A survey of multi-agent formation control : Position-, displacement-, and distance-based approaches

This report presents a brief survey of formation control of multi-agent systems. Focusing on types of actively controlled variables to achieve prescribed desired formations, we categorize the existing results on formation control into position, displacement-, and distance-based approaches. We summarize typical problem formulations in the approaches and review the existing results. Then, we provide some comments on these approaches as well as possible future research directions. Some other important recent results are also briefly reviewed.

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

[2]  Anthony Man-Cho So,et al.  Theory of semidefinite programming for Sensor Network Localization , 2005, SODA '05.

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

[4]  Yinyu Ye,et al.  Semidefinite programming for ad hoc wireless sensor network localization , 2004, Third International Symposium on Information Processing in Sensor Networks, 2004. IPSN 2004.

[5]  Jiangping Hu,et al.  Tracking control for multi-agent consensus with an active leader and variable topology , 2006, Autom..

[6]  Karl Henrik Johansson,et al.  On the stability of distance-based formation control , 2008, 2008 47th IEEE Conference on Decision and Control.

[7]  H.G. Tanner,et al.  On the controllability of nearest neighbor interconnections , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[8]  George J. Pappas,et al.  Input-to-state stability on formation graphs , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

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

[10]  Chi-Tsong Chen,et al.  Linear System Theory and Design , 1995 .

[11]  Ying Zhang,et al.  Localization from mere connectivity , 2003, MobiHoc '03.

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

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

[14]  George J. Pappas,et al.  Stable flocking of mobile agents part I: dynamic topology , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[15]  R. Beard,et al.  Formation feedback control for multiple spacecraft via virtual structures , 2004 .

[16]  Vincent D. Blondel,et al.  Three and higher dimensional autonomous formations: Rigidity, persistence and structural persistence , 2007, Autom..

[17]  B. Francis,et al.  Stabilizing a Multi-Agent System to an Equilateral Polygon Formation , 2006 .

[18]  Hyo-Sung Ahn,et al.  Distance-based formation control using euclidean distance dynamics matrix: Three-agent case , 2011, Proceedings of the 2011 American Control Conference.

[19]  Brian D. O. Anderson,et al.  Control of a three-coleader formation in the plane , 2007, Syst. Control. Lett..

[20]  Randal W. Beard,et al.  A coordination architecture for spacecraft formation control , 2001, IEEE Trans. Control. Syst. Technol..

[21]  Hyo-Sung Ahn,et al.  Formation Control of Mobile Agents Based on Distributed Position Estimation , 2013, IEEE Transactions on Automatic Control.

[22]  S. E. Tuna.  LQR-based coupling gain for synchronization of linear systems , 2008, 0801.3390.

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

[24]  Hyo-Sung Ahn,et al.  Formation control of mobile agents without an initial common sense of orientation , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

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

[26]  Kar-Han Tan,et al.  Virtual structures for high-precision cooperative mobile robotic control , 1996, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. IROS '96.

[27]  B. Anderson,et al.  Directed graphs for the analysis of rigidity and persistence in autonomous agent systems , 2007 .

[28]  Nathan van de Wouw,et al.  Formation control of unicycle mobile robots: a virtual structure approach , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[29]  Hyo-Sung Ahn,et al.  Formation control of mobile agent groups based on localization , 2011, 2011 IEEE International Symposium on Intelligent Control.

[30]  M. Egerstedt,et al.  Leader-based multi-agent coordination: controllability and optimal control , 2006, 2006 American Control Conference.

[31]  Kevin L. Moore,et al.  High-Order and Model Reference Consensus Algorithms in Cooperative Control of MultiVehicle Systems , 2007 .

[32]  Hyo-Sung Ahn,et al.  Formation control of mobile agents based on inter-agent distance dynamics , 2011, Autom..

[33]  Timothy W. McLain,et al.  Coordination Variables and Consensus Building in Multiple Vehicle Systems , 2004 .

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

[35]  Mehran Mesbahi,et al.  On the controlled agreement problem , 2006, 2006 American Control Conference.

[36]  Hyo-Sung Ahn,et al.  Distance-based formation control using Euclidean distance dynamics matrix: General cases , 2011, Proceedings of the 2011 American Control Conference.

