{"title":"Approximating Maximum Speed on Road from Curvature Information of Bezier Curve","authors":"M. Y. Misro, A. Ramli, J. M. Ali","country":null,"institution":"","volume":108,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":734,"pagesEnd":742,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10003165","abstract":"Bezier curves have useful properties for path\r\ngeneration problem, for instance, it can generate the reference\r\ntrajectory for vehicles to satisfy the path constraints. Both algorithms\r\njoin cubic Bezier curve segment smoothly to generate the path. Some\r\nof the useful properties of Bezier are curvature. In mathematics,\r\ncurvature is the amount by which a geometric object deviates from\r\nbeing flat, or straight in the case of a line. Another extrinsic example\r\nof curvature is a circle, where the curvature is equal to the reciprocal\r\nof its radius at any point on the circle. The smaller the radius, the\r\nhigher the curvature thus the vehicle needs to bend sharply. In this\r\nstudy, we use Bezier curve to fit highway-like curve. We use\r\ndifferent approach to find the best approximation for the curve so that\r\nit will resembles highway-like curve. We compute curvature value by\r\nanalytical differentiation of the Bezier Curve. We will then compute\r\nthe maximum speed for driving using the curvature information\r\nobtained. Our research works on some assumptions; first, the Bezier\r\ncurve estimates the real shape of the curve which can be verified\r\nvisually. Even though, fitting process of Bezier curve does not\r\ninterpolate exactly on the curve of interest, we believe that the\r\nestimation of speed are acceptable. We verified our result with the\r\nmanual calculation of the curvature from the map.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"International Science Index 108, 2015"}