Deviated linear cyclic pursuit

This paper analyses deviated linear cyclic pursuit in which an agent pursues its leader with an angle of deviation in both the continuous- and discrete-time domains, while admitting heterogeneous gains and deviations for the agents. Sufficient conditions for the stability of such systems, in both the domains, are presented in this paper along with the derivation of the reachable set, which is a set of points where the agents may converge asymptotically. The stability conditions are derived based on Gershgorin's theorem. Simulations validating the theoretical results presented in this paper are provided.

[1]  F. Behroozi,et al.  Cyclic pursuit in a plane , 1979 .

[2]  Donald J. Newman,et al.  Cyclic Pursuit or “the Three Bugs Problem” , 1971 .

[3]  E.M. Atkins,et al.  A survey of consensus problems in multi-agent coordination , 2005, Proceedings of the 2005, American Control Conference, 2005..

[4]  Debasish Ghose,et al.  Generalization of Linear Cyclic Pursuit With Application to Rendezvous of Multiple Autonomous Agents , 2006, IEEE Transactions on Automatic Control.

[5]  B. Anderson,et al.  A simple test for zeros of a complex polynomial in a sector , 1974 .

[6]  Mireille E. Broucke,et al.  Formations of vehicles in cyclic pursuit , 2004, IEEE Transactions on Automatic Control.

[7]  Emilio Frazzoli,et al.  Decentralized Policies for Geometric Pattern Formation and Path Coverage , 2007 .

[8]  Alfred M. Bruckstein,et al.  Ants, Crickets and Frogs in Cyclic Pursuit , 1991 .

[9]  Wei Ding,et al.  Formations on two-layer pursuit systems , 2009, 2009 IEEE International Conference on Robotics and Automation.

[10]  Debasish Ghose,et al.  Generalization of deviated linear cyclic pursuit , 2013, 2013 American Control Conference.

[11]  I. J. Good.  Pursuit Curves and Mathematical Art , 1959 .

[12]  Kevin S. Galloway,et al.  Symmetry and reduction in collectives: cyclic pursuit strategies , 2013, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[13]  Fu Lin,et al.  Optimal Control of Vehicular Formations With Nearest Neighbor Interactions , 2011, IEEE Transactions on Automatic Control.