We propose a framework for synthesizing real-time trajectories for a wide class of coordinating multi-agent systems. The class of problems considered is characterized by the ability to decompose a given formation objective into an equivalent set of lower dimensional problems. These include the so called radar deception problem and the formation control problems that fall under formation keeping and/or formation reconfiguration tasks. The decomposition makes the approach scalable, computationally economical, and decentralized. Most importantly, the designed trajectories are dynamically feasible, meaning that they maintain the formation while satisfying the nonholonomic and saturation type velocity and acceleration constraints of each individual agent. The main contributions of this paper are (i) explicit consideration of second order dynamics for agents, (ii) explicit consideration of nonholonomic and saturation type velocity and acceleration constraints, (iii) unification of a wide class of formation control problems, and (iv) development of a real-time, distributed, scalable, computationally economical motion planning algorithm.

1.
Cao
,
Y. U.
,
Fukunaga
,
A.
,
Kahng
,
A.
, and
Meng
,
F.
, 1995, “
Cooperative Mobile Robotics: Antecedents and Directions
,”
Proceedings of the 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems
, pp.
226
234
.
2.
Parker
,
L. E.
, 2000, “
Current State of the Art in Distributed Autonomous Mobile Robotics
,”
Distributed Autonomous Robotic Systems
,
L. E.
Parker
,
G.
Bekey
, and
J.
Barhen
, eds.,
Springer-Verlag
,
Tokyo, Japan
, Vol.
4
, pp.
3
12
.
3.
Betts
,
J. T.
, 1998, “
Survey of Numerical Methods for Trajectory Optimization
,”
J. Guid. Control Dyn.
0731-5090,
21
(
2
), pp.
193
207
.
4.
Milam
,
M. B.
,
Mushambi
,
K.
, and
Murray
,
R. M.
, 2000, “
A Computational Approach to Real-Time Trajectory Generation for Constrained Mechanical Systems
,”
Proceedings of the IEEE Conference on Decision and Control
, Sydney, Australia, pp.
845
851
.
5.
Faiz
,
N.
,
Agrawal
,
S. K.
, and
Murray
,
R. M.
, 2001, “
Trajectory Planning of Differentially Flat Systems With Dynamics and Inequalities
,”
J. Guid. Control Dyn.
0731-5090,
24
, pp.
219
227
.
6.
Justh
,
E. W.
, and
Krishnaprasad
,
P. S.
, 2004, “
Equilibria and Steering Laws for Planar Formations
,”
Syst. Control Lett.
0167-6911,
52
(
1
), pp.
25
38
.
7.
Paley
,
D.
,
Leonard
,
N. E.
, and
Sepulchre
,
R.
, 2005, “
Oscillator Models and Collective Motion: Splay State Stabilization of Self-Propelled Particles
,”
Proceedings of the 44th IEEE Conference on Decision and Control
, pp.
3935
3940
.
8.
Dunbar
,
W. B.
, and
Murray
,
R. M.
, 2006, “
Distributed Receding Horizon Control for Multi-Vehicle Formation Stabilization
,”
Automatica
0005-1098,
42
(
4
), pp.
549
558
.
9.
Belta
,
C.
, and
Kumar
,
V.
, 2004, “
Optimal Motion Generation for Groups of Robots: A Geometric Approach
,”
ASME J. Mech. Des.
0161-8458,
126
, pp.
63
70
.
10.
Tabuada
,
P.
,
Pappas
,
G. J.
, and
Lima
,
P.
, 2005, “
Motion Feasibility of Multiagent Formations
,”
IEEE Trans. Robot.
,
21
, pp.
387
392
.
11.
Giulietti
,
F.
,
Pollini
,
L.
, and
Innocenti
,
M.
, 2000, “
Autonomous Formation Flight
,”
IEEE Control Syst. Mag.
0272-1708,
20
, pp.
34
44
.
12.
Chichka
,
D. F.
,
Speyer
,
J. L.
, and
Park
,
C. G.
, 1999, “
Peak-Seeking Control With Application To Formation Flight
,”
Proceedings of the 38th IEEE Conference on Decision and Control
.
13.
Lewis
,
M. A.
, and
Tan
,
K. H.
, 1997, “
High Precision Formation Control of Mobile Robots Using Virtual Structures
,”
Auton. Rob.
0929-5593,
4
, pp.
387
403
.
14.
Mataric
,
M. J.
,
Nilsson
,
M.
