Generating Parameterized Smooth Paths with a Curve-Fitting Algorithm

Path smoothness is essential in path tracking for autonomous driving, while smooth means that the curvature of path is continuous. Parameterizing the path as a profile of $$curvature\ \kappa $$ , that is a function of $$arc\ length\ s$$ , not only simplifies description of the reference path, but also improve path tracking performance. To achieve this, there must be a trade-off between the smoothness of the curvature profile and the precision of the curve-fitting. This paper describes an algorithm which fits the reference path described by a sequence of cartesian points. The algorithm utilizes piecewise linearized $$\kappa -s$$ profile to represent the reference path. The curvature profile is smooth subject to the constraints of lateral deviation.