1. F. Dörfler. Geometric Analysis of the Formation Problem for Autonomous Robots. Diploma thesis, University of Toronto, August 2008. Keyword(s): Distributed Control Algorithms, Robotic Coordination, Nonlinear Control Design, Game Theory. Abstract:

   This thesis considers the formation control problem for autonomous robots, where the target formation is specified as an initesimally rigid formation. A general control law based on potential functions is derived from a directed sensor graph. The control law is distributed and relies on sensory information only. The resulting closed-loop dynamics contain various invariant sets and the stability properties of these sets are analyzed with Lyapunov set stability theory and differential geometric considerations. By methods of inverse optimality a certain class of sensor graphs is identifed, which is related to a cooperative behavior among the robots. These graphs are referred to as cooperative graphs, and undirected graphs, directed cycles, and directed open chain graphs can be identified as such graphs. Cooperative graphs admit a local stability result of the target formation together with a guaranteed region of attraction, which depends on the rigidity properties of the formation. Moreover, in order to show instability of the undesired equilibria of the robots' closed-loop dynamics, a local stability and instability theorem is derived for differentiable manifolds. This theorem allows us to perform a global stability analysis for the benchmark example of three robots interconnected in a directed, cyclic sensor graph.

   
   

   @phdthesis{FD-Diploma,
   abstract = {This thesis considers the formation control problem for autonomous robots, where the target formation is specified as an initesimally rigid formation. A general control law based on potential functions is derived from a directed sensor graph. The control law is distributed and relies on sensory information only. The resulting closed-loop dynamics contain various invariant sets and the stability properties of these sets are analyzed with Lyapunov set stability theory and differential geometric considerations. By methods of inverse optimality a certain class of sensor graphs is identifed, which is related to a cooperative behavior among the robots. These graphs are referred to as cooperative graphs, and undirected graphs, directed cycles, and directed open chain graphs can be identified as such graphs. Cooperative graphs admit a local stability result of the target formation together with a guaranteed region of attraction, which depends on the rigidity properties of the formation. Moreover, in order to show instability of the undesired equilibria of the robots' closed-loop dynamics, a local stability and instability theorem is derived for differentiable manifolds. This theorem allows us to perform a global stability analysis for the benchmark example of three robots interconnected in a directed, cyclic sensor graph.},
   advisor = {B. Francis},
   author = {F. Dörfler},
   date-added = {2011-01-22 21:39:50 -0800},
   date-modified = {2018-05-01 12:18:59 +0000},
   keywords = {Distributed Control Algorithms, Robotic Coordination, Nonlinear Control Design, Game Theory},
   month = {August},
   pdf = {http://people.ee.ethz.ch/~floriand/docs/Theses/Dorfler_Diploma_Thesis.pdf},
   school = {University of Toronto},
   title = {{Geometric Analysis of the Formation Problem for Autonomous Robots}},
   type = {Diploma thesis},
   year = {2008} 
   }
   

1. J. K. Johnsen, F. Dörfler, and F. Allgöwer. L2-gain of Port-Hamiltonian systems and application to a biochemical fermenter. In American Control Conference, Seattle, Washinton, USA, pages 153-158, June 2008. Keyword(s): Nonlinear Control Design, Process Control.
   

   @inproceedings{JKJ-FD-FA:08,
   address = {Seattle, Washinton, USA},
   author = {J. K. Johnsen and F. D{ö}rfler and F. Allg{ö}wer},
   booktitle = {American Control Conference},
   date-added = {2012-07-02 13:47:24 -0600},
   date-modified = {2018-05-01 12:17:32 +0000},
   journal = {{A}merican {C}ontrol {C}onference},
   keywords = {Nonlinear Control Design, Process Control},
   month = jun,
   pages = {153-158},
   pdf = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4586483},
   title = {L2-gain of {P}ort-{H}amiltonian systems and application to a biochemical fermenter},
   url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4586483},
   year = {2008},
   bdsk-url-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4586483} 
   }
   

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