In this paper, a new framework for evolution of multi-agent systems (MAS) based on principles of continuum mechanics is developed. Agents are treated as mass particles of a continuum whose evolution (both translation and deformation) is modeled as a homeomorphism from a reference to the current configuration. Such a mapping assures that no two mass particles of the continuum occupy the same location at any given time, thus guaranteeing that inter-agent collision is avoided during motion. We show that a special class of mappings whose Jacobian is only time varying and not spatially varying has some desirable properties that are advantageous in studying swarms. Two specific scenarios are studied where the evolution of a swarm from one configuration to another occurs with no inter-agent collisions while avoiding obstacles, under (i) zero inter-agent communication and (ii) local inter-agent communication. In the first case, a desired map is computed by each agent all knowing the positions of a few leader agents in a reference and the desired configurations. In the second case, paths of n + 1 leader agents evolving in an n-D space are known only to the leaders, while positions of follower agents evolve through updates that are based on positions of n + 1 adjacent agent through local communication with them. The latter is based on a set of weights of communication of follower agents that are predicated on certain distance ratios assigned on the basis of the initial formation of the MAS. Properties of homogeneous maps are exploited to characterize the necessary communication protocol.

References

References
1.
Murray
,
R. M.
,
2007
, “
Recent Research in Cooperative Control of Multivehicle System
,”
ASME J. Dyn. Syst., Meas., Control
,
129
, pp.
571
583
.10.1115/1.2766721
2.
Consolinia
,
L.
,
Morbidib
,
F.
,
Prattichizzob
,
D.
, and
Tosques
,
M.
,
2008
, “
Leader–Follower Formation Control of Nonholonomic Mobile Robots With Input Constraints
,”
Automatica
,
44
, pp.
1343
1349
.10.1016/j.automatica.2007.09.019
3.
Vidal
,
R.
,
Shakernia
,
O.
, and
Sastry
,
S.
,
2004
, “
Distributed Formation Control With Omnidirectional Vision-Based Motion Segmentation and Visual Servoing
,”
IEEE Rob. Autom. Mag.
,
11
, pp.
1
13
.10.1109/MRA.2004.1371604
4.
Mariottini
,
G. L.
,
Morbidi
,
F.
,
Prattichizzo
,
D.
,
Vander Valk
,
N.
,
Michael
,
N.
,
Pappas
,
G.
, and
Daniilidis
,
K.
,
2009
, “
Vision-Based Localization for Leader–Follower Formation Control
,”
IEEE Trans. Rob.
,
25
(
6
), pp.
1431
1438
.10.1109/TRO.2009.2032975
5.
Gamage
,
G. W.
,
Mann
,
G. K. I.
, and
Gosine
,
R. G.
,
2010
, “
Leader Follower Based Formation Control Strategies for Nonholonomic Mobile Robots: Design, Implementation and Experimental Validation
,”
American Control Conference Marriott Waterfront
,
Baltimore, MD
.
6.
Mehrjerdi
,
H.
,
Ghommamb
,
J.
, and
Saad
,
M.
,
2011
, “
Nonlinear Coordination Control for a Group of Mobile Robots Using a Virtual Structure
,”
Mechatronics
,
21
, pp.
1147
1155
.10.1016/j.mechatronics.2011.06.006
7.
Wang
,
Sh.
, and
Schuab
,
H.
,
2011
, “
Nonlinear Feedback Control of a Spinning Two-Spacecraft Coulomb Virtual Structure
,”
IEEE Trans. Aerosp. Electron. Syst.
,
47
(
3
), pp.
2055
2067
.10.1109/TAES.2011.5937282
8.
Xin
,
M.
,
Balakrishnan
,
S. N.
, and
Pernicka
,
H. J.
,
2007
, “
Multiple Spacecraft Formation Control With O-D Method
,”
IET Control Theory Appl.
,
1
(
2
), pp.
485
493
.10.1049/iet-cta:20050410
9.
Li
,
Q.
, and
Jiang
,
Zh. P.
,
2008
, “
Formation Tracking Control of Unicycle Teams With Collision Avoidance
,”
Proceedings of the 47th IEEE Conference on Decision and Control Cancun
,
Mexico
.
