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- 1
- 
H. Ando, Y. Oasa, I. Suzuki, and M. Yamashita.
 Distributed memoryless point convergence algorithm for mobile robots
  with limited visibility.
 IEEE Trans. Robot. Automat., 15(5):818-828, October 1999.
- 2
- 
A. Bernhart.
 Polygons of pursuit.
 Scripta Math., 24:23-50, 1959.
- 3
- 
S. Bhattacharya, R. Murrieta-Cid, and S. Hutchinson.
 Optimal paths for landmark-based navigation by differential-drive
  vehicles with field-of-view constraints.
 IEEE Transactions on Robotics, 23(1):47-59, February 2007.
- 4
- 
R. W. Brockett and D. Liberzon.
 Quantized feedback stabilization of linear systems.
 IEEE Trans. Autom. Control, 45(7):1279-1289, 2000.
- 5
- 
A. M. Bruckstein, N. Cohen, and A. Efrat.
 Ants, crickets and frogs in cyclic pursuit.
 Technical Report CIS Report #9105, Computer Science Department,
  Israel Institute of Technology, July 1991.
- 6
- 
J. Cortés, S. Martinéz, and F. Bullo.
 Robust rendezvous for mobile autonomous agents via proximity graphs
  in arbitrary dimensions.
 IEEE Trans. Autom. Control, 51(8):1289-1298, August 2006.
- 7
- 
A. T. Samiloglu, V. Gazi, and A. B. Koku.
 Asynchronous cyclic pursuit.
 In SAB06, volume 4095 of Lecture Notes in Artificial
  Intelligence, pages 667-678. Springer, 2006.
- 8
- 
D. F. Delchamps.
 Stabilizing a linear system with quantized output record.
 IEEE Transactions on Automatic Control, 35(8):916-926, 1990.
- 9
- 
L. E. Dubins.
 On curves of minimal length with a constraint on average curvature,
  and with prescribed initial and terminal positions and tangents.
 American Journal of Mathematics, 79:497-516, 1957.
- 10
- 
N. Elia and S. K. Mitter.
 Stabilization of linear systems with limited information.
 IEEE Trans. Autom. Control, 46(9):1384-1400, 2001.
- 11
- 
M. A. Erdmann and M. T. Mason.
 An exploration of sensorless manipulation.
 IEEE Transactions on Robotics & Automation, 4(4):369-379,
  August 1988.
- 12
- 
V. Gazi.
 Stability of a discrete-time asynchronous swarm with time-dependent
  communication links.
 IEEE Transactions on Systems, Man, and Cybernetics: Part B,
  38(1):267-274, February 2008.
- 13
- 
K. Y. Goldberg.
 Orienting polygonal parts without sensors.
 Algorithmica, 10:201-225, 1993.
- 14
- 
J. P. Hespanha, A. Ortega, and L. Vasudevan.
 Towards the control of linear systems with minimum bit-rate.
 in Proc. 15th Int. Symp. Math. Theory Networks and Syst., 2002.
- 15
- 
H. Ishii and B. A. Francis.
 Stabilizing a linear system by switching control with dwell time.
 IEEE Trans. Autom. Control, 47(12):1962-1973, December 2002.
- 16
- 
A. Jadbabaie, J. Lin, and A. S. Morse.
 Coordination of groups of mobile autonomous agents using nearest
  neighbor rules.
 IEEE Trans. Automat. Control, 48:988-1001, 2003.
- 17
- 
H. Jung.
 Über die kleinste kugel, die eine räumliche figur
  einschließt.
 J. Reine Angew. Math., 123:241-257, 1901.
- 18
- 
H. Jung.
 Über den kleinsten kreis, der eine ebene figur einschließt.
 J. Reine Angew. Math., 137:310-313, 1910.
- 19
- 
I. Kamon, E. Rivlin, and E. Rimon.
 Range-sensor based navigation in three dimensions.
 In Proceedings IEEE International Conference on Robotics &
  Automation, 1999.
- 20
- 
S. M. LaValle.
 Planning Algorithms.
 Cambridge University Press, Cambridge, U.K., 2006.
 Also available at http://planning.cs.uiuc.edu/.
- 21
- 
D. Liberzon.
 Switching in Systems and Control.
 Birkhäuser, Boston, MA, 2003.
- 22
- 
J. Lin, A. S. Morse, and B. D. O. Anderson.
 The multi-agent rendezvous problem. part 1: The synchronous case.