[37]  Florian Dörfler,et al.  Formation control of autonomous robots based on cooperative behavior , 2009, 2009 European Control Conference (ECC).

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

[39]  Tyler H. Summers,et al.  Control of triangle formations with a mix of angle and distance constraints , 2012, 2012 IEEE International Conference on Control Applications.

[40]  Brian D. O. Anderson,et al.  Control of Minimally Persistent Formations in the Plane , 2009, SIAM J. Control. Optim..

[41]  L. Moreau,et al.  Stability of continuous-time distributed consensus algorithms , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[42]  Dimos V. Dimarogonas,et al.  A connection between formation infeasibility and velocity alignment in kinematic multi-agent systems , 2008, Autom..

[43]  Hyo-Sung Ahn,et al.  Modified gradient control for acyclic minimally persistent formations to escape from collinear position , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

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

[45]  Adrian N. Bishop.  Distributed Bearing-Only Quadrilateral Formation Control , 2011 .

[46]  Hyo-Sung Ahn,et al.  Distance-based control of cycle-free persistent formations , 2011, 2011 IEEE International Symposium on Intelligent Control.

[47]  Alan J. Laub,et al.  Matrix analysis - for scientists and engineers , 2004 .

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

[49]  George J. Pappas,et al.  Stable flocking of mobile agents, part I: fixed topology , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[50]  Jay A. Farrell,et al.  Consensus of multiple nonholonomic systems , 2008, 2008 47th IEEE Conference on Decision and Control.

[51]  Brian D. O. Anderson,et al.  Control of acyclic formations of mobile autonomous agents , 2008, 2008 47th IEEE Conference on Decision and Control.

[52]  Karl H. Johansson,et al.  Further results on the stability of distance-based multi-robot formations , 2009, 2009 American Control Conference.

[53]  Brian D. O. Anderson,et al.  Stabilization of rigid formations with direction-only constraints , 2011, IEEE Conference on Decision and Control and European Control Conference.

[54]  Chris Arney.  Sync: The Emerging Science of Spontaneous Order , 2007 .

[55]  Karl Henrik Johansson,et al.  Stability analysis for multi-agent systems using the incidence matrix: Quantized communication and formation control , 2010, Autom..

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

[57]  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).

[58]  Brian D. O. Anderson,et al.  A Theory of Network Localization , 2006, IEEE Transactions on Mobile Computing.

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

[60]  Frank L. Lewis,et al.  Optimal Design for Synchronization of Cooperative Systems: State Feedback, Observer and Output Feedback , 2011, IEEE Transactions on Automatic Control.

[61]  A.S. Morse,et al.  Information structures to secure control of rigid formations with leader-follower architecture , 2005, Proceedings of the 2005, American Control Conference, 2005..

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

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

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

[65]  Henry Wolkowicz,et al.  Solving Euclidean Distance Matrix Completion Problems Via Semidefinite Programming , 1999, Comput. Optim. Appl..

[66]  F. Bullo,et al.  Topological equivalence of a structure-preserving power network model and a non-uniform Kuramoto model of coupled oscillators , 2011, IEEE Conference on Decision and Control and European Control Conference.

[67]  Tyler H. Summers,et al.  Controlling rectangular formations , 2011, 2011 Australian Control Conference.

[68]  Brian D. O. Anderson,et al.  Wireless sensor network localization techniques , 2007, Comput. Networks.

[69]  B. Anderson,et al.  Controlling Four Agent Formations , 2010 .

[70]  Adrian N. Bishop,et al.  Bearing-only triangular formation control on the plane and the sphere , 2010, 18th Mediterranean Conference on Control and Automation, MED'10.

[71]  Wei Ren,et al.  Multi-vehicle consensus with a time-varying reference state , 2007, Syst. Control. Lett..

[72]  Adrian N. Bishop,et al.  A Very Relaxed Control Law for Bearing-Only Triangular Formation Control , 2011 .

[73]  Florian Dörfler,et al.  Geometric Analysis of the Formation Problem for Autonomous Robots , 2010, IEEE Transactions on Automatic Control.

[74]  Wei Ren,et al.  Information consensus in multivehicle cooperative control , 2007, IEEE Control Systems.

