Commenced in January 2007
Paper Count: 31108
Approximating Maximum Speed on Road from Curvature Information of Bezier Curve
Abstract:Bezier curves have useful properties for path generation problem, for instance, it can generate the reference trajectory for vehicles to satisfy the path constraints. Both algorithms join cubic Bezier curve segment smoothly to generate the path. Some of the useful properties of Bezier are curvature. In mathematics, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line. Another extrinsic example of curvature is a circle, where the curvature is equal to the reciprocal of its radius at any point on the circle. The smaller the radius, the higher the curvature thus the vehicle needs to bend sharply. In this study, we use Bezier curve to fit highway-like curve. We use different approach to find the best approximation for the curve so that it will resembles highway-like curve. We compute curvature value by analytical differentiation of the Bezier Curve. We will then compute the maximum speed for driving using the curvature information obtained. Our research works on some assumptions; first, the Bezier curve estimates the real shape of the curve which can be verified visually. Even though, fitting process of Bezier curve does not interpolate exactly on the curve of interest, we believe that the estimation of speed are acceptable. We verified our result with the manual calculation of the curvature from the map.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1110559Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3589
 Cai, H., & Wang, G. (2009). A new method in highway route design: joining circular arcs by a single C-Bézier curve with shape parameter. Journal of Zhejiang University SCIENCE A, 10(4), 562–569. doi:10.1631/jzus.A0820267.
 Choi, J., Curry, R. E., & Elkaim, G. H. (2012). Minimizing the maximum curvature of quadratic Bézier curves with a tetragonal concave polygonal boundary constraint. Computer-Aided Design, 44(4), 311–319. doi:10.1016/j.cad.2011.10.008H. Poor, An Introduction to Signal Detection and Estimation. New York: Springer-Verlag, 1985, ch. 4.
 G. Meyer and S. Deix, (2014). Research and Innovation for Automated Driving in Germany and Europe, in Road Vehicle Automation, Berlin, Springer.
 G. Meyer and S. Beiker (2014). Road Vehicle Automation, Springer, pp. 154.
 Gobithaasan, R. U. (2013). Various Types of Aesthetic Curves.
 Kaspar, C. (2009). Using Bezier Curves for Geometric Transformations.
 Kanellaidis G., Dimitropulos I., (1995), Investigation of current and proposed superelevation design practices on roadway curves, TRB (Transportation Research Board), International Symposium on highway geometric design practises, Boston, Massachussetts, pp. 2-3.
 Shen, T., Chang, C., Chang, K., & Lu, C. (2013). A Numerical Study of Cubic Parabolas On Railway Transition Curves Curves, 21(2), 191–197. doi:10.6119/JMST-012-0403-1.
 Walton, D. J., Meek, D. S., & Ali, J. M. (2003). Planar G2 transition curves composed of cubic Bezier spiral segments. Journal of Computational and Applied Mathematics, 157(2), 453–476. doi:10.1016/S0377-0427(03)00435-7.
 Wolhuter, K. (2015). Geometric Design of Roads Handbook. CRC Press. doi:10.1201/b18344.