Advanced quadratic optimization based smoothing framework for curved path planning in sustainable agricultural operations

Abstract

This research introduces an advanced quadratic optimization framework for the creation of smooth, curvature-continuous, and steerable waylines in precision agriculture. The framework combines curvature control, coverage uniformity, and steering feasibility into a single mathematical model to reduce skips and overlaps during field operations. Three smoothing techniques; B-spline, Bézier, and Non-Uniform Rational B-Spline (NURBS) are applied and compared to determine their impact on curvature continuity and field coverage efficiency. An extensive sensitivity analysis is performed to understand the effect of swath width tolerance, angular deviation, objective function cost weights, number of characteristic points of the spline curve, and solver configurations using IPOPT and Gurobi. Additionally, a versatile reference-line propagation method enables waylines to be created from either the field boundary or an interior line, thus, increasing flexibility in irregular geometries. The findings reveal that the NURBS-based method offers the greatest geometric flexibility and the most effective field utilization when compared to the other tested methods. The framework is shown to be performant and stable across irregular real-world fields, consequently, it is a scalable and practical solution for optimization-driven path planning in agriculture aiming at sustainability.