[75]  D. Taghirad.  Ieee Transactions on Robotics and Automation 1 Robust Torque Control of Harmonic Drive Systems , 1997 .

[76]  Reza Olfati-Saber,et al.  Flocking for multi-agent dynamic systems: algorithms and theory , 2006, IEEE Transactions on Automatic Control.

[77]  YangQuan Chen,et al.  Formation control: a review and a new consideration , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[78]  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).

[79]  Kaveh Pahlavan,et al.  Localization Algorithms and Strategies for Wireless Sensor Networks: Monitoring and Surveillance Techniques for Target Tracking , 2009 .

[80]  Magnus Egerstedt,et al.  Controllability of Multi-Agent Systems from a Graph-Theoretic Perspective , 2009, SIAM J. Control. Optim..

[81]  R.L. Moses,et al.  Locating the nodes: cooperative localization in wireless sensor networks , 2005, IEEE Signal Processing Magazine.

[82]  Brian D. O. Anderson,et al.  Sequential Localization of Sensor Networks , 2009, SIAM J. Control. Optim..

[83]  Patric Jensfelt,et al.  Distributed control of triangular formations with angle-only constraints , 2010, Syst. Control. Lett..

[84]  Rodolphe Sepulchre,et al.  Synchronization in networks of identical linear systems , 2009, Autom..

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

[86]  B.D.O. Anderson,et al.  Generalized Controller for Directed Triangle Formations , 2008 .

[87]  A. Ōkubo.  Dynamical aspects of animal grouping: swarms, schools, flocks, and herds. , 1986, Advances in biophysics.

[88]  R. Olfati-Saber,et al.  Consensus Filters for Sensor Networks and Distributed Sensor Fusion , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[89]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[90]  Jay A. Farrell,et al.  Cooperative Control of Multiple Nonholonomic Mobile Agents , 2008, IEEE Transactions on Automatic Control.

[91]  F.Y. Hadaegh,et al.  A survey of spacecraft formation flying guidance and control. Part II: control , 2004, Proceedings of the 2004 American Control Conference.

[92]  Tyler H. Summers,et al.  Formation shape control: Global asymptotic stability of a four-agent formation , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[93]  Tyler H. Summers,et al.  Control of Minimally Persistent Leader-Remote-Follower and Coleader Formations in the Plane , 2011, IEEE Transactions on Automatic Control.

[94]  Ella M. Atkins,et al.  Distributed multi‐vehicle coordinated control via local information exchange , 2007 .

[95]  K. D. Do,et al.  Nonlinear formation control of unicycle-type mobile robots , 2007, Robotics Auton. Syst..

[96]  Brian D. O. Anderson,et al.  Formation control using range-only measurements , 2011, Autom..

[97]  Lin Huang,et al.  Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[98]  Nathan van de Wouw,et al.  A virtual structure approach to formation control of unicycle mobile robots using mutual coupling , 2011, Int. J. Control.

[99]  P. Olver.  Nonlinear Systems , 2013 .

[100]  Yongcan Cao,et al.  Distributed Coordination of Multi-agent Networks: Emergent Problems, Models, and Issues , 2010 .

[101]  E.M. Atkins,et al.  A survey of consensus problems in multi-agent coordination , 2005, Proceedings of the 2005, American Control Conference, 2005..

[102]  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).

[103]  Randal W. Beard,et al.  A control scheme for improving multi-vehicle formation maneuvers , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[104]  Manfredi Maggiore,et al.  Necessary and sufficient graphical conditions for formation control of unicycles , 2005, IEEE Transactions on Automatic Control.

[105]  Brian D. O. Anderson,et al.  Controlling a triangular formation of mobile autonomous agents , 2007, 2007 46th IEEE Conference on Decision and Control.

[106]  H. Wolkowicz,et al.  Sensor Network Localization, Euclidean Distance Matrix completions, and graph realization , 2006, MELT '08.

[107]  Brian D. O. Anderson,et al.  Maintaining a directed, triangular formation of mobile autonomous agents , 2011, Commun. Inf. Syst..

[108]  Richard M. Murray,et al.  INFORMATION FLOW AND COOPERATIVE CONTROL OF VEHICLE FORMATIONS , 2002 .