Autonomous robot networks are an effective tool for monitoring large-scale environmental fields. This paper proposes distributed control strategies for localizing the source of a noisy signal, which could represent a physical quantity of interest such as magnetic force, heat, radio signal, or chemical concentration. We develop algorithms specific to two scenarios: one in which the sensors have a precise model of the signal formation process and one in which a signal model is not available. In the model-free scenario, a team of sensors is used to follow a stochastic gradient of the signal field. Our approach is distributed, robust to deformations in the group geometry, does not necessitate global localization, and is guaranteed to lead the sensors to a neighborhood of a local maximum of the field. In the model-based scenario, the sensors follow a stochastic gradient of the mutual information (MI) between their expected measurements and the expected source location in a distributed manner. The performance is demonstrated in simulation using a robot sensor network to localize the source of a wireless radio signal.

References

References
1.
Lux
,
R.
, and
Shi
,
W.
,
2004
, “
Chemotaxis-Guided Movements in Bacteria
,”
Crit. Rev. Oral. Biol. Med.
,
15
(
4
), pp. 207–220.10.1177/154411130401500404
2.
Frankel
,
R.
,
Bazylinski
,
D.
,
Johnson
,
M.
, and
Taylor
,
B.
,
1997
, “
Magneto-Aerotaxis in Marine Coccoid Bacteria
,”
Biophys. J.
,
73
(
2
), pp.
994
1000
.10.1016/S0006-3495(97)78132-3
3.
Ögren
,
P.
,
Fiorelli
,
E.
, and
Leonard
,
N.
,
2004
, “
Cooperative Control of Mobile Sensor Networks
,”
IEEE Trans. Autom. Control
,
49
(
8
), pp. 1292–1302.
4.
Sukhatme
,
G.
,
Dhariwal
,
A.
,
Zhang
,
B.
,
Oberg
,
C.
,
Stauffer
,
B.
, and
Caron
,
D.
,
2007
, “
Design and Development of a Wireless Robotic Networked Aquatic Microbial Observing System
,”
Environ. Eng. Sci.
,
24
(
2
), pp.
205
215
.10.1089/ees.2006.0046
5.
Rybski
,
P.
,
Stoeter
,
S.
,
Erickson
,
M.
,
Gini
,
M.
,
Hougen
,
D.
, and
Papanikolopoulos
,
N.
,
2000
, “
A Team of Robotic Agents for Surveillance
,”
International Conference on Autonomous Agents
,
Barcelona, Spain,
ACM
, New York, pp. 9–16.10.1145/336595.336607
6.
Kumar
,
V.
,
Rus
,
D.
, and
Singh
,
S.
,
2004
, “
Robot and Sensor Networks for First Responders
,”
IEEE Pervasive Comput.
,
3
(
4
), pp.
24
33
.10.1109/MPRV.2004.17
7.
Wu
,
W.
, and
Zhang
,
F.
,
2011
, “
Experimental Validation of Source Seeking With a Switching Strategy
,”
IEEE
International Conference on Robotics and Automation (ICRA
)
, pp. 3835–3840.10.1109/ICRA.2011.5979597
8.
Li
,
S.
, and
Guo
,
Y.
,
2012
, “
Distributed Source Seeking by Cooperative Robots: All-to-All and Limited Communications
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), pp. 1107–1112.10.1109/ICRA.2012.6224713
9.
Brinón-Arranz
,
L.
, and
Schenato
,
L.
,
2013
, “
Consensus-Based Source-Seeking With a Circular Formation of Agents
,”
European Control Conferenc
e
, pp. 2831–2836.
10.
Zhang
,
F.
, and
Leonard
,
N.
,
2010
, “
Cooperative Filters and Control for Cooperative Exploration
,”
IEEE Trans. Autom. Control
,
55
(
3
), pp. 650–663.10.1109/TAC.2010.2041612
11.
Choi
,
J.
,
Oh
,
S.
