We consider the problem of controlling a group of vehicles to a rigid formation. Our approach mimics the development of dynamics of a system of particles subject to constraints. In particular, we use the notion of constraint forces to achieve, and maintain, a given formation. As opposed to the potential function approach used in the literature, the proposed constraint force approach directly compensates for only those parts of the applied forces which act against the constraints. We develop a stable control algorithm that will achieve the formation while ensuring navigation of the group based on the desired trajectories that are consistent with the constraints. Simulation results on an example are shown to verify the proposed method.

1.
Desai
J. P.
,
Ostrowski
J. P.
, and
Kumar
V.
Modeling and control of formations of nonholonomic mobile robots
.
IEEE Transaction on Robotics and Automation
,
17
(
6)
:
905
908
,
2001
.
2.
D. V. Dimarogonas and K. J. Kyriakopoulos. Decentralized motion control of multiple agents with double integrator dynamics. In The 16th IFAC World Congress, 2005.
3.
Egerstedt
M.
and
Hu
X.
.
Formation constrainned multiagent control
.
IEEE Transaction on Robotics and Automation
,
17
(
6)
:
947
951
,
2001
.
4.
T. Eren. Rigid formation of autonomous agents. PhD thesis, Yale University,May 2004.
5.
H. Goldstein. Classical mechanics. Addison-Wesley, 1953.
6.
R. A. Horn and C. R. Johnson. Matrix Analysis. Cambridge University Press, 1999.
7.
Y. S. Krishna, S. Darbha, and K.R. Rajagopal. Information flow and its relation to the stability of the motion of vehicles in a rigid formation. In Proceedings of the American Control Conference, pages 1853-1858, 2005.
8.
Lawton
J. R.
,
Beard
R. W.
, and
Young
B. J.
.
A decentralized approach to formation maneuvers
.
IEEE Transaction on Robotics and Automation
,
19
(
6)
:
933
941
,
2003
.
9.
N. E. Leonard and E. Fiorello. Virtual leader, artificial potentials and coordinated control of groups. In Proceedings of the 40th IEEE Conference on Decision and Control, pages 2968–2973, 2001.
10.
R. Olfati-Saber. Flocking with obstacle avoidance. Technical Report 2003-006, California Institute of Technology, 2003.
11.
R. Olfati-Saber and R. M. Murray. Distributed cooperative control of multiple vehicle formations using structural potential functions. In The 15th IFAC World Congress, 2002.
12.
R. Olfati-Saber and R. M. Murray. Graph rigidity and distributed formation stabilization of multi-vehicle systems. In Proceedings of the 41th IEEE Conference on Decision and Control, pages 2965–2971, 2002.
13.
Olfati-Saberr
R.
.
Flocking for multi-agent dynamic systems: Algorithms and theory
.
IEEE Transaction on Automatic Control
,
51
(
3)
:
401
420
,
2006
.
14.
Rimon
E.
and
Koditschek
D. E.
.
Exact robot navigation using artificial potential function
.
IEEE Transaction on Robotics and Automation
,
8
(
5)
:
501
518
,
1992
.
15.
R.M. Rosenberg. Analytical Dynamics of Discrete Systems. Plenum Press, 1980.
16.
H. G. Tanner, A. Jadbabaie, and G. J. Pappas. Stable flocking of mobile agents, part I: Fixed topology. In Proceedings of the 42th IEEE Conference on Decision and Control, pages 2010–2015, 2003.
17.
Witkin
A.
,
Gleicher
M.
, and
Welch
W.
.
Interactive dynamics
.
Computer Graphics
,
24
(
2)
:
11
21
,
1990
.
This content is only available via PDF.
You do not currently have access to this content.