision avoidance scheme for multiple independent non-point agents, , 2006, Autom..

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

[7]  Kostas Daniilidis,et al.  Vision-based Distributed Coordination and Flocking of Multi-agent Systems , 2005, Robotics: Science and Systems.

[8]  R. Murray,et al.  Robust connectivity of networked vehicles , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[9]  Jie Lin,et al.  The multi-agent rendezvous problem , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[10]  Xiaoming Hu,et al.  A control Lyapunov function approach to multiagent coordination , 2002, IEEE Trans. Robotics Autom..

[11]  Craig W. Reynolds Flocks, herds, and schools: a distributed behavioral model , 1998 .

[12]  George J. Pappas,et al.  Distributed connectivity control of mobile networks , 2007, 2007 46th IEEE Conference on Decision and Control.

[13]  M. Mesbahi On State-dependent dynamic graphs and their controllability properties , 2005, IEEE Transactions on Automatic Control.

[14]  Naomi Ehrich Leonard,et al.  Stabilization of Planar Collective Motion: All-to-All Communication , 2007, IEEE Transactions on Automatic Control.

[15]  Vijay Kumar,et al.  Modeling and control of formations of nonholonomic mobile robots , 2001, IEEE Trans. Robotics Autom..

[16]  L. Edelstein-Keshet,et al.  Complexity, pattern, and evolutionary trade-offs in animal aggregation. , 1999, Science.

[17]  R. Beard,et al.  Consensus of information under dynamically changing interaction topologies , 2004, Proceedings of the 2004 American Control Conference.

[18]  George J. Pappas,et al.  Potential Fields for Maintaining Connectivity of Mobile Networks , 2007, IEEE Transactions on Robotics.

[19]  Petter Ögren,et al.  Cooperative control of mobile sensor networks:Adaptive gradient climbing in a distributed environment , 2004, IEEE Transactions on Automatic Control.

[20]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[21]  Norman Biggs Algebraic Graph Theory: Index , 1974 .

[22]  Tucker R. Balch,et al.  Behavior-based formation control for multirobot teams , 1998, IEEE Trans. Robotics Autom..

[23]  Kevin M. Passino,et al.  Stability analysis of swarms , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[24]  Sonia Martínez,et al.  Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions , 2006, IEEE Transactions on Automatic Control.

[25]  Ali Jadbabaie,et al.  Decentralized Control of Connectivity for Multi-Agent Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

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

[27]  Vijay Kumar,et al.  Controlling Swarms of Robots Using Interpolated Implicit Functions , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[28]  Gaurav S. Sukhatme,et al.  Constrained coverage for mobile sensor networks , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[29]  Gerardo Lafferriere,et al.  Decentralized control of vehicle formations , 2005, Syst. Control. Lett..