Graph-theoretic connectivity control of mobile robot networks

In this paper, we provide a theoretical framework for controlling graph connectivity in mobile robot networks. We discuss proximity-based communication models composed of disk-based or uniformly-fading-signal-strength communication links. A graph-theoretic definition of connectivity is provided, as well as an equivalent definition based on algebraic graph theory, which employs the adjacency and Laplacian matrices of the graph and their spectral properties. Based on these results, we discuss centralized and distributed algorithms to maintain, increase, and control connectivity in mobile robot networks. The various approaches discussed in this paper range from convex optimization and subgradient-descent algorithms, for the maximization of the algebraic connectivity of the network, to potential fields and hybrid systems that maintain communication links or control the network topology in a least restrictive manner. Common to these approaches is the use of mobility to control the topology of the underlying communication network. We discuss applications of connectivity control to multirobot rendezvous, flocking and formation control, where so far, network connectivity has been considered an assumption.

[1]  Gaurav S. Sukhatme,et al.  Using Local Geometry for Tunable Topology Control in Sensor Networks , 2009, IEEE Transactions on Mobile Computing.

[2]  A. Jadbabaie,et al.  Distributed topology control of dynamic networks , 2008, 2008 American Control Conference.

[3]  Jack M. Holtzman,et al.  Wireless information networks , 2010, 2010 International Conference on Wireless Information Networks and Systems (WINSYS).

[4]  W ReynoldsCraig.  Flocks, herds and schools: A distributed behavioral model , 1987 .

[5]  Yasamin Mostofi,et al.  Decentralized Communication-Aware Motion Planning in Mobile Networks: An Information-Gain Approach , 2009, J. Intell. Robotic Syst..

[6]  Masafumi Yamashita,et al.  Distributed memoryless point convergence algorithm for mobile robots with limited visibility , 1999, IEEE Trans. Robotics Autom..

[7]  Nicola Santoro,et al.  Gathering of Asynchronous Oblivious Robots with Limited Visibility , 2001, STACS.

[8]  Amir G. Aghdam,et al.  A class of bounded distributed controllers for connectivity preservation of unicycles , 2010, 49th IEEE Conference on Decision and Control (CDC).

[9]  Aleksandar Neskovic,et al.  Modern approaches in modeling of mobile radio systems propagation environment , 2000, IEEE Communications Surveys & Tutorials.

[10]  Stephen P. Boyd.  Convex optimization of graph Laplacian eigenvalues , 2006 .

[11]  Oliver Sawodny,et al.  A distributed minimum restrictive connectivity maintenance algorithm , 2009 .

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

[13]  Nancy A. Lynch,et al.  Connectivity Service for Mobile Ad-Hoc Networks , 2008, 2008 Second IEEE International Conference on Self-Adaptive and Self-Organizing Systems Workshops.

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

[15]  Karl Henrik Johansson,et al.  Decentralized connectivity maintenance in mobile networks with bounded inputs , 2008, 2008 IEEE International Conference on Robotics and Automation.

[16]  Paramvir Bahl,et al.  A cone-based distributed topology-control algorithm for wireless multi-hop networks , 2005, IEEE/ACM Transactions on Networking.

[17]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[18]  Mireille E. Broucke,et al.  Local control strategies for groups of mobile autonomous agents , 2004, IEEE Transactions on Automatic Control.

[19]  Per Capita,et al.  About the authors , 1995, Machine Vision and Applications.

[20]  Pierre-Alexandre Bliman,et al.  Average consensus problems in networks of agents with delayed communications , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

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

[22]  Ram Ramanathan,et al.  Topology control of multihop wireless networks using transmit power adjustment , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[23]  Nicola Santoro,et al.  Gathering of asynchronous robots with limited visibility , 2005, Theor. Comput. Sci..

[24]  Naomi Ehrich Leonard,et al.  Virtual leaders, artificial potentials and coordinated control of groups , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[25]  George J. Pappas,et al.  Flocking while preserving network connectivity , 2007, 2007 46th IEEE Conference on Decision and Control.

