© The Institution of Engineering and Technology
In this paper, distributed discrete-time coupled harmonic oscillators are studied. Convergence conditions for synchronisation of the discrete-time coupled harmonic oscillators are given. The distributed discrete-time coupled harmonic oscillators are then used to design a control strategy for symmetric formations. The purpose of the control strategy is for groups of mobile robots to move in a synchronised manner with local interaction. Both simulation and experimental results on networked mobile robots are presented. Based on the results of both simulation and experimentation, this strategy is an effective method for synchronising the motions of multiple mobile robots.
References
-
-
1)
-
A. Jadbabaie ,
J. Lin ,
A.S. Morse
.
Coordination of groups of mobile autonomous agents using nearest neighbor rules.
IEEE Trans. Autom. Control
,
6 ,
988 -
1001
-
2)
-
Ballard, L., Ren, W.: `Experiments with coupled harmonic oscillators with local interaction', IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics, July 2008, Xi'an, China, p. 716–721.
-
3)
-
L. Xiao ,
S. Boyd
.
Fast linear iterations for distributed averaging.
Syst. Control Lett.
,
1 ,
65 -
78
-
4)
-
C.W. Wu ,
L.O. Chua
.
Synchronization in an array of linearly coupled dynamical systems.
IEEE Trans. Circuits Syst., Part I
,
8 ,
430 -
447
-
5)
-
Bruckstein, A.M., Cohen, N., Efrat, A.: ‘Ants, crickets and frogs in cyclic pursuit’ [Online], citeseer.ist.psu.edu/416762.html.
-
6)
-
J.J.P. Veerman ,
G. Lafferriere ,
J.S. Caughman ,
A. Williams
.
Flocks and formations.
J. Stat. Phys.
,
901 -
936
-
7)
-
A. Sinha ,
D. Ghose
.
Generalization of linear cyclic pursuit with application to rendezvous of multiple autonomous agents.
IEEE Trans. Autom. Control
,
11 ,
1819 -
1824
-
8)
-
A. Olshevsky ,
J.N. Tsitsiklis
.
Convergence speed in distributed consensus and averaging.
SIAM J. Control Optim.
,
1 ,
33 -
55
-
9)
-
W. Ren ,
R.W. Beard ,
E.M. Atkins
.
Information consensus in multivehicle cooperative control.
IEEE Control Syst. Mag.
,
2 ,
71 -
82
-
10)
-
W. Ren ,
R.W. Beard
.
Consensus seeking in multiagent systems under dynamically changing interaction topologies.
IEEE Trans. Autom. Control
,
5 ,
655 -
661
-
11)
-
W. Lu ,
F.M. Atay ,
J. Jost
.
Synchronization of discrete-time dynamical networks with time-varying couplings.
SIAM J. Math. Anal.
,
4 ,
1231 -
1259
-
12)
-
J.A. Fax ,
R.M. Murray
.
Information flow and cooperative control of vehicle formations.
IEEE Trans. Autom. Control
,
9 ,
1465 -
1476
-
13)
-
G. Lafferriere ,
A. Williams ,
J. Caughman ,
J.J.P. Veerman
.
Decentralized control of vehicle formations.
Syst. Control Lett.
,
9 ,
899 -
910
-
14)
-
G. Xie ,
L. Wang
.
Consensus control for a class of networks of dynamic agents.
Int. J. Robust Nonlinear Control
,
941 -
959
-
15)
-
Lin, J., Morse, A.S., Anderson, B.D.O.: `The multi-agent rendezvous problem', Proc. IEEE Conf. on Decision and Control, 2003, Maui, HI, p. 1508–1513.
-
16)
-
W. Ren
.
Synchronization of coupled harmonic oscillators with local interaction.
Automatica
,
12 ,
3195 -
3200
-
17)
-
D.V. Dimarogonas ,
K.J. Kyriakopoulos
.
On the rendezvous problem for multiple non-holonomic agents.
IEEE Trans. Autom. Control
,
5 ,
916 -
922
-
18)
-
D. Lee ,
M.W. Spong
.
Stable flocking of multiple inertial agents on balanced graphs.
IEEE Trans. Autom. Control
,
8 ,
1469 -
1475
-
19)
-
M. Porfiri ,
D.G. Roberson ,
D.J. Stilwell
.
Tracking and formation control of multiple autonomous agents: a two-level consensus approach.
Automatica
,
8 ,
1318 -
1328
-
20)
-
G. Xiong ,
S. Kishore
.
Discrete-time second-order distributed consensus time synchronization algorithm for wireless sensor networks.
EURASIP J. Wireless Commun. Netw.
-
21)
-
R. Olfati-Saber ,
R. Murray
.
Consensus problems in networks of agents with switching topology and time-delays.
IEEE Trans. Autom. Control
,
9 ,
1520 -
1533
-
22)
-
R. Olfati-Saber
.
Flocking for multi-agent dynamic systems: algorithms and theory.
IEEE Trans. Autom. Control
,
3 ,
401 -
420
-
23)
-
Y. Hatano ,
M. Mesbahi
.
Agreement over random networks.
IEEE Trans. Autom. Control
,
11 ,
1867 -
1872
-
24)
-
C.W. Wu ,
L.O. Chua
.
Application of graph theory to the synchronization in an array of coupled nonlinear oscillators.
IEEE Trans. Circuits Syst., Part I
,
8 ,
494 -
497
-
25)
-
Shi, H., Wang, L., Chu, T.: `Virtual leader approach to coordinated control of multiple mobile agents with asymmetric interactions', Proc. IEEE Conf. on Decision and Control, and the European Control Conf., December 2005, Seville, Spain, p. 6250–6255.
-
26)
-
H.G. Tanner ,
A. Jadbabaic ,
G.J. Pappas
.
Flocking in fixed and switching networks.
IEEE Trans. Autom. Control
,
5 ,
863 -
868
-
27)
-
R. Olfati-Saber ,
J.A. Fax ,
R.M. Murray
.
Consensus and cooperation in networked multi-agent systems.
Proc. IEEE
,
1 ,
215 -
233
-
28)
-
W. Ren ,
E. Atkins
.
Distributed multi-vehicle coordinated control via local information exchange.
Int. J. Robust Nonlinear Control
,
1002 -
1033
-
29)
-
J. Cortes
.
Distributed algorithms for reaching consensus on general functions.
Automatica
,
3 ,
726 -
737
-
30)
-
J. Zabczyk
.
(1992)
Mathematical control theory: an introduction.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2009.0053
Related content
content/journals/10.1049/iet-cta.2009.0053
pub_keyword,iet_inspecKeyword,pub_concept
6
6