Formation control of directed multi-agent networks based on complex Laplacian

Real graph Laplacians are of great importance in consensus of multi-agent systems. This paper introduces complex graph Laplacians as a new tool to study the formation control problem in the plane. It is shown that complex graph Laplacians are of equally great importance for planar formation control like real Laplacians for consensus. First, complex graph Laplacians are used to characterize planar formations under given topology of networked agents. Second, complex graph Laplacians are used to derive local and distributed control strategies for asymptotically achieving formations. This paper explores the relations between graph topology, complex Laplacians, and planar formations, and obtains several graphical and algebraic conditions for realizability of spatial formations. Both simulation and experiment results are provided to illustrate our results.

[1]  W. Ren.  Consensus strategies for cooperative control of vehicle formations , 2007 .

[2]  Yongcan Cao,et al.  Distributed Coordinated Tracking With Reduced Interaction via a Variable Structure Approach , 2012, IEEE Transactions on Automatic Control.

[3]  Mireille E. Broucke,et al.  Stabilisation of infinitesimally rigid formations of multi-robot networks , 2009, Int. J. Control.

[4]  Shmuel Friedland,et al.  On inverse multiplicative eigenvalue problems for matrices , 1975 .

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

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

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

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

[9]  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.

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

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

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

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

[14]  Z. Duan,et al.  Consensus of multi-agent systems with intrinsic nonlinear dynamics and sampled-data information , 2011, 2011 8th Asian Control Conference (ASCC).

[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.