![](bg5.png)
0 2 4 6 8 10 12 14 16 18 20
0
0.05
0.1
0.15
0.2
0.25
Time [s]
Distance [m]
Distance of robots − Real
first to second robot
second to third robot
Figure 6: Distance between robots - experiment.
robots is an arc, which results in
L
arch
=
∆θ
2sin(∆θ/2)
× D (18)
where D is the straight line between the robots and ∆θ
is the difference in their orientation angles. It is clear
that after a transition phase (the merging and splitting
of the platoons is currently under investigation) the
second and third vehicle follow with acceptable accu-
racy. The results of the real experiments are slightly
worse due to the noise in the position estimation and
due to the time delay of the optical tracking and recog-
nition. The accuracyof the integration method and the
associated error, which is equivalent to the slipping of
the vehicle’s wheels, is analysed and illustrated in the
Fig. 7, where the distance between the leading and
the following platoon robots in a straight path is illus-
trated. It can be seen that the constant slipping of the
wheels has no influence on the steady-state distance
of the platoon vehicles. This conclusion makes sense
since servoing accuracy should not be destroyed be-
cause relative information among vehicles (distances
and azimuth orientations) are always obtained from
accurate relative sensor.
5 CONCLUSIONS
A new algorithm for the control of vehicle platoons
was proposed. The following vehicle only has infor-
mation about its own orientation and about the dis-
tance and azimuth of the leading vehicle. Its own po-
sition is determined using odometry and a compass. It
calculates the reference path in a parametric polyno-
mial form, and the parameters of the polynomials are
determined by the least-squares method. Having the
reference path, the feed-forward and feed-back con-
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0.15
0.2
0.25
Time [s]
Distance [m]
Slip = 0%
Slip = 10%
Slip = 20%
Slip = 30%
Figure 7: Distance between robots with slip in a straight
path (simulation).
trol are applied to the following vehicle. The fol-
lowing vehicle calculates its own position by means
of a simple Euler integration. It was established that
the error in the integration procedure (equivalent to
the errors due the wheel slipping) has a minor influ-
ence on the accuracy of the platoon distance. The pro-
posed algorithm was tested on a robot-soccer test bed.
The results confirm the applicability of the proposed
method.
REFERENCES
Balluchi, A., Bicchi, A., Balestrino, A., and Casalino, G.
(1996). Tracking control for dubin’s cars. In Pro-
ceedings of the 1996 IEEE International Conference
on Robotics and Automation,Minneapolis, Minnesota,
pp. 3123-3128.
Bom, J., Thuilot, B., Marmoiton, F., and Martinet, P.
(2005). A global control strategy for urban vehicles
platooning. relying on nonlinear decoupling laws. In
Proceedings of the 2005 IEEE/RSJ International Con-
ference on Intelligent Robots and Systems, Alberta,
pp. 1995-2000,.
Canudas de Wit, C. and Sordalen, O. J. (1992). Exponen-
tial stabilization of mobile robots with nonholonomic
constraints. In IEEE Transactions on Automatic Con-
trol, Vol. 37, No. 11, pp. 1791-1797.
Contet, J., Gechter, F., Gruer, P., and Koukam, A. (2007).
Application of reactive multiagent system to linear
vehicle platoon. In Annual IEEE International Con-
ference on Tools with Artificial Intelligence(*ICTAI*),
Grece, Patras.
Daviet, P. and M.Parent (1996). Longitudinal and lateral
servoing of vehicles in a pltoon. In IEEE Intelligent
Vehicles Symposium, Proceedings, pages 41-46,.
Gehrig, S. K. and Stein, F. (2001). Elastic bands to en-
hance vehicle following. In IEEE Conference on In-
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