Passivity-based output synchronization of networked Euler-Lagrange systems subject to nonholonomic constraints

In this paper, we study the output synchronization problem of networked Euler-Lagrange(EL) systems subject to nonholonomic constraints. An EL system subject to nonholonomic constraints can be input-output linearized if a proper decoupling matrix can be found, and the linearized form is equivalent to a double integrator. Although a double integrator is not a passive system, with proper design of the control law and some coordinate transformation, we are able to obtain a new state-space representation of the EL system which is a linear passive system. The underlying assumption is that the communication graph is bidirectional and strongly connected. To deal with time-varying communication delays among the interconnected agents, we embed the scattering transformation into our proposed setup and show that output synchronization can be achieved in this case as well.

[1]  Mark W. Spong,et al.  Passivity-Based Control of Multi-Agent Systems , 2006 .

[2]  Emilio Frazzoli,et al.  On synchronous robotic networks Part II: Time complexity of rendezvous and deployment algorithms , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

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

[4]  A. Isidori,et al.  Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems , 1991 .

[5]  P.J. Antsaklis,et al.  Control of multiple networked passive plants with delays and data dropouts , 2008, 2008 American Control Conference.

[6]  Mark W. Spong,et al.  PASSIVATION OF FORCE REFLECTING BILATERAL TELEOPERATORS WITH TIME VARYING DELAY , 2002 .

[7]  A. Schaft,et al.  Mechanical Nonlinear Control Systems , 1990 .

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

[9]  P.J. Antsaklis,et al.  Asynchronous Consensus Protocols: Preliminary Results, Simulations and Open Questions , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[10]  Richard M. Murray,et al.  Information flow and cooperative control of vehicle formations , 2004, IEEE Transactions on Automatic Control.

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

[12]  F. Bullo,et al.  On Synchronous Robotic Networks—Part I: Models, Tasks, and Complexity , 2005, IEEE Transactions on Automatic Control.

[13]  R. Olfati-Saber.  Ultrafast consensus in small-world networks , 2005, Proceedings of the 2005, American Control Conference, 2005..

[14]  Mrdjan J. Jankovic,et al.  Constructive Nonlinear Control , 2011 .

[15]  Randal W. Beard,et al.  Distributed Consensus in Multi-vehicle Cooperative Control - Theory and Applications , 2007, Communications and Control Engineering.

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

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

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

[19]  M. Spong,et al.  On Synchronization of Kuramoto Oscillators , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[20]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[21]  Eduardo D. Sontag,et al.  Diagonal stability of a class of cyclic systems and its connection with the secant criterion , 2006, Autom..

[22]  Eduardo D. Sontag,et al.  Passivity gains and the "secant condition" for stability , 2006, Syst. Control. Lett..

[23]  J. P. Lasalle.  Some Extensions of Liapunov's Second Method , 1960 .

[24]  F. Bullo,et al.  On Synchronous Robotic Networks—Part II: Time Complexity of Rendezvous and Deployment Algorithms , 2007, IEEE Transactions on Automatic Control.

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

[26]  Murat Arcak,et al.  Passivity as a Design Tool for Group Coordination , 2007, IEEE Transactions on Automatic Control.

[27]  Xiaoping Yun,et al.  Coordinating locomotion and manipulation of a mobile manipulator , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[28]  Emilio Frazzoli,et al.  On synchronous robotic networks Part I: Models, tasks and complexity notions , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[29]  Vasile Mihai Popov,et al.  Hyperstability of Control Systems , 1973 .

[30]  Nikhil Chopra,et al.  Passivity results for interconnected systems with time delay , 2008, 2008 47th IEEE Conference on Decision and Control.

[31]  Romeo Ortega,et al.  Passivity-based Control of Euler-Lagrange Systems , 1998 .

[32]  A. Fettweis.  Wave digital filters: Theory and practice , 1986, Proceedings of the IEEE.