Rigid formations of autonomous agents

This thesis addresses rigid formations of autonomous agents. A key element in all future multi-agent systems will be the role of sensor and communication networks as an integral part of coordination. Network topologies are critically important for autonomous systems involving mobile underwater, ground and air vehicles and for sensor networks. This thesis focuses on developing techniques and strategies for the analysis and design of sensor and network topologies required to achieve a rigid formation for cooperative tasks. We address using different types of information, such as distances, directions, bearings, and angles between agents, to maintain rigid formations. Energy efficiency and communication bandwidth are critically important in formations of mobile autonomous agents, and hence strategies that make efficient use of power and energy are beneficial. Therefore, we develop topologies for providing sensing and communications with the minimum number of links, and propose methods requiring the minimum number of changes in the set of links in dynamic missions and maneuvers, including agent departure from a rigid formation, splitting a rigid formation and merging rigid sub-formations. To do this in a systematic manner, it is necessary to develop a framework for modeling agent formations that characterizes the communication/sensing links needed to maintain the formations. The challenge is that a comprehensive theory of such topologies of formations with sensing/communication limitations is in the earliest stage of development. We propose to use triangulations for creating sensing/communication links between agents. We address their local properties in rigidity. In particular, we propose to use the Delaunay triangulations. We address their geometric properties that are useful in formations. We also address and formulate the localization problem in sensor networks and formations of multiple mobile autonomous agents. Then we propose to use global rigidity in the study of this problem. Central to the development of these techniques and strategies will be the use of tools from rigidity theory, discrete and computational geometry, CAD programming and graph theory.

[1]  Brad Karp,et al.  GPSR: greedy perimeter stateless routing for wireless networks , 2000, MobiCom '00.

[2]  Robert Connelly,et al.  Generic Global Rigidity , 2005, Discret. Comput. Geom..

[3]  Kar-Han Tan,et al.  High Precision Formation Control of Mobile Robots Using Virtual Structures , 1997, Auton. Robots.

[4]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[5]  J.P. Desai,et al.  Control of changes in formation for a team of mobile robots , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[6]  R. D'Andrea,et al.  Distributed control of close formation flight , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

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

[8]  David Eppstein,et al.  The expected extremes in a Delaunay triangulation , 1991, Int. J. Comput. Geom. Appl..

[9]  Michael Emile Hermary.  Rigidity of graphs , 1986 .

[10]  Peter J Seiler,et al.  Analysis of bird formations , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

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

[12]  George J. Pappas,et al.  Feasible formations of multi-agent systems , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[13]  Vijay Kumar,et al.  Motion planning with uncertainty , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

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

[15]  B. Anderson,et al.  Structural controllability and matrix nets , 1982 .

[16]  R.M. Murray,et al.  Distributed structural stabilization and tracking for formations of dynamic multi-agents , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[17]  John Zahorjan,et al.  The challenges of mobile computing , 1994, Computer.

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

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

[20]  W. Whiteley,et al.  Statics of Frameworks and Motions of Panel Structures: A projective Geometric Introduction , 1982 .

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

[22]  Lebrecht Henneberg,et al.  Die graphische Statik der Starren Systeme , 1911 .

[23]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[24]  A. Recski.  Matroid theory and its applications in electric network theory and in statics , 1989 .

[25]  Mani B. Srivastava,et al.  Dynamic fine-grained localization in Ad-Hoc networks of sensors , 2001, MobiCom '01.

[26]  K. Passino,et al.  A class of attraction/repulsion functions for stable swarm aggregations , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[27]  Robert E. Tarjan,et al.  Dividing a Graph into Triconnected Components , 1973, SIAM J. Comput..

[28]  J. Shewchuk,et al.  Delaunay refinement mesh generation , 1997 .

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

[30]  Hiroshi Imai,et al.  On combinatorial structures of line drawings of polyhedra , 1985, Discret. Appl. Math..

[31]  Walter Whiteley,et al.  Constraining Plane Configurations in Computer-Aided Design: Combinatorics of Directions and Lengths , 1999, SIAM J. Discret. Math..

[32]  Bill Jackson,et al.  Egerváry Research Group on Combinatorial Optimization Connected Rigidity Matroids and Unique Realizations of Graphs Connected Rigidity Matroids and Unique Realizations of Graphs , 2022 .

[33]  Tian He,et al.  Range-free localization schemes in large scale sensor network , 2003, MobiCom 2003.

[34]  Walter Whiteley,et al.  A matroid on hypergraphs, with applications in scene analysis and geometry , 1989, Discret. Comput. Geom..

[35]  Tiong-Seng Tay,et al.  Rigidity of multi-graphs. I. Linking rigid bodies in n-space , 1984, J. Comb. Theory, Ser. B.

[36]  Vijay Kumar,et al.  Motion generation for formations of robots: A geometric approach , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[37]  Mark Weiser,et al.  Some Computer Science Problems in Ubiquitous Computing , 1993 .

[38]  Gary L. Miller,et al.  A new graph triconnectivity algorithm and its parallelization , 1992, Comb..

[39]  Robin Sibson,et al.  Locally Equiangular Triangulations , 1978, Comput. J..

[40]  B. R. Badrinath,et al.  Ad hoc positioning system (APS) using AOA , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[41]  Walter Whiteley,et al.  Rigidity and scene analysis , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

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

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

[44]  Harold N. Gabow,et al.  Forests, frames, and games: Algorithms for matroid sums and applications , 1992, STOC '88.

[45]  Herbert Edelsbrunner,et al.  Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.

[46]  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).

[47]  J. A. Fax,et al.  Graph Laplacians and Stabilization of Vehicle Formations , 2002 .

[48]  John Baillieul,et al.  Information patterns and Hedging Brockett's theorem in controlling vehicle formations , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[49]  Béla Bollobás,et al.  Modern Graph Theory , 2002, Graduate Texts in Mathematics.

[50]  J. P. Corfmat,et al.  Structurally controllable and structurally canonical systems , 1976 .

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

[52]  杉原 厚吉,et al.  On Redundant Bracing in Plane Skeletal Structures , 1980 .

[53]  B. Hofmann-Wellenhof,et al.  Global Positioning System , 1992 .

[54]  David P. Dobkin,et al.  Delaunay graphs are almost as good as complete graphs , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[55]  Frank Harary,et al.  Graph Theory , 2016 .

[56]  Walter Whiteley,et al.  Vertex Splitting in Isostatic Frameworks , 1990 .

[57]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[58]  Vijay Kumar,et al.  Stability Properties of Interconnected Vehicles , 2002 .

[59]  Walter Whiteley,et al.  Some matroids from discrete applied geometry , 1996 .

[60]  Bruce Hendrickson,et al.  Conditions for Unique Graph Realizations , 1992, SIAM J. Comput..

[61]  Peter N. Belhumeur,et al.  Closing ranks in vehicle formations based on rigidity , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[62]  Vijay Kumar,et al.  Controlling formations of multiple mobile robots , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

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

[64]  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..

[65]  B. Anderson,et al.  Sensor and network topologies of formations with direction, bearing, and angle information between agents , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).