A NEW CLOTHOID APPROXIMATION METHOD FOR INTERACTIVE ROAD DESIGN

Abstract

The article considers the problem of approximating a plane curve given by a sequence of points by a clothoid. This problem arises when designing a plan for a railway or highway route, both in new construction and in reconstruction. Instead of manually assigning the parameters of the clothoid, which ensures a smooth transition from a straight line to a circular curve or between circular curves of different radii, the task of approximation is posed: that is, the best approximation of the original curve by a piece of clothoid. The purpose of the article: To present a new method for solving this problem, in which the approximation quality criterion (objective function) is a simple or weighted sum of squared deviations of given points from the desired clothoid, subject to curvature restrictions. The independent variables are the parameters that determine the position of the clothoid. The problem is solved in two stages. At the first stage, an initial approximation is constructed, that is, the permissible values of the clothoid parameters are determined using the evolvent method, and at the second stage, these parameters are optimized using nonlinear programming. Formulas are given for calculating the derivatives of the objective function, despite the absence of an analytical expression for this function in terms of the desired parameters of the clothoid. The small dimension of the problem makes it possible to implement and use gradient optimization methods in the interactive design mode. A numerical example is given. The clothoid approximation algorithm can be used not only in the interactive design of road routes, but also in other tasks.