Stable flocking of mobile formation in 3-dimensional space

The paper investigates the flocking behaviors of multi-agent formation in 3-dimensional space which are based on leader following. A class of decentralized control laws for a group of mobile agents are proposed under the conditions that the topology of the control interconnections is fixed and dynamically time-variant, respectively. These control laws are a combination of attractive/repulsive and alignments forces which can guarantee the collision avoidance and cohesion of the formation and an aggregate motion along the same heading direction of the leader. According to the algebraic graph theory, differential inclusions and non-smooth analysis, we model the interconnection relationship of multi-agent formation, and achieve the stability analysis of the system by Lyapunov theory.

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

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

[3]  B. Paden,et al.  Lyapunov stability theory of nonsmooth systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

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

[5]  Demetri Terzopoulos,et al.  Artificial life for computer graphics , 1999, CACM.

[6]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[7]  Marios M. Polycarpou,et al.  Stability analysis of M-dimensional asynchronous swarms with a fixed communication topology , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[8]  Brian D. O. Anderson,et al.  Use of meta-formations for cooperative control , 2006 .

[9]  B. Anderson,et al.  Information Structures to Secure Control of Rigid Formations with Leader-Follower Structure , 2004 .

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

[11]  M. Spong,et al.  Stable flocking of multiple inertial agents on balanced graphs , 2006, 2006 American Control Conference.

[12]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

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

[14]  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..

[15]  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..

[16]  Yu. S. Ledyaev,et al.  Nonsmooth analysis and control theory , 1998 .

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

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

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

[20]  Changbin Yu,et al.  Rigidity and Persistence of Meta-Formations , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[21]  Craig W. Reynolds.  Flocks, herds, and schools: a distributed behavioral model , 1987, SIGGRAPH.

[22]  Yong-Ji Wang,et al.  Stable flocking motion of mobile agents following a leader in fixed and switching networks , 2006, Int. J. Autom. Comput..

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

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

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

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

[27]  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).

[28]  V V Filippov.  ON THE THEORY OF THE CAUCHY PROBLEM FOR AN ORDINARY DIFFERENTIAL EQUATION WITH DISCONTINUOUS RIGHT-HAND SIDE , 1995 .

[29]  Vijay Kumar,et al.  Leader-to-formation stability , 2004, IEEE Transactions on Robotics and Automation.

[30]  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).

[31]  Guangming Xie,et al.  Leader-following formation control of multiple mobile vehicles , 2007 .

[32]  B.D.O. Anderson,et al.  Information Architecture and Control Design for Rigid Formations , 2006, 2007 Chinese Control Conference.

[33]  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).

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