One of the main challenges in robotics applications is dealing with inaccurate sensor data. Specifically, for a group of mobile robots, the measurement of the exact location of the other robots relative to a particular robot is often inaccurate due to sensor measurement uncertainty or detrimental environmental conditions. In this paper, we address the consensus problem for a group of agent robots with a connected, undirected, and time-invariant communication graph topology in the face of uncertain interagent measurement data. Using agent location uncertainty characterized by norm bounds centered at the neighboring agent's exact locations, we show that the agents reach an approximate consensus state and converge to a set centered at the centroid of the agents' initial locations. The diameter of the set is shown to be dependent on the graph Laplacian and the magnitude of the uncertainty norm bound. Furthermore, we show that if the network is all-to-all connected and the measurement uncertainty is characterized by a ball of radius r, then the diameter of the set to which the agents converge is 2r. Finally, we also formulate our problem using set-valued analysis and develop a set-valued invariance principle to obtain set-valued consensus protocols. Two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approximate consensus protocol framework.

References

References
1.
Moreau
,
L.
,
2005
, “
Stability of Multiagent Systems With Time-Dependent Communication Links
,”
IEEE Trans. Autom. Control
,
50
(
2
), pp.
169
182
.
2.
Angeli
,
D.
, and
Bliman
,
P. A.
,
2006
, “
Stability of Leaderless Discrete-Time Multi-Agent Systems
,”
Math. Control Signals Syst.
,
18
(
4
), pp.
293
322
.
3.
Lorenz
,
J.
, and
Lorenz
,
D. A.
,
2010
, “
On Conditions for Convergence to Consensus
,”
IEEE Trans. Autom. Control
,
55
(
7
), pp.
1651
1656
.
4.
Goebel
,
R.
,
2011
, “
Set-Valued Lyapunov Functions for Difference Inclusions
,”
Automatica
,
47
(
1
), pp.
127
132
.
5.
Xiao
,
F.
, and
Wang
,
L.
,
2012
, “
Asynchronous Rendezvous Analysis Via Set-Valued Consensus Theory
,”
SIAM J. Control Optim.
,
50
(
1
), pp.
196
221
.
6.
Goebel
,
R.
,
2014
, “
Robustness of Stability Through Necessary and Sufficient Lyapunov-Like Conditions for Systems With a Continuum of Equilibria
,”
Syst. Control Lett.
,
65
, pp.
81
88
.
7.
Porfiri
,
M.
, and
Stilwell
,
D. J.
,
2007
, “
Consensus Seeking Over Random Weighted Directed Graphs
,”
IEEE Trans. Autom. Control
,
52
(
9
), pp.
1767
1773
.
8.
Tahbaz-Salehi
,
A.
, and
Jadbabaie
,
A.
,
2008
, “
A Necessary and Sufficient Condition for Consensus Over Random Networks
,”
IEEE Trans. Autom. Control
,
53
(
3
), pp.
791
795
.
9.
Fagnani
,
F.
, and
Zampieri
,
S.
,
2009
, “
Average Consensus With Packet Drop Communication
,”
SIAM J. Control Optim.
,
48
(
1
), pp.
102
133
.
10.
Li
,
T.
, and
Zhang
,
J.-F.
,
2010
, “
Consensus Conditions of Multi-Agent Systems With Time-Varying Topologies and Stochastic Communication Noises
,”
IEEE Trans. Autom. Control
,
55
(
9
), pp.
2043
2057
.
11.
Zhang
,
Y.
, and
Tian
,
Y.-P.
,
2010
, “
Consensus of Data-Sampled Multi-Agent Systems With Random Communication Delay and Packet Loss
,”
IEEE Trans. Autom. Control
,
55
(
4
), pp.
939
943
.
12.
Ma
,
C.
,
Li
,
T.
, and
Zhang
,
J.
,
2010
, “
Consensus Control for Leader-Following Multi-Agent Systems With Measurement Noises
,”
J. Syst. Sci. Complexity
,
23
(
1
), pp.
35
49
.
13.
Abaid
,
N.
,
Igel
,
I.
, and
Porfiri
,
M.
,
2012
, “
On the Consensus Protocol of Conspecific Agents
,”
Linear Algebra Appl.
,
437
(
1
), pp.
221
235
.
14.
Liu
,
J.
,
Zhang
,
H.
