In this paper, we consider cooperative control issues for a multi-unmanned aerial vehicle (UAV) system. We propose a cooperative formation control strategy with unidirectional network connections between UAVs. Our strategy is to apply a consensus-based algorithm to the UAVs so that they can cooperatively fly in formation. First, we show that UAV models on the horizontal plane and in the vertical direction are expressed as a fourth- and second-order system, respectively. Then, we show that the stability discriminants of the multi-UAV system on the horizontal plane and in the vertical direction are expressed as polynomials. For a network structure composed of bidirectional or unidirectional network connections under the assumption that the network has a directed spanning tree, we provide conditions for formation control gains such that all roots of the polynomials have negative real parts in order for the UAVs to asymptotically converge to the positions for a desired formation by using the generalized Routh stability criterion. The proposed control algorithms are validated through simulations, and experiments are performed on multiple commercial small UAVs to validate the proposed control algorithm.

References

References
1.
Murray
,
R.
,
2007
, “
Recent Research in Cooperative Control of Multivehicle Systems
,”
ASME J. Dyn. Syst. Meas. Control
,
129
(5), pp.
571
583
.
2.
Ma
,
C.-Q.
, and
Zhang
,
J.-F.
,
2010
, “
Necessary and Sufficient Conditions for Consensusability of Linear Multi-Agent Systems
,”
IEEE Trans. Autom. Control
,
55
(
5
), pp.
1263
1268
.
3.
Dong
,
X.
,
Zhou
,
Y.
,
Ren
,
Z.
, and
Zhong
,
Y.
,
2016
, “
Time-Varying Formation Control for Unmanned Aerial Vehicles With Switching Interaction Topologies
,”
Control Eng. Pract.
,
46
, pp.
26
36
.
4.
Li
,
Z.
,
Liu
,
X.
,
Ren
,
W.
, and
Xie
,
L.
,
2013
, “
Distributed Tracking Control for Linear Multiagent Systems With a Leader of Bounded Unknown Input
,”
IEEE Trans. Autom. Control
,
58
(
2
), pp.
518
523
.
5.
Turpin
,
M.
,
Michael
,
N.
, and
Kumar
,
V.
,
2012
, “
Trajectory Design and Control for Aggressive Formation Flight With Quadrotors
,”
Auton. Robots
,
33
(
1–2
), pp.
143
156
.
6.
Kan
,
Z.
,
Yucelen
,
T.
,
Doucette
,
E.
, and
Pasiliao
,
E.
,
2017
, “
A Finite-Time Consensus Framework Over Time-Varying Graph Topologies With Temporal Constraints
,”
ASME J. Dyn. Syst. Meas. Control
,
139
(
7
), p.
071012
.
7.
Xi
,
J.
,
Shi
,
Z.
, and
Zhong
,
Y.
,
2012
, “
Consensus and Consensualization of High-Order Swarm Systems With Time Delays and External Disturbances
,”
ASME J. Dyn. Syst. Meas. Control
,
134
(
4
), p.
041011
.
8.
Olfati-Saber
,
R.
, and
Murray
,
R.
,
2004
, “
Consensus Problems in Networks of Agents With Switching Topology and Time-Delays
,”
IEEE Trans. Autom. Control
,
49
(
9
), pp.
1520
1532
.
9.
Olfati-Saber
,
R.
,
Fax
,
J.
, and
Murray
,
R.
,
2007
, “
Consensus and Cooperation in Networked Multi-Agent Systems
,”
Proc. IEEE
,
95
(
1
), pp.
215
233
.
10.
Ren
,
W.
,
2010
, “
Consensus Tracking Under Directed Interaction Topologies: Algorithms and Experiments
,”
IEEE Trans. Control Syst. Technol.
,
18
(
1
), pp.
230
237
.
11.
Meng
,
Z.
,
Ren
,
W.
,
Cao
,
Y.
, and
You
,
Z.
,
2011
, “
Leaderless and Leader-Following Consensus With Communication and Input Delays Under a Directed Network Topology
,”
IEEE Trans. Syst. Man Cybern.
,
41
(
1
), pp.
75
88
.
12.
Zelazo
,
D.
, and
Allgöwer
,
F.
,
2012
, “
Growing Optimally Rigid Formations
,”
American Control Conference
(
ACC
), Montreal, QC, Canada, June 27–29, pp.
3901
3906
.
13.
Yang
,
A.
,
Naeem
,
W.
,
Irwin
,
G. W.
, and
Li
,
K.
,
2014
, “
Stability Analysis and Implementation of a Decentralized Formation Control Strategy for Unmanned Vehicles
,”
IEEE Trans. Control Syst. Technol.
,
22
(
2
), pp.
706
720
.
14.
Porfiri
,
M.
,
Roberson
,
D. G.
, and
Stilwell
,
D. J.
,
2007
, “
Tracking and Formation Control of Multiple Autonomous Agents: A Two-Level Consensus Approach
,”
Automatica
,
43
(
8
), pp.
1318
1328
.
15.
Listmann
,
K. D.
,
Masalawala
,
M. V.
, and
Adamy
,
J.
,
2009
, “
Consensus for Formation Control of Nonholonomic Mobile Robots
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Kobe, Japan, May 12–17, pp.
3886
3891
.
16.
Anderson
,
R. P.
, and
Milutinović
,
D.
,
2014
, “
Stochastic Optimal Enhancement of Distributed Formation Control Using Kalman Smoothers
,”
Robotica
,
32
(
2
), pp.
305
324
.
17.
Kuriki
,
Y.
, and
Namerikawa
,
T.
,
2013
, “
Formation Control of UAVs With a Fourth-Order Flight Dynamics
,”
IEEE 52nd Annual Conference on Decision and Control
(
CDC
), Florence, Italy, Dec. 10–13, pp.
6706
6711
.
18.
Kuriki
,
Y.
, and
Namerikawa
,
T.
,
2014
, “
Consensus-Based Cooperative Formation Control With Collision Avoidance for a Multi-UAV System
,”
American Control Conference
(
ACC
), Portland, OR, June 4–6, pp.
2077
2082
.
19.
Kuriki
,
Y.
, and
Namerikawa
,
T.
,
2015
, “
Experimental Validation of Cooperative Formation Control With Collision Avoidance for a Multi-UAV System
,”
Sixth International Conference on Automation, Robotics and Applications
(
ICARA
), Queenstown, New Zealand, Feb. 17–19, pp.
531
536
.
20.
Godsil
,
C.
, and
Royle
,
G.
,
2001
,
Algebraic Graph Theory
,
Springer
, New York.
21.
Egerstedt
,
M.
, and
Hu
,
X.
,
2001
, “
Formation Constrained Multi-Agent Control
,”
IEEE Trans. Rob. Autom.
,
17
(
6
), pp.
947
951
.
22.
Leonard
,
N. E.
, and
Fiorelli
,
E.
,
2001
, “
Virtual Leaders, Artificial Potentials and Coordinated Control of Groups
,”
40th IEEE Conference on Decision and Control
(
CDC
), Orlando, FL, Dec. 4–7, pp.
2968
2973
.
23.
Xie
,
X.
,
1985
, “
Stable Polynomials With Complex Coefficients
,”
IEEE 24th Annual Conference Decision and Control
(
CDC
), Fort Lauderdale, FL, Dec. 11–13, pp.
324
325
.
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