From 2D to 3D terrain-following area coverage path planning

TL;DR

The paper tackles full area coverage on uneven terrain by ground-based agricultural vehicles, requiring adjacent lanes spaced by the working width $w$ and maintaining a boom projection height $h$. It directly plans in 3D to generate adjacent mainfield lanes that preserve both $w$ spacing and a height $h$ above the terrain, using a reference lane and terrain data $z=f(x,y)$ with an IDW-based elevation look-up. Key contributions include a concrete 3D lane-generation algorithm, an elevation look-up strategy with $\Delta g=1$m and $Q_{IDW}=3$, and a tangential spacing heuristic to ensure smooth adjacent paths; numerical experiments on real-field data demonstrate reduced gaps/overlaps compared with 2D-first approaches, achieving lateral deviations on the order of a few meters for a 36m width. These results support practical deployment of 3D terrain-aware coverage planning for precise spraying and similar ground-based operations, reducing waste and improving application accuracy.

Abstract

An algorithm for 3D terrain-following area coverage path planning is presented. Multiple adjacent paths are generated that are (i) locally apart from each other by a distance equal to the working width of a machinery, while (ii) simultaneously floating at a projection distance equal to a specific working height above the terrain. The complexities of the algorithm in comparison to its 2D equivalent are highlighted. These include uniformly spaced elevation data generation using an Inverse Distance Weighting-approach and a local search. Area coverage path planning results for real-world 3D data within an agricultural context are presented to validate the algorithm.

Figures (10)

• Figure 1: Illustration of an important disadvantage of the method from hameed2016side. A zero vehicle height is implicitly assumed. While adjacent paths are spaced by nominal working width $w$ along the ground surface, this is not the case anymore as soon as a vehicle height larger than zero, $h>0$, is assumed.
• Figure 2: Bird's view: visualisation of the terms headland path, mainfield lane and a vehicle covering an area with a working width to spray an area (e.g., pesticide application). Top: Real-world visualization. Bottom: Abstract visualisation where a vehicle might travel from location Q towards R or D.
• Figure 3: Goal: area coverage paths floating at a projection distance $h$ above the terrain while adjacent mainfield lanes are spaced by distance $w$.
• Figure 4: (i) Vehicle visualization, and (ii) illustration of the assumption that boombar halves can be controlled independently up to a specific angle. The control of two boombar halves over two adjacent paths enables full working width $w$.
• Figure 5: Visualization of variables used in the Algorithm of Sect. \ref{['subsec_algo']}.