Distributed combinatorial rigidity control in multi-agent networks

In this paper, we propose a distributed control law to maintain the combinatorial rigidity of a multi-agent system in the plane, when interaction is proximity-limited. Motivated by the generic properties of rigidity as a function of the underlying network graph, local link addition and deletion rules are proposed that preserve combinatorial rigidity through agent mobility. Specifically, redundancy of network links over local sub-graphs allows the determination of topological transitions that preserve rigidity. It is shown that local redundancy of a network link is sufficient for global redundancy, and thus applying minimal communication, and computation that scales like O(n2), the generic topological rigidity of a network can be preserved.

[1]  T. Eren,et al.  Using Angle of Arrival (Bearing) Information in Network Localization , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[2]  Antonio Franchi,et al.  Rigidity Maintenance Control for Multi-Robot Systems , 2012, Robotics: Science and Systems.

[3]  H. Gluck.  Almost all simply connected closed surfaces are rigid , 1975 .

[4]  Andrea Gasparri,et al.  Decentralized centroid estimation for multi-agent systems in absence of a common reference frame: A convergence analysis , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

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

[6]  Christos G. Cassandras,et al.  Distributed Coverage Control and Data Collection With Mobile Sensor Networks , 2010, IEEE Transactions on Automatic Control.

[7]  Gaurav S. Sukhatme,et al.  Constrained Interaction and Coordination in Proximity-Limited Multiagent Systems , 2013, IEEE Transactions on Robotics.

[8]  B. Hendrickson,et al.  Regular ArticleAn Algorithm for Two-Dimensional Rigidity Percolation: The Pebble Game , 1997 .

[9]  J. Hendrickx,et al.  Rigid graph control architectures for autonomous formations , 2008, IEEE Control Systems.

[10]  Mac Schwager,et al.  Persistent Robotic Tasks: Monitoring and Sweeping in Changing Environments , 2011, IEEE Transactions on Robotics.

[11]  Mireille E. Broucke,et al.  Stabilization of infinitesimally rigid formations of multi-robot networks , 2008, 2008 47th IEEE Conference on Decision and Control.

[12]  G. Laman.  On graphs and rigidity of plane skeletal structures , 1970 .

[13]  B. Roth,et al.  The rigidity of graphs, II , 1979 .

[14]  W. Whiteley,et al.  Generating Isostatic Frameworks , 1985 .

[15]  L. Lovász,et al.  On Generic Rigidity in the Plane , 1982 .

[16]  Richard M. Murray,et al.  DISTRIBUTED COOPERATIVE CONTROL OF MULTIPLE VEHICLE FORMATIONS USING STRUCTURAL POTENTIAL FUNCTIONS , 2002 .

[17]  B. Hendrickson,et al.  An Algorithm for Two-Dimensional Rigidity Percolation , 1997 .

[18]  R. Murray,et al.  Graph rigidity and distributed formation stabilization of multi-vehicle systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

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

[20]  Frank Allgöwer,et al.  Growing optimally rigid formations , 2012, 2012 American Control Conference (ACC).

[21]  Gaurav S. Sukhatme,et al.  Probabilistic spatial mapping and curve tracking in distributed multi-agent systems , 2012, 2012 IEEE International Conference on Robotics and Automation.

[22]  Gaurav S. Sukhatme,et al.  Topology-constrained flocking in locally interacting mobile networks , 2013, 2013 IEEE International Conference on Robotics and Automation.

[23]  Yasamin Mostofi,et al.  Communication-aware surveillance in mobile sensor networks , 2011, Proceedings of the 2011 American Control Conference.

[24]  Brian D. O. Anderson,et al.  Analysis of Noisy Bearing-Only Network Localization , 2013, IEEE Transactions on Automatic Control.

[25]  Fumin Zhang,et al.  Robust Cooperative Exploration With a Switching Strategy , 2012, IEEE Transactions on Robotics.

[26]  B. Anderson,et al.  A FRAMEWORK FOR MAINTAINING FORMATIONS BASED ON RIGIDITY , 2002 .

[27]  Reza Olfati-Saber,et al.  Collaborative target tracking using distributed Kalman filtering on mobile sensor networks , 2011, Proceedings of the 2011 American Control Conference.

[28]  B. Roth,et al.  The rigidity of graphs , 1978 .