, and
Simsarian
,
K. T.
, 1995, “
Cooperative Multi-Robot Box-Pushing
,”
Proceedings of the IEEE/RSJ Conference on Intelligent Robots and Systems
, pp.
556
561
.
15.
Balch
,
T.
, and
Arkin
,
R.
, 1998, “
Behavior-Based Formation Control for Multirobot Systems
,”
IEEE Trans. Rob. Autom.
1042-296X,
14
(
6
), pp.
926
939
.
16.
Cook
,
D. J.
,
Gmytrasiewicz
,
P.
, and
Holder
,
L. B.
, 1996, “
Decision-Theoretic Cooperative Sensor Planning
,”
IEEE Trans. Pattern Anal. Mach. Intell.
0162-8828,
18
, pp.
1013
1023
.
17.
Desai
,
J. P.
,
Ostrowski
,
J. P.
, and
Kumar
,
V.
, 2001, “
Modeling and Control of Formations of Nonholonomic Mobile Robots
,”
IEEE Trans. Rob. Autom.
1042-296X,
17
, pp.
905
908
.
18.
Desai
,
J.
,
Kumar
,
V.
, and
Ostrowski
,
J. P.
, 1999, “
Control of Changes in Formation for a Team of Mobile Robots
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, Detroit, pp.
1556
1561
.
19.
Yamaguchi
,
H.
, 2003, “
A Distributed Motion Coordination Strategy for Multiple Nonholonomic Mobile Robots in Cooperative Hunting Operations
,”
Rob. Auton. Syst.
0921-8890,
43
(
4
), pp.
257
282
.
20.
Sugihara
,
K.
, and
Suzuki
,
I.
, 1996, “
Distributed Algorithms for Formation of Geometric Patterns With Many Mobile Robots
,”
J. Rob. Syst.
0741-2223,
13
(
3
), pp.
127
139
.
21.
Purvis
,
K. B.
,
Chandler
,
P. R.
, and
Pachter
,
M.
, 2006, “
Feasible Flight Paths for Cooperative Generation of a Phantom Radar Track
,”
J. Guid. Control Dyn.
0731-5090,
29
(
3
), pp.
653
661
.
22.
Maithripala
,
D. H. A.
,
Jayasuriya
,
S.
, and
Mears
,
M. J.
, 2007, “
Phantom Track Generation Through Cooperative Control of Multiple ECAVs Based on Feasibility Analysis
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
129
, pp.
708
715
.
23.
Maithripala
,
D. H. A.
,
Woo
,
S.
, and
Jayasuriya
,
S.
, 2007, “
Rigid Formation Control of Nonholonomic Multi-Agents
,”
Proceedings of the ASME International Mechanical Engineering Congress and Exposition
, Seattle.
24.
Maithripala
,
D. H. A.
, and
Jayasuriya
,
S.
, 2008, “
Rigid Formation Keeping and Formation Reconfiguration of Multi-Agent Systems
,”
Proceedings of the 17th World Congress of the International Federation of Automatic Control
, Seoul, Korea, pp.
5155
5160
.
25.
Maithripala
,
D. H. A.
,
Maithripala
,
D. H. S.
, and
Jayasuriya
,
S.
, 2008, “
Unifying Geometric Approach to Real-Time Formation Control
,”
Proceedings of the American Control Conference
, Seattle, pp.
789
794
.
26.
Bullo
,
F.
, and
Lewis
,
A.
, 2004,
Geometric Control of Mechanical Systems
(
Texts in Applied Mathematics, Ser. No. 49
),
Springer-Verlag
,
Berlin
.
27.
Frankel
,
T.
, 1997,
The Geometry of Physics: An Introduction
,
Cambridge University Press
,
Cambridge, UK
.
28.
Zhang
,
J.
, and
Jayasuriya
,
S.
, 2009, “
Finite-Time Settling Real-Time Control for Multi-Robot Formation
,”
Proceedings of the 48th IEEE Conference on Decision and Control
, Shanghai, China, pp.
2990
2995
.
29.
Lewis
,
A. D.
, 2000, “
Simple Mechanical Control Systems With Constraints
,”
IEEE Trans. Autom. Control
0018-9286,
45
(
8
), pp.
1420
1436
.
30.
Maithripala
,
D. H. A.
, 2008, “
Coordinated Multi-Agent Motion Planning Under Realistic Constraints
,” Ph.D. thesis, Texas A&M University, College Station, TX.
You do not currently have access to this content.