In this paper, the multi-agent flocking problem is investigated in a unified optimal control framework. The flocking characteristics, such as velocity alignment, navigation, cohesion, and collision/obstacle avoidance, are accomplished by formulating them into respective cost function terms. The resultant nonquadratic cost function poses a challenging optimal control problem. A novel inverse optimal control strategy is adopted to derive an analytical optimal control law. The optimality and asymptotic stability are proved and the distributed feedback control law only requires local information to achieve the flocking behaviors. Various simulation scenarios are used to demonstrate the effectiveness of the optimal flocking algorithm.

References

References
1.
Reynolds
,
C. W.
,
1987
, “
Flocks, Herds, and Schools: A Distributed Behavioral Model
,”
Comput. Graphics
,
21
(
4
), pp.
26
34
.
2.
Vicsek
,
T.
,
Czirok
,
A.
,
Ben-Jacob
,
E.
,
Cohen
, I
.
, and
Shochet
,
O.
,
1995
, “
Novel Type of Phase Transition in a System of Self-driven Particles
,”
Phys. Rev. Lett.
,
75
(
6
), pp.
1226
1229
.10.1103/PhysRevLett.75.1226
3.
Tanner
,
H. G.
,
Jadbabaie
,
A.
, and
Papps
,
G. J.
,
2007
, “
Flocking in Fixed and Switching Networks
,”
IEEE Trans. Autom. Control
,
52
(
5
), pp.
863
868
.10.1109/TAC.2007.895948
4.
Lee
,
D.
, and
Spong
,
M. W.
,
2007
, “
Stable Flocking of Multiple Inertial Agents on Balanced Graphs
,”
IEEE Trans. Autom. Control
,
52
(
8
), pp.
1469
1475
.10.1109/TAC.2007.902752
5.
Regmi
,
A.
,
Sandoval
,
R.
,
Byrne
,
R.
,
Tanner
,
H.
, and
Abdallah
,
C. T.
,
2005
, “
Experimental Implementation of Flocking Algorithms in Wheeled Mobile Robots
,”
Proceedings of 2005 American Control Conference
,
Portland, OR
, pp.
894
911
.
6.
Moshtagh
,
N.
, and
Jadbabaie
,
A.
,
2007
, “
Distributed Geodesic Control Laws for Flocking of Nonholonomic Agents
,”
IEEE Trans. Autom. Control
,
52
(
4
), pp.
681
686
.10.1109/TAC.2007.894528
7.
Cucker
,
F.
, and
Smale
,
S.
,
2007
, “
Emergent Behavior in Flocks
,”
IEEE Trans. Autom. Control
,
52
(
5
), pp.
852
862
.10.1109/TAC.2007.895842
8.
Dong
,
W. J.
,
2011
, “
Flocking of Multiple Mobile Robots Based on Backstepping
,”
IEEE Trans. Syst., Man, Cybern., Part B: Cybern.
,
41
(
2
), pp.
414
424
.10.1109/TSMCB.2010.2056917
9.
Tanner
,
H. G.
,
2004
, “
Flocking With Obstacle Avoidance in Switching Networks of Interconnected Vehicles
,”
Proceedings of 2004 IEEE International Conference on Robotics and Automation
,
New Orleans, LA
, pp.
3006
3011
.
10.
Gu
,
D. B.
, and
Hu
,
H. S.
,
2007
, “
Using Fuzzy Logic to Design Separation Function in Flocking Algorithms
,”
IEEE Trans. Fuzzy Syst.
,
16
(
4
), pp.
826
838
.10.1109/TFUZZ.2008.917289
11.
Zavlanos
,
M. M.
,
Tanner
,
H. G.
,
Jadbabaie
,
A.
, and
Pappas
,
G. J.
,
2009
, “
Hybrid Control for Connectivity Preserving Flocking
,”
IEEE Trans. Autom. Control
,
54
(
12
), pp.
2869
2875
.10.1109/TAC.2009.2033750
12.
Cucker
,
F.
, and
Dong
,
J. G.
,
2010
, “
Avoiding Collisions in Flocks
,”
IEEE Trans. Autom. Control
,
55
(
5
), pp.
1238
1243
.10.1109/TAC.2010.2042355
13.
Zhang
,
H. T.
,
Zhai
,
C.
, and
Chen
,
Z. Y.
,
2011
, “
A General Alignment Repulsion Algorithm for Flocking of Multi-Agent Systems
,”
IEEE Trans. Autom. Control
,
56
(
2
), pp.
430
435
.10.1109/TAC.2010.2089652
14.
Belta
,
C.
, and
Kumar
, V
.
,
2004
, “
Abstraction and Control for Groups of Robots
,”
IEEE Trans. Rob.
,
20
(
5
), pp.
865
875
.10.1109/TRO.2004.829498
15.
Olfati-Saber
,
R.
,
2006
, “
Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory
,”
IEEE Trans. Autom. Control
,
51
(
3
), pp.
401
419
.10.1109/TAC.2005.864190
16.
Su
,
H. S.
,
Wang
,
X. F.
, and
Lin
,
Z. L.
,
2009
, “
Flocking of Multi-Agent With A Virtual Leader
,”
IEEE Trans. Autom. Control
,
54
(
2
), pp.
293
307
.10.1109/TAC.2008.2010897
17.
Gu
,
D. B.
, and
Wang
,
Z. Y.
,
2009
, “
Leader-Follower Flocking: Algorithms and Experiments
,”
IEEE Trans. Control Syst. Technol.
,
17
(
5
), pp.
1211
1219
.10.1109/TCST.2008.2009461
18.
Haddad
,
W. M.
, and
Chellaboina
,
V.
,
2000
,
Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach
,
Princeton University Press
,
Princeton, NJ
.
19.
Bernstein
,
D. S.
,
1993
, “
Nonquadratic Cost and Nonlinear Feedback Control
,”
Int. J. Robust Nonlinear Control
,
3
(
3
), pp.
211
229
.10.1002/rnc.4590030303
20.
Ren
,
W.
, and
Beard
,
R. W.
,
2008
,
Distributed Consensus in Multi-Vehicle Cooperative Control
,
Springer-Verlag
,
London
.
21.
Bernstein
,
D. S.
,
2005
,
Matrix Mathematics: Theory, Facts, and Formulas With Application to Linear Systems Theory
,
Princeton University Press
,
Princeton, NJ
.
22.
Wang
,
J. N.
, and
Xin
,
M.
,
2012
, “
Distributed Optimal Cooperative Tracking Control of Multiple Autonomous Robots
,”
Rob. Auton. Syst.
,
60
(
4
), pp.
572
583
.10.1016/j.robot.2011.12.002
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