Abstract
We study a multi-agent cyclic pursuit model where each of the identical agents moves like a Dubins car and maintains a fixed heading angle with respect to the next agent. We establish that stationary shapes for this system are regular polygons. We derive a sufficient condition for local convergence to such regular polygon formations, which takes the form of an inequality connecting the angles of the regular polygon with the heading angle of the agents. A block-circulant structure of the system's linearization matrix in suitable coordinates facilitates and elucidates our analysis. Our results are complementary to the conditions for rendezvous obtained in earlier work [Yu et al., IEEE Trans. Autom. Contr., Feb. 2012].
| Original language | English |
|---|---|
| Article number | 7040359 |
| Pages (from-to) | 6191-6196 |
| Number of pages | 6 |
| Journal | Proceedings of the IEEE Conference on Decision and Control |
| Volume | 2015-February |
| Issue number | February |
| DOIs | |
| Publication status | Published - Jan 1 2014 |
| Externally published | Yes |
| Event | 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States Duration: Dec 15 2014 → Dec 17 2014 |
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All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Modelling and Simulation
- Control and Optimization
Cite this
Cyclic pursuit without coordinates : Convergence to regular polygon formations. / Arnold, Maxim; Baryshnikov, Yuliy; Liberzon, Daniel.
In: Proceedings of the IEEE Conference on Decision and Control, Vol. 2015-February, No. February, 7040359, 01.01.2014, p. 6191-6196.Research output: Contribution to journal › Conference article
}
TY - JOUR
T1 - Cyclic pursuit without coordinates
T2 - Convergence to regular polygon formations
AU - Arnold, Maxim
AU - Baryshnikov, Yuliy
AU - Liberzon, Daniel
PY - 2014/1/1
Y1 - 2014/1/1
N2 - We study a multi-agent cyclic pursuit model where each of the identical agents moves like a Dubins car and maintains a fixed heading angle with respect to the next agent. We establish that stationary shapes for this system are regular polygons. We derive a sufficient condition for local convergence to such regular polygon formations, which takes the form of an inequality connecting the angles of the regular polygon with the heading angle of the agents. A block-circulant structure of the system's linearization matrix in suitable coordinates facilitates and elucidates our analysis. Our results are complementary to the conditions for rendezvous obtained in earlier work [Yu et al., IEEE Trans. Autom. Contr., Feb. 2012].
AB - We study a multi-agent cyclic pursuit model where each of the identical agents moves like a Dubins car and maintains a fixed heading angle with respect to the next agent. We establish that stationary shapes for this system are regular polygons. We derive a sufficient condition for local convergence to such regular polygon formations, which takes the form of an inequality connecting the angles of the regular polygon with the heading angle of the agents. A block-circulant structure of the system's linearization matrix in suitable coordinates facilitates and elucidates our analysis. Our results are complementary to the conditions for rendezvous obtained in earlier work [Yu et al., IEEE Trans. Autom. Contr., Feb. 2012].
UR - http://www.scopus.com/inward/record.url?scp=84988273931&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84988273931&partnerID=8YFLogxK
U2 - 10.1109/CDC.2014.7040359
DO - 10.1109/CDC.2014.7040359
M3 - Conference article
AN - SCOPUS:84988273931
VL - 2015-February
SP - 6191
EP - 6196
JO - Proceedings of the IEEE Conference on Decision and Control
JF - Proceedings of the IEEE Conference on Decision and Control
SN - 0191-2216
IS - February
M1 - 7040359
ER -