[26]  Xiaoming Hu,et al.  Sufficient conditions for connectivity maintenance and rendezvous in leader-follower networks , 2010, Autom..

[27]  P. R. Kumar,et al.  Critical power for asymptotic connectivity , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

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

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

[30]  M.W. Spong,et al.  Multi-agent coordination under connectivity constraints , 2008, 2008 American Control Conference.

[31]  Vincent K. N. Lau,et al.  The Mobile Radio Propagation Channel , 2007 .

[32]  Vijay Kumar,et al.  Connectivity management in mobile robot teams , 2008, 2008 IEEE International Conference on Robotics and Automation.

[33]  M. Ani Hsieh,et al.  Maintaining network connectivity and performance in robot teams , 2008, J. Field Robotics.

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

[35]  Robert Tappan Morris,et al.  Span: An Energy-Efficient Coordination Algorithm for Topology Maintenance in Ad Hoc Wireless Networks , 2001, MobiCom '01.

[36]  Reid G. Simmons,et al.  Maintaining line of sight communications networks between planetary rovers , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[37]  Roger Wattenhofer,et al.  XTC: a practical topology control algorithm for ad-hoc networks , 2004, 18th International Parallel and Distributed Processing Symposium, 2004. Proceedings..

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

[39]  Richard M. Murray,et al.  Information flow and cooperative control of vehicle formations , 2004, IEEE Transactions on Automatic Control.

[40]  Matthew Powers,et al.  Value-Based Communication Preservation for Mobile Robots , 2004, DARS.

[41]  Miroslav Fiedler,et al.  Absolute algebraic connectivity of trees , 1990 .

[42]  Panganamala Ramana Kumar,et al.  The Number of Neighbors Needed for Connectivity of Wireless Networks , 2004, Wirel. Networks.

[43]  Ronald C. Arkin,et al.  Multi-robot communication-sensitive reconnaissance , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[44]  R.M. Murray,et al.  Distributed Averaging on Asynchronous Communication Networks , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[45]  Francesco Bullo,et al.  Multirobot Rendezvous With Visibility Sensors in Nonconvex Environments , 2006, IEEE Transactions on Robotics.

[46]  Paramvir Bahl,et al.  Analysis of a cone-based distributed topology control algorithm for wireless multi-hop networks , 2001, PODC '01.

[47]  Mireille E. Broucke,et al.  Local control strategies for groups of mobile autonomous agents , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[48]  François Baccelli,et al.  Impact of interferences on connectivity in ad hoc networks , 2005, IEEE/ACM Transactions on Networking.

[49]  David Kempe,et al.  A decentralized algorithm for spectral analysis , 2004, STOC '04.

[50]  Vijay Kumar,et al.  Maintaining Connectivity in Mobile Robot Networks , 2008, ISER.

[51]  Francesco Bullo,et al.  Maintaining limited-range connectivity among second-order agents , 2006 .

[52]  Richard M. Murray,et al.  Flocking with obstacle avoidance: cooperation with limited communication in mobile networks , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

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

[54]  Andrea J. Goldsmith,et al.  Design challenges for energy-constrained ad hoc wireless networks , 2002, IEEE Wirel. Commun..

[55]  Mehran Mesbahi,et al.  On state-dependent dynamic graphs and their controllability properties , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

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

[57]  Lui Sha,et al.  Design and analysis of an MST-based topology control algorithm , 2005, IEEE Trans. Wirel. Commun..

[58]  George J. Pappas,et al.  Distributed Connectivity Control of Mobile Networks , 2008, IEEE Trans. Robotics.

[59]  Luis Montano,et al.  Enforcing Network Connectivity in Robot Team Missions , 2010, Int. J. Robotics Res..

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

[61]  G. Galvin,et al.  Global connectivity from local geometric constraints for sensor networks with various wireless footprints , 2006, 2006 5th International Conference on Information Processing in Sensor Networks.

[62]  Magnus Egerstedt,et al.  Graph Theoretic Methods in Multiagent Networks , 2010, Princeton Series in Applied Mathematics.