, and
Horowitz
,
R.
,
2009
, “
Distributed Learning and Cooperative Control for Multi-Agent Systems
,”
Automatica
,
45
(
12
), pp. 2802–2814.
12.
Jadaliha
,
M.
,
Lee
,
J.
, and
Choi
,
J.
,
2012
, “
Adaptive Control of Multiagent Systems for Finding Peaks of Uncertain Static Fields
,”
ASME J. Dyn. Syst. Meas. Control
,
134
(
5
), p.
051007
.10.1115/1.4006369
13.
Azuma
,
S.
,
Sakar
,
M.
, and
Pappas
,
G.
,
2012
, “
Stochastic Source Seeking by Mobile Robots
,”
IEEE Trans. Autom. Control
,
57
(
9
), pp. 2308–2321.
14.
Zhang
,
C.
,
Arnold
,
D.
,
Ghods
,
N.
,
Siranosian
,
A.
, and
Krstić
,
M.
,
2007
, “
Source Seeking With Non-Holonomic Unicycle Without Position Measurement and With Tuning of Forward Velocity
,”
Syst. Control Lett.
,
56
(
3
), pp. 245–252.
15.
Liu
,
S.
, and
Krstić
,
M.
,
2010
, “
Stochastic Source Seeking for Nonholonomic Unicycle
,”
Automatica
,
46
(
9
), pp. 1443–1453.
16.
Stanković
,
M.
, and
Stipanović
,
D.
,
2010
, “
Extremum Seeking Under Stochastic Noise and Applications to Mobile Sensors
,”
Automatica
,
46
(
8
), pp. 1243–1251.
17.
Ghods
,
N.
, and
Krstić
,
M.
,
2011
, “
Source Seeking With Very Slow or Drifting Sensors
,”
ASME J. Dyn. Syst. Meas. Control
,
133
(
4
), p.
044504
.10.1115/1.4003639
18.
Atanasov
,
N.
,
Le Ny
,
J.
,
Michael
,
N.
, and
Pappas
,
G.
,
2012
, “
Stochastic Source Seeking in Complex Environments
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), pp. 3013–3018.10.1109/ICRA.2012.6225289
19.
Charrow
,
B.
,
Kumar
,
V.
, and
Michael
,
N.
,
2013
, “
Approximate Representations for Multi-Robot Control Policies That Maximize Mutual Information
,”
Robotics: Science and Systems (RSS)
, Berlin, Germany.
20.
Hoffmann
,
G.
, and
Tomlin
,
C.
,
2010
, “
Mobile Sensor Network Control Using Mutual Information Methods and Particle Filters
,”
IEEE Trans. Autom. Control
,
55
(
1
), pp.
32
47
.10.1109/TAC.2009.2034206
21.
Dames
,
P.
,
Schwager
,
M.
,
Kumar
,
V.
, and
Rus
,
D.
,
2012
, “
A Decentralized Control Policy for Adaptive Information Gathering in Hazardous Environments
,”
IEEE
Conference on Decision and Control (CDC
)
, Dec., pp. 2807–2813.10.1109/CDC.2012.6426239
22.
Julian
,
B.
,
Angermann
,
M.
,
Schwager
,
M.
, and
Rus
,
D.
,
2012
, “
Distributed Robotic Sensor Networks: An Information-Theoretic Approach
,”
Int. J. Rob. Res.
,
31
(
10
), pp.
1134
1154
.10.1177/0278364912452675
23.
Yin
,
G.
,
Yuan
,
Q.
, and
Wang
,
L.
,
2013
, “
Asynchronous Stochastic Approximation Algorithms for Networked Systems: Regime-Switching Topologies and Multiscale Structure
,”
SIAM Multiscale Model. Simul.
,
11
(
3
), pp.
813
839
.10.1137/120871614
24.
Yu
,
W.
,
Zheng
,
W.
,
Chen
,
G.
,
Ren
,
W.
, and
Cao
,
J.
