1. F. Dörfler and B. Francis. Geometric Analysis of the Formation Problem for Autonomous Robots. IEEE Transactions on Automatic Control, 55(10):2379-2384, October 2010. Keyword(s): Distributed Control Algorithms, Robotic Coordination, Nonlinear Control Design. Abstract:

   In the formation control problem for autonomous robots, a distributed control law steers the robots to the desired target formation. A local stability result of the target formation can be derived by methods of linearization and center manifold theory or via a Lyapunov-based approach. Besides the target formation, the closed-loop dynamics of the robots feature various other undesired invariant sets such as nonrigid formations. This note addresses a global stability analysis of the closed-loop formation control dynamics. We pursue a differential geometric approach and derive purely algebraic conditions for local stability of invariant embedded submanifolds. These theoretical results are then applied to the well-known example of a cyclic triangular formation and result in instability of all invariant sets other than the target formation.

   
   

   @article{FD-BF:10,
   abstract = {In the formation control problem for autonomous robots, a distributed control law steers the robots to the desired target formation. A local stability result of the target formation can be derived by methods of linearization and center manifold theory or via a Lyapunov-based approach. Besides the target formation, the closed-loop dynamics of the robots feature various other undesired invariant sets such as nonrigid formations. This note addresses a global stability analysis of the closed-loop formation control dynamics. We pursue a differential geometric approach and derive purely algebraic conditions for local stability of invariant embedded submanifolds. These theoretical results are then applied to the well-known example of a cyclic triangular formation and result in instability of all invariant sets other than the target formation.},
   author = {F. D{ö}rfler and B. Francis},
   date-added = {2008-11-27 22:11:55 +0100},
   date-modified = {2018-05-01 11:58:46 +0000},
   journal = {IEEE Transactions on Automatic Control},
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   month = {October},
   number = {10},
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   title = {{Geometric Analysis of the Formation Problem for Autonomous Robots}},
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   volume = {55},
   year = {2010},
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   }
   

1. F. Dörfler and F. Bullo. Spectral Analysis of Synchronization in a Lossless Structure-Preserving Power Network Model. In Proceedings of the 1st IEEE Conference on Smart Grid Communications in Gaithersburg, Maryland, USA, pages 179-184, October 2010. Keyword(s): Algebraic Graph Theory, Power Networks, Complex Oscillator Networks.
   

   @inproceedings{FD-FB:10-c,
   author = {F. Dörfler and F. Bullo},
   booktitle = {Proceedings of the 1st IEEE Conference on Smart Grid Communications in Gaithersburg, Maryland, USA},
   date-added = {2011-01-20 21:42:57 -0800},
   date-modified = {2013-10-01 05:38:37 +0000},
   keywords = {Algebraic Graph Theory, Power Networks, Complex Oscillator Networks},
   month = {October},
   pages = {179-184},
   pdf = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5622040},
   title = {{Spectral Analysis of Synchronization in a Lossless Structure-Preserving Power Network Model}},
   url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=5622040&queryText%3D{Spectral+Analysis+of+Synchronization+in+a+Lossless+Structure-Preserving+Power+Network+Model}},
   year = {2010},
   bdsk-url-1 = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=5622040&queryText%3D%7BSpectral+Analysis+of+Synchronization+in+a+Lossless+Structure-Preserving+Power+Network+Model%7D} 
   }
   




2. F. Dörfler and F. Bullo. Synchronization and Transient Stability in Power Networks and Non-Uniform Kuramoto Oscillators. In Proceedings of the American Control Conference in Baltimore, Maryland, USA, pages 930-937, June 2010. Keyword(s): Power Networks, Complex Oscillator Networks.
   

   @inproceedings{FD-FB:10-a,
   author = {F. Dörfler and F. Bullo},
   booktitle = {Proceedings of the American Control Conference in Baltimore, Maryland, USA},
   date-added = {2011-01-20 21:39:43 -0800},
   date-modified = {2013-10-01 05:36:16 +0000},
   keywords = {Power Networks, Complex Oscillator Networks},
   month = {June},
   pages = {930-937},
   pdf = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5530690},
   title = {{Synchronization and Transient Stability in Power Networks and Non-Uniform Kuramoto Oscillators}},
   url = {http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5530690},
   year = {2010},
   bdsk-url-1 = {http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5530690} 
   }
   




3. F. Dörfler and F. Bullo. Synchronization of Power Networks: Network Reduction and Effective Resistance. In Proceedings of the 2nd IFAC Workshop on Distributed Estimation and Control in Networked Systems in Annecy, France, pages 197-202, September 2010. Keyword(s): Power Networks, Algebraic Graph Theory, Complex Oscillator Networks.
   

   @conference{FD-FB:10-b,
   author = {F. Dörfler and F. Bullo},
   booktitle = {Proceedings of the 2nd IFAC Workshop on Distributed Estimation and Control in Networked Systems in Annecy, France},
   date-added = {2011-01-20 21:41:16 -0800},
   date-modified = {2013-10-01 05:38:26 +0000},
   keywords = {Power Networks, Algebraic Graph Theory, Complex Oscillator Networks},
   month = {September},
   pages = {197-202},
   pdf = {http://motion.me.ucsb.edu/pdf/2010o-db-ifac.pdf},
   title = {{Synchronization of Power Networks: Network Reduction and Effective Resistance}},
   url = {http://www.ifac-papersonline.net/Detailed/44691.html},
   year = {2010},
   bdsk-url-1 = {http://www.ifac-papersonline.net/Detailed/44691.html} 
   }
   

1. F. Dörfler and F. Bullo. On the Critical Coupling for Kuramoto Oscillators, November 2010. Note: Available at http://arxiv.org/abs/1011.3878. Keyword(s): Power Networks, Complex Oscillator Networks.
   

   @misc{FD-FB:10wa,
   author = {F. D{ö}rfler and F. Bullo},
   date-added = {2012-11-21 18:44:11 +0000},
   date-modified = {2013-10-01 04:55:02 +0000},
   funding = {IIS-0904501, CNS-0834446, CPS-1135819},
   keywords = {Power Networks, Complex Oscillator Networks},
   month = {November},
   note = {Available at {http://arxiv.org/abs/1011.3878}},
   pdf = {http://motion.me.ucsb.edu/pdf/2010w-db.pdf},
   title = {On the Critical Coupling for {K}uramoto Oscillators},
   year = 2010 
   }
   




2. F. Dörfler and B. Francis. Geometric Analysis of the Formation Problem for Autonomous Robots, January 2010. Note: Available at http://arxiv.org/abs/1001.4494. Keyword(s): Distributed Control Algorithms, Robotic Coordination, Nonlinear Control Design.
   

   @misc{FD-BF:10b,
   author = {F. Dörfler and B. Francis},
   date-added = {2012-11-22 22:57:25 +0000},
   date-modified = {2018-05-01 12:24:31 +0000},
   keywords = {Distributed Control Algorithms, Robotic Coordination, Nonlinear Control Design},
   month = {January},
   note = {{Available at {http://arxiv.org/abs/1001.4494}}},
   pdf = {http://arxiv.org/pdf/1001.4494v1.pdf},
   title = {{Geometric Analysis of the Formation Problem for Autonomous Robots}},
   year = {2010} 
   }
   

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