Smoothing curvature of trajectories constructed by noisy measurements in path planning problems for wheeled robots

摘要

A path planning problem for a wheeled robot is considered. The problem consists in constructing a trajectory that approximates a given ordered sequence of points on the plane and satisfies certain smoothness requirements and curvature constraints. Such a problem arises, for example, when it is required to follow in an automated mode a path stored as a discrete set of points measured in the course of the first passage of this path in a manual mode. Due to errors inherent in the data points, the shape of the curve approximating the desired path may turn out inappropriate or even unacceptable from the control standpoint. The shape of the curve can be improved by applying the so-called fairing, which consists in moving the original data points with the aim to minimize some functional. Adequate small variations of the data points (within the measurement error) preserve the proximity of the resulting path to the original data points and, at the same time, may considerably improve its shape. In the paper, a new global fairing method for improving shape of curves consisting of elementary B-splines is proposed. The improvement is achieved through minimization of jumps of the spline third derivative. The problem of finding desired variations reduces to solving a quadratic programming problem with simple constraints. The discussion is illustrated by numerical examples.