![](bg6.png)
The image quality of the robot markers for the pre-
sented robot race are presented in Figure 11 and the
variance of the estimated robot position is presented
in Figure 12. Whenever the image quality decreases
the variance error of position estimate increases com-
promising the controller performance. On the other
hand whenever the image quality increases the error
variance is reduced and when the state update is done
the position estimate error is reduced.
Figure 11: a) Image quality of the center marker Q1,
b)Image quality of the angle marker Q2.
Figure 12: a) x and y variance, and (b) Angle variance.
5 CONCLUSIONS
Omnidirectional vehicles have many advantages in
robotics soccer applications, allowing movements in
every direction. The fact that the robot is able to move
from one place to another with independent linear and
angular velocities contributes to minimize the time to
react, the number of maneuvers is reduced and conse-
quently the game strategy can be simplified.
The robot relative position estimation is based on
the odometry calculation. The odometry calculation
uses each wheel velocity in order to estimate the robot
position, the disadvantage is that the position estimate
error is cumulative and increases over time.
It was made for the global vision localization sys-
tem an analysis of the error probability distributions.
The number of obtained pixels for the blue marker
(Q1), affects the error variance in x and y. On the
other hand the variance of the angle error probability
distribution is affected by the number of pixels ob-
tained for both makers, for the blue (Q1) and for the
yellow (Q2).
Odometry and global vision real time data fu-
sion was achieved applying an extended Kalman fil-
ter. This method was chosen because the robot motion
equations are nonlinear and also because the measure-
ments error probability distributions can be approxi-
mated to Gaussian distributions.
REFERENCES
(2008). Robocup. http://www.robocup.org/.
Borestein, Everett, and Feng (1996). where am I, Sensores
and Methods for Mobile Robot Positioning. Prepared
by the University of Michigan.
Choset, H., Lynch, K., Hutchinson, S., Kantor, G., Burgard,
W., Kavraki, L., and Thrun, S. (2005). Principles of
Robot Motion : Theory, Algorithms, and Implementa-
tions. MIT Press.
Dudek, G. and Jenkin, M. (2000). Computational Princi-
ples of Mobile Robotics. Cambridge University Press.
Gonc¸alves, J., Costa, P., and Moreira, A. (2005). Controlo
e estimac¸
˜
ao do posicionamento absoluto de um robot
omnidireccional de tr
ˆ
es rodas. Revista Rob
´
otica, Nr
60, pp 18-24.
Gonc¸alves, J., Pinheiro, P., Lima, J., and Costa, P. (2007).
Tutorial introdut
´
orio para as competic¸
˜
oes de futebol
rob
´
otico. IEEE RITA - Latin American Learning Tech-
nologies Journal, 2(2):63–72.
Kalm
´
ar-Nagy, T., D’Andrea, R., and Ganguly, P. (2002).
Near-optimal dynamic trajectory generation and con-
trol of an omnidirectional vehicle. In Sibley School of
Mechanical and Aerospace Engineering.
Negenborn, R. (2003). Robot Localization and Kalman Fil-
ters - On finding your position in a noisy world. Mas-
ter Thesis, Utrecht University.
Ribeiro, F., Moutinho, I., Silva, P., Fraga, C., and Pereira,
N. (2004). Controlling omni-directional wheels of a
robocup msl autonomous mobile robot. In Proceed-
ings of the Scientific Meeting of the Robotics Por-
tuguese Open.
Ribeiro, M. I. (2004). Gaussian Probability Density Func-
tions: Properties and Error Characterization. Tech-
nical Report, IST.
Sousa, A. (2003). Arquitecturas de Sistemas Rob
´
oticos e
Localizac¸
˜
ao em Tempo Real Atrav
´
es de Vis
˜
ao. PHD
Thesis, Faculty of Engineering of the University of
Porto.
Thrun, S., Burgard, W., and Fox, D. (2005). Probabilistic
robotics. MIT Press.
Welch, G. and Bishop, G. (2001). An introduction to the
Kalman filter. Technical Report, University of North
Carolina at Chapel Hill.
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