10.
Balch
,
T.
, and
Arkin
,
R. C.
,
1998
, “
Behavior-Based Formation Control for Multirobot Teams
,”
IEEE Trans. Rob. Autom.
,
14
(
6
), pp.
156
160
.10.1109/70.736776
11.
Antonelli
,
G.
,
Arrichiello
,
F.
, and
Chiaverini
,
S.
,
2009
, “
Experiments of Formation Control With Multirobot Systems Using the Null-Space-Based Behavioral Control
,”
IEEE Trans. Control Syst. Technol.
,
17
(
5
), pp.
1173
1182
.10.1109/TCST.2008.2004447
12.
Roussos
,
G.
, and
Kyriakopoulos
,
K. J.
,
2010
, “
Completely Decentralised Navigation of Multiple Unicycle Agents With Prioritisation and Fault Tolerance
,”
49th IEEE Conference on Decision and Control Hilton Atlanta Hotel
,
Atlanta, GA
.
13.
Gerdes
,
J. C.
, and
Rossetter
,
E. J.
,
2001
, “
A Unified Approach to Driver Assistance Systems Based on Artificial Potential Fields
,”
ASME J. Dyn. Syst., Meas., Control
,
123
(
3
), pp.
431
438
.10.1115/1.1386788
14.
Gazi
,
V.
, and
Passino
,
K. M.
,
2011
, Swarm Stability and Optimization,
Springer
,
New York
.
15.
Kang
,
Y. H.
,
Lee
,
M. Ch.
,
Kim
,
Ch. Y.
,
Yoon
,
S. M.
, and
Noh
,
Ch. B.
,
2011
, “
A Study of Cluster Robots Line Formatted Navigation Using Potential Field Method
,”
Proceedings of the IEEE International Conference on Mechatronics and Automation
,
Beijing
.
16.
Ghods
,
N.
, and
Krstic
,
M.
,
2012
, “
Multi-Agent Deployment Over a Source
,”
IEEE Trans. Control Syst. Technol.
,
20
(
1
), pp.
277
285
.10.1109/TCST.2011.2104959
17.
Frihauf
,
P.
, and
Krstic
,
M.
,
2011
, “
Leader-Enabled Deployment onto Planar Curves: A PDE-Based Approach
,”
IEEE Trans. Autom. Control
,
56
(
8
), pp.
1791
1806
.10.1109/TAC.2010.2092210
18.
Frihauf
,
P.
, and
Krstic
,
M.
,
2010
, “
Multi-Agent Deployment to a Family of Planar Arcs
,”
American Control Conference Marriott Waterfront
,
Baltimore, MD
.
19.
Kim
,
J.
,
Kim
,
K. D.
,
Natarajan
,
V.
,
Kelly
,
S. D.
, and
Bentsman
,
J.
,
2008
, “
PdE-Based Model Reference Adaptive Control of Uncertain Heterogeneous Multi-Agent Networks
,”
Nonlinear Anal.: Hybrid Syst.
,
2
, pp.
1152
1167
.10.1016/j.nahs.2008.09.008
20.
Rastgoftar
,
H.
,
2013
, “
Planning and Control of Swarm Motion as Continua
,” M.S. thesis, University of Central Florida, Orlando, FL, http://ucf.catalog.fcla.edu/cf.jsp?st=rastgoftar&ix=kw&S=0311390934586915&fl=bo
21.
Rastgoftar
,
H.
, and
Jayasuriya
,
S.
,
2013
, “
Distributed Control of Swarm Motions as Continua Using Homogeneous Maps and Agent Triangulation
,”
European Control Conference
,
Zurich, Switzerland
.
22.
Rastgoftar
,
H.
, and
Jayasuriya
,
S.
,
2013
, “
Preserving Stability Under Communication Delays in Multi-Agent Systems
,”
ASME Dynamic Systems and Control Conference
,
Palo Alto, CA
, Oct. 21–23.
23.
Qu
,
Z.
,
2009
,
Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles
,
Springer
,
London
.
You do not currently have access to this content.