Weight-Optimized NURBS Curves: Headland Paths for Nonholonomic Field Robots

In this work we develop a method for generating smooth headland paths which satisfy mechanical constraints of a nonholonomic field robot, while simultaneously fulfilling given optimization criteria. The feasibility of the method is explored in the context of agricultural fields. The headland paths are based on Non-Uniform Rational B-Spline (NURBS) curves, which offer a high level of customizability in terms of the degree of smoothness and continuity of the curves. We present the approach for setting control points for the NURBS curves for convex and concave vertices of the field, and formulate a nonlinear optimization problem (NLP) for computing the associated weights. We demonstrate the effectiveness of our method by showing the resulting paths along with their smooth curvature profiles for an example as well as a real field.