Multi-agent compositional stability exploiting system symmetries

This paper considers nonlinear symmetric control systems. By exploiting the symmetric structure of the system, stability results are derived that are independent of the number of components in the system. This work contributes to the fields of research directed toward compositionality and composability of large-scale system in that a system can be ''built-up'' by adding components while maintaining system stability. The modeling framework developed in this paper is a generalization of many existing results which focus on interconnected systems with specific dynamics. The main utility of the stability result is one of scalability or compositionality. If the system is stable for a given number of components, under appropriate conditions stability is then guaranteed for a larger system composed of the same type of components which are interconnected in a manner consistent with the smaller system. The results are general and applicable to a wide class of problems. The examples in this paper focus on the formation control problems for multi-agent robotic systems.

[1]  Bill Goodwine,et al.  Reduction and nonlinear controllability of symmetric distributed robotic systems with drift , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[2]  Bill Goodwine,et al.  Reduction and nonlinear controllability of symmetric distributed systems with robotic applications , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[3]  Panos J. Antsaklis,et al.  Fault-tolerant multiagent robotic formation control exploiting system symmetries , 2011, 2011 IEEE International Conference on Robotics and Automation.

[4]  Masao Ikeda,et al.  Decentralized stabilization for expanding construction of large-scale systems , 1990 .

[5]  Bill Goodwine,et al.  Reduced order motion planning for nonlinear symmetric distributed robotic systems , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[6]  B. Goodwine.  Engineering Differential Equations: Theory and Applications , 2010 .

[7]  Geir E. Dullerud,et al.  Distributed control design for spatially interconnected systems , 2003, IEEE Trans. Autom. Control..

[8]  Benjamin Recht,et al.  Distributed control of systems over discrete Groups , 2004, IEEE Transactions on Automatic Control.

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

[10]  A. J. van der Schaft,et al.  On symmetries in optimal control , 1986 .

[11]  J. Rotman.  An Introduction to the Theory of Groups , 1965 .

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

[13]  Bill Goodwine,et al.  Reduction and control of nonlinear symmetric distributed robotic systems , 2004 .

[14]  Bill Goodwine,et al.  Reduction and non-linear controllability of symmetric distributed systems , 2003 .

[15]  Pablo A. Parrilo,et al.  Structured semidefinite programs for the control of symmetric systems , 2008, Autom..

[16]  Bernhard von Stengel,et al.  Symmetry and p-Stability , 2004, Int. J. Game Theory.

[17]  A. J. van der Schaft,et al.  On symmetries in optimal control , 1986, 1986 25th IEEE Conference on Decision and Control.

[18]  Bill Goodwine,et al.  Motion Planning for Nonlinear Symmetric Distributed Robotic Formations , 2007, Int. J. Robotics Res..

[19]  Daniel E. Koditschek,et al.  Exact robot navigation using artificial potential functions , 1992, IEEE Trans. Robotics Autom..

[20]  Alessandro De Luca,et al.  Stabilization of the Unicycle Via Dynamic Feedback Linearization , 2000 .

[21]  Bill Goodwine,et al.  Bifurcations and symmetries of optimal solutions for distributed robotic systems , 2009, 2009 American Control Conference.

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

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

[24]  Jacques Julliand,et al.  Composability, compatibility, compositionality: automatic preservation of timed properties during incremental development , 2007 .

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

[26]  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).

[27]  Gabor Karsai,et al.  Toward a Science of Cyber–Physical System Integration , 2012, Proceedings of the IEEE.

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

[29]  Bill Goodwine,et al.  Bifurcations of optimal solutions for coordinated robotic systems: Numerical and homotopy methods , 2010, 2010 IEEE International Conference on Robotics and Automation.

[30]  Naomi Ehrich Leonard,et al.  Virtual Leaders, Artificial Potentials Control of Groups' , 2001 .

[31]  Bill Goodwine,et al.  MICAbot: a robotic platform for large-scale distributed robotics , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).