![](bg6.png)
Future work lines are: the problem definition can
add as many constraints as necessary. The matrix is
defined with blocks, and it implies only to change or
to include a new block in the matrix. It is important
to work with the curvature or the total length of the
path because in a vehicle robot there is a maximum
curvature that the vehicle can follow and the path
length affects the total travel time. Both functions
could be including in the definition problem as a
cost function or as a constraint.
Finally, another future research is how to extend
it to 3D space. In this way, the trajectory of an UAV
or a robot arm could be simulated.
ACKNOWLEDGEMENTS
This research work is financially supported by the
project GV/2010/054 of the Generalitat Valenciana.
REFERENCES
Aleotti, J., Caselli, S., 2005. Trajectory Clustering and
Stochastic Approximation for Robot Programming by
Demonstration. In IROS 2005, IEEE Int. Conf. On
Intelligent Robots and Systems, pp. 1029 - 1034.
Aleotti, J., Caselli, S., 2005. Trajectory Reconstruction with
NURBS Curves for Robot Programming by
Demostration. In CIRA 2005, IEEE Int. Symp. on
Computational Intelligence in Robotics and
Automation, pp. 73-78.
Choi, J., Elkaim, G. 2008. Bézier Curves for Trajectory
Guidance. In WCECS 2008, World Congress on
Engineering and Computer Science, pp. 625-630.
Choi, J., Curry, R., Elkaim, G., 2008. Path Planning based
on Bézier Curve for Autonomous Ground Vehicles. In
WCECS 2008, World Congress on Engineering and
Computer Science, pp. 158 - 166
Choi, J., Curry, R., Elkaim, G. 2009. Smooth Path
Generation Based on Bézier Curves for Autonomous
Vehicles. In WCECS 2009, World Congress on
Engineering & Computer Science Vol II, pp.668-673.
Connors, J., Elkaim, G. 2007. Analysis of a Spline Based,
Obstacle Avoiding Path Planning Algorithm. In
VTC2007, IEEE Vehicle Technology Conference, pp.
2565-2569
Fowler, B., Bartels, R., 1993. Constrained-based curve
manipulation. IEEE Computer Graphics and
Applications 13, 5, pp. 43-49.
Hwang, J. H., Arkin, R. C., Kwon, D. S., 2003. Mobile
Robots at your fingertip: Bézier curve on-line trajectory
generation for supervisory control. In IROS 2003, Int.
Conf. on Int. Robots and Systems, pp.1444-1449.
Khatib, O., 1986. Real-time obstacle avoidance for
manipulators and mobile robots. In The International
Journal of Robotics Research, 5, 1, pp. 90-98.
Lizarraga, M., Elklaim, G., 2008. Spatially Deconflicted
Path Generation for Multiple UAVs in a Bounded
Airspace. In PLANS 2008, ION/IEEE Position,
Location and Navigation Symposium, pp. 1213 - 1218.
Meek, D. S., Ong, B. H., Walton, D. J., 2003. Constrained
interpolation with rational cubics. In Computer Aided
Geometric Design 20, pp. 253-275.
Montés, N., Sánchez, F., Hilario, L., Falcó, A. 2008. Flow
Numerical Computation through Bézier Shape
Deformation for LCM process simulation methods. In
Int. Journal of Material Forming, 1, pp. 919-922.
Montés, N., Herráez, A., Armesto, L., Tornero, J., 2008.
Real-time clothoid approximation by Rational Bézier
curves. In ICRA 2008, IEEE Int. Conf. on Robotics
and Automation, pp.2246 – 2251.
Mora, M. C., Pizá, R., Tornero, J., 2007. Multirate obstacle
tracking and path planning for intelligent vehicles. In
IV’07, IEEE Int.Vehicles Symposium, pp. 172-177.
Mora, M. C., Tornero, J., 2007. Planificación de
movimientos mediante la propagación de campos
potenciales artificiales. In CIBIM8, 8º Congreso
Iberoamericano de Ingeniería Mecánica, e-book.
Nagatani, K., Iwai, Y., Tanaka, Y., 2001. Sensor Based
Navigation for car-like mobile robots using Generalized
Voronoi Graph. In IROS 2001, Int. Conf. on Intelligent
Robots and Systems, pp. 1017-1022.
Pizá, R., 2003. Modelado del entorno y localización de
robots móviles autónomos mediante técnicas de
muestreo no convencional, PhD Thesis, Universidad
Politécnica de Valencia, Valencia.
Wu, Q. B., Xia, F. H., 2005. Shape modification of Bézier
curves by constrained optimization. In Journal of
Zhejiang University-Science A, pp 124-127.
Skrjanc, I., Klancar, G., 2007. Cooperative Collision
Avoidance between Multiple Robots Based on Bézier
Curves.In ITI 2007, 29
th
Int. Conf. on Information
Technology Interfaces, pp. 451-456.
Tornero, J., Salt, J., Albertos, P., 1999. LQ Optimal
Control for Multirate Sampled Data Systems. In 14
th
IFAC World Congress, pp. 211-216.
Xu, L., Chen, Y. J., Hu, N., 2002. Shape modification of
Bézier curves by constrined optimization. In Journal
of software (china), 13, 6, pp. 1069-1074.
ICEC 2010 - International Conference on Evolutionary Computation
248