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

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

[65]  Jorge Cortés,et al.  Distributed Tree Rearrangements for Reachability and Robust Connectivity , 2009, SIAM J. Control. Optim..

[66]  M. Fiedler.  Algebraic connectivity of graphs , 1973 .

[67]  R.M. Murray,et al.  Motion planning with wireless network constraints , 2005, Proceedings of the 2005, American Control Conference, 2005..

[68]  Siddhartha S. Srinivasa,et al.  Decentralized estimation and control of graph connectivity in mobile sensor networks , 2008, 2008 American Control Conference.

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

[70]  Robert Shorten,et al.  A framework for decentralised feedback connectivity control with application to sensor networks , 2010, Int. J. Control.

[71]  A. Barbosa,et al.  The effects of predation risk on scanning and flocking behavior in dunlin , 1997 .

[72]  Jorge Cortés,et al.  Distributed Motion Constraints for Algebraic Connectivity of Robotic Networks , 2008, 2008 47th IEEE Conference on Decision and Control.

[73]  Sandip Roy,et al.  On the structure of graph edge designs that optimize the algebraic connectivity , 2008, 2008 47th IEEE Conference on Decision and Control.

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

[75]  Vijay Kumar,et al.  Experimental Testbed for Large Multirobot Teams , 2008, IEEE Robotics Autom. Mag..

[76]  Magnus Egerstedt,et al.  Distributed Coordination Control of Multiagent Systems While Preserving Connectedness , 2007, IEEE Transactions on Robotics.

[77]  Michael William Newman,et al.  The Laplacian spectrum of graphs , 2001 .

[78]  Geoffrey A. Hollinger,et al.  Multi-robot coordination with periodic connectivity , 2010, 2010 IEEE International Conference on Robotics and Automation.

[79]  Madhav V. Marathe,et al.  Algorithmic Aspects of Topology Control Problems for Ad Hoc Networks , 2005, Mob. Networks Appl..

[80]  Jorge Cortés,et al.  Distributed algorithms for reaching consensus on general functions , 2008, Autom..

[81]  Stephen P. Boyd,et al.  Growing Well-connected Graphs , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[82]  George J. Pappas,et al.  Controlling Connectivity of Dynamic Graphs , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[83]  Siddhartha S. Srinivasa,et al.  Decentralized estimation and control of graph connectivity in mobile sensor networks , 2008, ACC.

[84]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[85]  Francesco Bullo,et al.  Distributed Control of Robotic Networks , 2009 .

[86]  J. Toner,et al.  Flocks, herds, and schools: A quantitative theory of flocking , 1998, cond-mat/9804180.

[87]  Laura Giarré,et al.  Non-linear protocols for optimal distributed consensus in networks of dynamic agents , 2006, Syst. Control. Lett..

[88]  Ronald C. Arkin,et al.  Line-of-sight constrained exploration for reactive multiagent robotic teams , 2002, 7th International Workshop on Advanced Motion Control. Proceedings (Cat. No.02TH8623).

[89]  Kamal K. Gupta,et al.  Backbone-based connectivity control for mobile networks , 2009, 2009 IEEE International Conference on Robotics and Automation.

[90]  B. Mohar.  THE LAPLACIAN SPECTRUM OF GRAPHS y , 1991 .

[91]  Mehran Mesbahi,et al.  On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian , 2006, IEEE Transactions on Automatic Control.

[92]  David Kempe,et al.  A decentralized algorithm for spectral analysis , 2008, J. Comput. Syst. Sci..

[93]  Dimos V. Dimarogonas,et al.  Connectedness Preserving Distributed Swarm Aggregation for Multiple Kinematic Robots , 2008, IEEE Transactions on Robotics.

[94]  J. Cortés.  Achieving coordination tasks in finite time via nonsmooth gradient flows , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[95]  Robert Shorten,et al.  A framework for decentralised feedback connectivity control with application to sensor networks , 2009, Int. J. Control.

[96]  Amir G. Aghdam,et al.  A Class of Bounded Distributed Control Strategies for Connectivity Preservation in Multi-Agent Systems , 2010, IEEE Transactions on Automatic Control.