 SIAM Journal on Control and Optimization, 46(6):2096-2119,
  November 2007.
- 23
- 
J. Lin, A. S. Morse, and B. D. O. Anderson.
 The multi-agent rendezvous problem. part 2: The asynchronous case.
 SIAM Journal on Control and Optimization, 46(6):2120-2147,
  November 2007.
- 24
- 
Y. Lin, E. D. Sontag, and Y. Wang.
 A smooth converse Lyapunov theorem for robust stability.
 SIAM J. Control Optim., 34:124-160, 1996.
- 25
- 
Z. Lin, M. Broucke, and B. Francis.
 Local control strategies for groups of mobile autonomous agents.
 IEEE Trans. Autom. Control, 49(4):622-629, April 2004.
- 26
- 
D. G. Luenberger.
 Linear and Nonlinear Programming.
 Addison Wesley, 2nd edition, 1984.
- 27
- 
V. J. Lumelsky and A. A. Stepanov.
 Path planning strategies for a point mobile automaton moving amidst
  unknown obstacles of arbitrary shape.
 Algorithmica, 2:403-430, 1987.
- 28
- 
J. A. Marshall, M. E. Broucke, and B. A. Francis.
 Formations of vehicles in cyclic pursuit.
 IEEE Trans. Autom. Control, 49(11):1963-1974, July 2004.
- 29
- 
L. Moreau.
 Stability of multiagent systems with time-dependent communication
  links.
 IEEE Trans. Autom. Control, 50(2):169-182, February 2005.
- 30
- 
G. N. Nair and R. J. Evans.
 Stabilizability of stochastic linear systems with finite feedback
  data rates.
 SIAM J. Control Optim, 43:413-436, 2004.
- 31
- 
M. Pavone and E. Frazzoli.
 Decentralized policies for geometric pattern formation and path
  coverage.
 Journal of Dynamic Systems, Measurement, and Control,
  129(5):633-643, 2007.
- 32
- 
I. R. Petersen and A. V. Savkin.
 Multi-rate stabilization of multivariable discrete-time linear
  systems via a limited capacity communication channel.
 in Proc. 40th IEEE Conf. Decision Control, pages 304-309,
  2001.
- 33
- 
W. Ren and R. W. Beard.
 Consensus seeking in multi-agent systems under dynamically changing
  interaction topologies.
 IEEE Trans. Autom. Control, 50(5):655-661, May 2005.
- 34
- 
T. Richardson.
 Stable polygons of cyclic pursuit.
 Annals of Mathematics and Artificial Intelligence, 31:147-172,
  2001.
- 35
- 
J. Roe.
 Elementary geometry.
 Oxford University Press, 1993.
- 36
- 
A. V. Savkin and H. Teimoori.
 Bearings-only guidance of a unicycle-like vehicle following a moving
  target with a smaller minimum turning radius.
 IEEE Trans. Autom. Control, 55(10):2390-2395, October 2010.
- 37
- 
A. Sinha and D. Ghose.
 Generalization of linear cyclic pursuit with application to
  rendezvous of multiple autonomous agents.
 IEEE Trans. Autom. Control, 51(11):1819-1824, November 2006.
- 38
- 
S. L. Smith, M. E. Broucke, and B. A. Francis.
 Curve shortening and the rendezvous problem for mobile autonomous
  robots.
 IEEE Trans. Autom. Control, 52(6):1154-1159, June 2007.
- 39
- 
S. Tatikonda and S. K. Mitter.
 Control under communication constraints.
 IEEE Trans. Autom. Control, 49(7):1056-1068, July 2004.
- 40
- 
B. Tovar, R Murrieta, and S. M. LaValle.
 Distance-optimal navigation in an unknown environment without sensing
  distances.
 IEEE Transactions on Robotics, 23(3):506-518, June 2007.
- 41
- 
D. B. West.
 Introduction to Graph Theory.
 Prentice Hall, 2nd edition, 2001.
- 42
- 
W. S. Wong and R. W. Brockett.
 Systems with finite communication bandwidth constraints II:
  Stabilization with limited information feedback.
 IEEE Trans. Autom. Control, 44(5):1049-1053, May 1999.
- 43
- 
J. Yu, S. M. LaValle, and D. Liberzon.
 Rendezvous without coordinates.
 Proc. IEEE Conf. Decision and Control, pages 1803-1808, 2008.
Jingjin Yu
2011-01-18