Control of 2D Minimally Persistent Formations with the Fault Tolerance of Three Co-Leaders in Cycle

This paper mainly addresses a novel control law with rigidity matrix based on three co-leaders minimally persistent formations in the plane. This control law particularly considers the fault tolerance of the leaders, and in this way, the three co-leaders model is better than leader-first follower model, leader-remote follower model, etc. in persistent formation. Firstly, the first order kinematic model is adopted for every agent. Then the fundamental moving principal of the leaders and the followers are described in detail. On the basis of these principals, the control law with the rigidity matrix for the whole formation is proposed. Moreover, the stability analysis is also supplied. Finally, simulations show that the proposed controllers ensure the group formation stabilized to maintain the rigid shape, while the distances between the agents remain unchanged.

[1]  William B. Dunbar,et al.  Cooperative control of multi-vehicle systems using cost graphs and optimization , 2003, Proceedings of the 2003 American Control Conference, 2003..

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

[3]  Huagang Liu,et al.  Distributed rigid formation control algorithm for multi-agent systems , 2012, Kybernetes.

[4]  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).

[5]  Hao Fang,et al.  Control of 2D Minimally Persistent Formations with Three Co-Leaders in a Cycle , 2013 .

[6]  Suk-Gyu Lee,et al.  A Stable Formation Control Using Approximation of Translational and Angular Accelerations , 2011 .

[7]  Brian D. O. Anderson,et al.  Multi-agent rigid formations: A study of robustness to the loss of multiple agents , 2011, IEEE Conference on Decision and Control and European Control Conference.

[8]  J. Hendrickx,et al.  Closing ranks in rigid multi‐agent formations using edge contraction , 2010 .

[9]  Rubo Zhang,et al.  Stable Formation Control of Multi-robot System with Communication Delay , 2012 .

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

[11]  Mireille E. Broucke,et al.  Formations of vehicles in cyclic pursuit , 2004, IEEE Transactions on Automatic Control.

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

[13]  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).

[14]  A. Stephen Morse,et al.  Operations on Rigid Formations of Autonomous Agents , 2003, Commun. Inf. Syst..

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

[16]  B.D.O. Anderson,et al.  Rigidity and Persistence of Directed Graphs , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

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

[18]  Vincent D. Blondel,et al.  Formation Reorganization by Primitive Operations on Directed Graphs , 2008, IEEE Transactions on Automatic Control.

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

[20]  Wei Ren,et al.  A Unified Formation Control Scheme with a Single or Multiple Leaders , 2007, 2007 American Control Conference.

[21]  B. Anderson,et al.  Development of redundant rigidity theory for formation control , 2009 .

[22]  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).

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