,
2011
, “
Second-Order Consensus in Multi-Agent Dynamical Systems With Sampled Position Data
,”
Automatica
,
47
(
7
), pp.
1496
1503
.10.1016/j.automatica.2011.02.027
25.
Derenick
,
J.
, and
Spletzer
,
J.
,
2007
, “
Convex Optimization Strategies for Coordinating Large-Scale Robot Formations
,”
IEEE Trans. Rob.
,
23
(
6
), pp.
1252
1259
.10.1109/TRO.2007.909833
26.
Fornberg
,
B.
,
Lehto
,
E.
, and
Powell
,
C.
,
2013
, “
Stable Calculation of Gaussian-Based RBF-FD Stencils
,”
Comput. Math. Appl.
,
65
(
4
), pp.
627
637
.10.1016/j.camwa.2012.11.006
27.
Kushner
,
H.
, and
Yin
,
G.
,
2003
,
Stochastic Approximation and Recursive Algorithms and Applications
,
2 ed.
, Springer-Verlag, New York.
28.
Borkar
,
V.
,
2008
,
Stochastic Approximation: A Dynamical Systems Viewpoint
,
Cambridge University
Press, Cambridge, UK.
29.
Ljung
,
L.
,
1977
, “
Analysis of Recursive Stochastic Algorithms
,”
IEEE Trans. Autom. Control
,
22
(
4
), pp. 551–575.
30.
Spall
,
J.
,
2003
,
Introduction to Stochastic Search and Optimization
, John Wiley & Sons, Hoboken, NJ.
31.
Schwager
,
M.
,
Dames
,
P.
,
Rus
,
D.
, and
Kumar
,
V.
,
2011
, “
A Multi-Robot Control Policy for Information Gathering in the Presence of Unknown Hazards
,”
Proceedings of International Symposium on Robotics Research
, Aug.
32.
Thrun
,
S.
,
Burgard
,
W.
, and
Fox
,
D.
,
2005
,
Probabilistic Robotics
,
MIT
, Cambridge, MA.
33.
Rad
,
K.
, and
Tahbaz-Salehi
,
A.
,
2010
, “
Distributed Parameter Estimation in Networks
,”
IEEE
Conference on Decision and Control (CDC)
, pp. 5050–5055.10.1109/CDC.2010.5717946
34.
Shahrampour
,
S.
, and
Jadbabaie
,
A.
,
2013
, “
Exponentially Fast Parameter Estimation in Networks Using Distributed Dual Averaging
,”
IEEE
Conference on Decision and Control (CDC
)
, pp. 6196–6201.10.1109/CDC.2013.6760868
35.
Tahbaz-Salehi
,
A.
, and
Jadbabaie
,
A.
,
2010
, “
Consensus Over Ergodic Stationary Graph Processes
,”
IEEE Trans. Autom. Control
,
55
(
1
), pp. 225–230.
36.
Atanasov
,
N.
,
Le Ny
,
J.
, and
Pappas
,
G.
,
2014
, “
Distributed Algorithms for Stochastic Source Seeking With Mobile Robot Networks: Technical Report
,” preprint arXiv: 1402.0051.
37.
Spanos
,
D.
,
Olfati-Saber
,
R.
, and
Murray
,
R.
,
2005
, “
Dynamic Consensus on Mobile Networks
,”
16th IFAC World Congress
, International Federation of Automatic Control, Prague, Czech Republic.
38.
Capulli
,
F.
,
Monti
,
C.
,
Vari
,
M.
, and
Mazzenga
,
F.
,
2006
, “
Path Loss Models for IEEE 802.11a Wireless Local Area Networks
,”
3rd International Symposium
on Wireless Communication Systems, pp. 621–624.10.1109/ISWCS.2006.4362375
39.
Durrett
,
R.
,
2010
,
Probability: Theory and Examples
, Vol.
4
,
Cambridge University
, Cambridge University Press, New York.
You do not currently have access to this content.