Curved path approximation in vehicle guidance systems and methods

A method of autonomous vehicle guidance comprising the steps of:

• providing a vehicle having a controller configured to guide the vehicle;
• receiving a set of two-dimensional reference points comprising a vehicle trajectory path;
• generating a guidance curve for the vehicle trajectory path by summing a weighted plurality of basis functions for each component of a coordinate pair, wherein the weighted plurality of basis functions has a cardinality less than a cardinality of the two-dimensional reference points, and uses linear least-squares regression with minimal approximation error between the basis functions of the guidance curve and the reference points of the vehicle trajectory path;
• generating guidance instructions comprising:
• (a) determining a nearest location point along the guidance curve relative to the vehicle;
• (b) determining a tangent direction of the guidance curve at the nearest location point;
• (c) determining curvature of the guidance curve based, at least in part, on the tangent direction at the nearest location point;
• and
• autonomously guiding the vehicle along the guidance curve with the guidance instructions provided to the controller of the vehicle, wherein the guidance curve is approximate the vehicle trajectory path and configured to provide an intermediate route between deviations along the vehicle trajectory path with the minimal approximation error.