On the Formation Control of Multiagent Systems Under Nearly Cyclic Pursuit

We consider the problem of formation control of multiple agents under the nearly cyclic pursuit strategy. A control law is designed under this strategy for n agents to rendezvous at a point and also form a specific formation, dictated by an extra agent, called beacon. We derive constraint on the gain in k–circulant matrix to make the system stable. Formation tracking for n agents is achieved by applying an exogenous input to the beacon. We prove that the agents in nearly cyclic interaction are controllable under the beacon. Simulations and analytical results demonstrate the effectiveness of the proposed method.

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

[2]  Eugene Boman,et al.  The Moore-Penrose Pseudoinverse of an Arbitrary, Square, k -circulant Matrix , 2002 .

[3]  Dimos V. Dimarogonas,et al.  Distributed cooperative control and collision avoidance for multiple kinematic agents , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

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

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

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

[7]  Frédérique E. Oggier,et al.  On Cyclic and Nearly Cyclic Multiagent Interactions in the Plane , 2009, ArXiv.

[8]  E. Flytzanis.  Linear dynamical systems , 1976 .

[9]  J. A. Marshall,et al.  Brief paper periodic formations of multivehicle systems , 2011 .

[10]  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).

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

[12]  Mireille E. Broucke,et al.  A hierarchical cyclic pursuit scheme for vehicle networks , 2005, Autom..

[13]  Gerardo Lafferriere,et al.  Decentralized control of vehicle formations , 2005, Syst. Control. Lett..

[14]  Emilio Frazzoli,et al.  Decentralized Policies for Geometric Pattern Formation and Path Coverage , 2007 .

[15]  Eduardo Aranda-Bricaire,et al.  Convergence and Collision Avoidance in Formation Control: A Survey of the Artificial Potential Functions Approach , 2011 .

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

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

[18]  J. Lygeros,et al.  Behavior based robotics using regularized hybrid automata , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[19]  K.L. Moore,et al.  Forced and constrained consensus among cooperating agents , 2005, Proceedings. 2005 IEEE Networking, Sensing and Control, 2005..

[20]  Amit Kumar,et al.  Towards Decentralization of Multi-robot Navigation Functions , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.