,
Liu
,
X.
, and
Xie
,
W.-C.
,
2013
, “
Distributed Stochastic Consensus of Multi-Agent Systems With Noisy and Delayed Measurements
,”
IET Control Theory Appl.
,
7
(
10
), pp.
1359
1369
.
15.
Wu
,
Z.
,
Peng
,
L.
,
Xie
,
L.
, and
Wen
,
J.
,
2013
, “
Stochastic Bounded Consensus Tracking of Leader–Follower Multi-Agent Systems With Measurement Noises Based on Sampled-Data With Small Sampling Delay
,”
Phys. A: Stat. Mech. Appl.
,
392
(
4
), pp.
918
928
.
16.
Das
,
A.
, and
Lewis
,
F. L.
,
2010
, “
Distributed Adaptive Control for Synchronization of Unknown Nonlinear Networked Systems
,”
Automatica
,
46
(
12
), pp.
2014
2021
.
17.
Yucelen
,
T.
, and
Egerstedt
,
M.
,
2012
, “
Control of Multiagent Systems Under Persistent Disturbances
,”
American Control Conference
(ACC), Montreal, Canada, June 27–29, pp.
5264
5269
.
18.
Yucelen
,
T.
, and
Johnson
,
E. N.
,
2013
, “
Control of Multivehicle Systems in the Presence of Uncertain Dynamics
,”
Int. J. Control
,
86
(
9
), pp.
1540
1553
.
19.
Li
,
Z.
,
Duan
,
Z.
, and
Lewis
,
F. L.
,
2014
, “
Distributed Robust Consensus Control of Multi-Agent Systems With Heterogeneous Matching Uncertainties
,”
Automatica
,
50
(
3
), pp.
883
889
.
20.
De La Torre
,
G.
, and
Yucelen
,
T.
,
2015
, “
State Emulator-Based Adaptive Architectures for Resilient Networked Multiagent Systems Over Directed and Time-Varying Graphs
,”
ASME
Paper No. DSCC2015-9802.
21.
Yucelen
,
T.
,
Peterson
,
J. D.
, and
Moore
,
K. L.
,
2015
, “
Control of Networked Multiagent Systems With Uncertain Graph Topologies
,”
ASME
Paper No. DSCC2015-9649.
22.
Arabi
,
E.
,
Yucelen
,
T.
, and
Haddad
,
W. M.
,
2016
, “
Mitigating the Effects of Sensor Uncertainties in Networked Multiagent Systems
,”
American Control Conference
(
ACC
), Boston, MA, July 6–8, pp.
5545
5550
.
23.
Ren
,
W.
,
Beard
,
R. W.
, and
Atkins
,
E. M.
,
2007
, “
Information Consensus in Multivehicle Cooperative Control
,”
IEEE Control Syst. Mag.
,
27
(
2
), pp.
71
82
.
24.
Hui
,
Q.
, and
Haddad
,
W. M.
,
2008
, “
Distributed Nonlinear Control Algorithms for Network Consensus
,”
Automatica
,
44
(
9
), pp.
2375
2381
.
25.
Mesbahi
,
M.
, and
Egerstedt
,
M.
,
2010
,
Graph Theoretic Methods for Multiagent Networks
,
Princeton University Press
,
Princeton, NJ
.
26.
Godsil
,
C.
, and
Royle
,
G.
,
2001
,
Algebraic Graph Theory
,
Springer-Verlag
,
New York
.
27.
Olfati-Saber
,
R.
,
Fax
,
J. A.
, and
Murray
,
R. M.
,
2007
, “
Consensus and Cooperation in Networked Multi-Agent Systems
,”
Proc. IEEE
,
95
(
1
), pp.
215
233
.
28.
Rockafellar
,
R.
, and
Wets
,
R. J. B.
,
1998
,
Variational Analysis
,
Springer
,
Berlin
.
29.
Bryson
,
A. E.
,
1993
,
Control of Aircraft and Spacecraft
,
Princeton University Press
,
Princeton, NJ
.
30.
Yucelen
,
T.
, and
Haddad
,
W. M.
,
2014
, “
Consensus Protocols for Networked Multiagent Systems With a Uniformly Continuous Quasi-Resetting Architecture
,”
Int. J. Control
,
87
(
8
), pp.
1716
1727
.
You do not currently have access to this content.