Complex Laplacian based algorithm for output synchronization of multi-agent systems using internal model principle

The paper considers the problem of motion synchronization in multi-agent systems while maintaining a specific inter-agent formation pattern. The agents are modelled as double integrator dynamical systems with motion reference generated by a virtual leader referred to as exosystem. The main essence of this paper lies in integration of output regulation techniques with complex Laplacian based consensus algorithm to synchronize motion of the multi-agent system. The stability properties of designed controller for overall dynamics of multi-agent network are discussed. Simulation results are also presented to illustrate the effectiveness of the proposed control law.

[1]  Wei Ren.  Consensus tracking under directed interaction topologies: Algorithms and experiments , 2008, ACC.

[2]  Petter Ögren,et al.  Cooperative control of mobile sensor networks:Adaptive gradient climbing in a distributed environment , 2004, IEEE Transactions on Automatic Control.

[3]  A. Isidori,et al.  Output regulation of nonlinear systems , 1990 .

[4]  Frank Allgöwer,et al.  On Synchronous Steady States and Internal Models of Diffusively Coupled Systems , 2013, IEEE Transactions on Automatic Control.

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

[6]  M.W. Spong,et al.  Multi-agent coordination under connectivity constraints , 2008, 2008 American Control Conference.

[7]  Tamio Arai,et al.  A distributed control scheme for multiple robotic vehicles to make group formations , 2001, Robotics Auton. Syst..

[8]  Zhiyun Lin,et al.  Complex Laplacian and pattern formation in multi-agent systems , 2012, 2012 24th Chinese Control and Decision Conference (CCDC).

[9]  R. Olfati-Saber,et al.  Collision avoidance for multiple agent systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

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

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

[12]  F. Allgower,et al.  An internal model principle for synchronization , 2009, 2009 IEEE International Conference on Control and Automation.

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

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

[15]  Lili Wang,et al.  Distributed Formation Control of Multi-Agent Systems Using Complex Laplacian , 2014, IEEE Transactions on Automatic Control.

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

[17]  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..

[18]  Frank L. Lewis,et al.  Synchronization of multi-agent systems with delayed control input information from neighbors , 2011, Autom..

[19]  Richard M. Murray,et al.  Recent Research in Cooperative Control of Multivehicle Systems , 2007 .

[20]  Lihua Xie,et al.  Containment control of multi‐agent systems by exploiting the control inputs of neighbors , 2014 .

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

[22]  Carlos Canudas-de-Wit,et al.  Cooperative Control Design for Time-Varying Formations of Multi-Agent Systems , 2014, IEEE Transactions on Automatic Control.

[23]  Randal W. Beard,et al.  A decentralized approach to formation maneuvers , 2003, IEEE Trans. Robotics Autom..

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

[25]  Frank L. Lewis,et al.  Cooperative Optimal Control for Multi-Agent Systems on Directed Graph Topologies , 2014, IEEE Transactions on Automatic Control.

[26]  Soura Dasgupta,et al.  The relation between redundancy and convergence rate in distributed multi-agent formation control , 2008, 2008 47th IEEE Conference on Decision and Control.

[27]  Alessandro Giua,et al.  Leader-follower formation via complex Laplacian , 2013, Autom..

[28]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

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

[30]  Masayuki Fujita,et al.  Passivity-Based Attitude Synchronization in $SE(3)$ , 2009, IEEE Transactions on Control Systems Technology.

[31]  C. Ballantine,et al.  Stabilization by a diagonal matrix , 1970 .

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

[33]  Bruce A. Francis,et al.  The internal model principle of control theory , 1976, Autom..

[34]  Huijun Gao,et al.  On Discrete-Time Convergence for General Linear Multi-Agent Systems Under Dynamic Topology , 2014, IEEE Transactions on Automatic Control.