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Corner Cases: Headland Coverage Path Planning for Autonomous Driving in Arable Farming
Riikka Soitinaho, Timo Oksanen
TL;DR
Headland coverage is important in arable farming, yet previous methods do not fully cover field corners, where reversing manoeuvres are required. This method modifies headland-track polygon corners to accommodate reversing turns, and comparisons report better coverage especially around 90 degrees and at 240 degrees and above.
Problem
Previous headland-planning methods do not provide a complete description of how to fully cover field corners, where reversing manoeuvres are needed.
Source: §1 · p. 1Method
The method modifies nested headland-track polygon corners into boundary-reaching polylines that accommodate reversing turns.
Source: §1 · p. 1Results
The method provides better gap, overlap, and boundary-crossing coverage results than two adapted methods, especially around 90 degrees and at 240 degrees and above.
Source: §1 · p. 1, §6 · pp. 5–6Takeaways & Limitations
A case-by-case mix of the three methods can adapt the critical-angle threshold to choose trade-offs based on gap, overlap, crossing, and vehicle-implement limits.
Source: §6 · p. 6The method assumes sufficiently long field sides and may fail with alternating convex and concave critical vertices or narrow passages that cannot fit the required tracks.
Source: §6 · p. 6
Abstract
from arXiv · showhide
This paper presents a new method for headland coverage path planning for arable fields. Several earlier approaches suggest covering the headland with nested polygons and smooth turns, however, covering the field corners entirely requires manoeuvres with reversing. In the new method, the polygon corners are modified to allow a reversing turn. A comparison to two other methods considering gap, overlap, and crossing the field boundary shows an improvement in the coverage result especially in field corners of around 90 degrees, and 240 degrees and above. Applicability of the new method is shown with several examples of real polygonal field maps.
1. INTRODUCTION
Headland coverage matters for arable operations, but prior approaches leave field corners uncovered or do not fully cover the outermost track. This paper modifies nested headland-track polygons to accommodate reversing turns and reports improved coverage across a range of corner angles.
1. INTRODUCTION
- Headland coverage is needed for operations such as harrowing and seeding, and the headland provides space for vehicles to turn between tracks.The paper focuses on coverage paths, decoupling them from fieldwork-pattern and turn-path planning.Source: §1 · p. 1
- The literature lacks a complete headland coverage method that fully covers field corners.Earlier nested-polygon approaches round corners and leave areas uncovered; fully covering corners requires reversing manoeuvres.Source: §1 · p. 1
- The proposed method modifies nested-polygon vertices into boundary-reaching polylines so implements can reach closer to field corners.It is compared with rounded corners and an adaptation of X-type turns.Source: §1 · p. 1
- Compared with rounded-corner tracks and an adaptation of X-type turns, the proposed headland path method improves gap, overlap, and crossing across a range of field-corner angles.Source: §1 · p. 1
2. METHOD AND IMPLEMENTATION
The method represents a field as a polygon, offsets its boundaries to form headland-track outlines, identifies vertices requiring turns, and modifies those outlines at critical vertices. The resulting tracks accommodate reversing turns and extend toward the field corners, with a selected corner construction that trades reduced gaps for overlap and boundary crossing.
2.1 Definitions and scope
- A field is modelled as a simple polygon; a corner may contain multiple vertices but is assumed to have at most one critical vertex.A polyline is an open polygonal chain, while a polygon is closed; a criticality threshold distinguishes turns from small heading changes that the vehicle can follow with negligible deviation.Source: §2.1 · p. 2
2.2 Number of headland track polygons
- The number of headland-track polygons is chosen to cover the required headland width, using tracks as wide as the implement's operating width.The examples use a predefined number of tracks because the paper focuses on the coverage algorithm.Source: §2.2 · p. 2
2.3 Generating the headland track polygons
- The method generates linearised inner-offset polygons for the headland tracks and headland-mainland boundary, with offsets based on implement width.The outermost track polygon is offset by half an operating width from the field boundary; subsequent polygons are spaced by one operating width, and the innermost polygon is offset by half a width for the boundary.Source: §2.3 · p. 2
2.4 Critical vertices of the headland track polygons
- A critical-angle threshold, chosen for vehicle-implement manoeuvrability, identifies polygon vertices where turns are required.Turn-path planning is separate from this method; the turn path can reverse to the field boundary.Source: §2.4 · p. 2, Figure 1 · p. 2
2.5 Modifying the headland track polygon corners
- At critical vertices, the algorithm cuts and extends the track polygons to create tracks that accommodate reversing turns and reach toward field corners.At convex corners it cuts at the inner boundary and extends to the outer boundary; at concave corners, it switches those roles.Source: §2.5 · p. 3
- Extending tracks exactly to the field boundary reduces gaps but introduces overlap and boundary crossing; extending beyond avoids gaps while increasing both.Stopping short avoids overlap and crossing but leaves corner gaps; the method implements the exact-boundary option, yielding a combined area made up of 50% gap, 25% overlap, and 25% crossing in a simple convex corner.Source: §2.5 · p. 3
- When nearby non-critical vertices prevent parallel extensions, the algorithm extends from a later parallel segment and discards intervening vertices, potentially adding gap, overlap, and crossing.This is a special case in the corner-modification procedure.Source: §2.5 · p. 3
3. ALGORITHM PROPERTIES
The section compares three headland-planning methods on corner coverage, gap, overlap, and boundary crossing. Method C modifies nested headland tracks to let the vehicle reverse toward field corners.
3. ALGORITHM PROPERTIES
- Method C cuts and modifies nested offset tracks so the vehicle can reverse toward field corners; methods A and B use rounded tracks and an adapted X-type turn, respectively.Method A assumes infinite steering speed or stopping to reorient the wheels, with the implement operating during the turn.Source: §3 · p. 4
- Gap, overlap, and boundary crossing are measured geometrically from the areas swept by an implement-width line following each headland track.The calculation assumes the vehicle-implement combination follows the planned path exactly.Source: §3 · p. 4
- Method B has zero field-boundary crossing, while method A crosses in concave corners and method C’s crossing area falls to zero there.Method B’s crossing advantage comes at the cost of additional gap in convex corners.Source: §3 · p. 5
- Method A mostly has less overlap than methods B and C, but more gap, especially below 120° and above 240°.Method A has overlap in convex corners and crossing in concave corners.Source: §3 · p. 5
- Between 128° and 180°, method A performs best on gap, overlap, and crossing.Method C can provide the most gains near 90° and 270°.Source: §3 · p. 5
- Method C outperforms methods A and B on gap between 35° and 120° and generally performs better above 240°, while method B leaves no gap in concave corners.The comparison covers corner angles from 30° to 330°.Source: Figure 6 · p. 5, §3 · p. 5
4. EXPERIMENT
The proposed method is tested on polygonal field maps from a 101-field dataset. With the example parameter settings, 65 fields remain for testing after 36 are identified as having specified characteristics.
4. EXPERIMENT
- The field shapes come from a dataset of 101 fields whose geographic coordinates were converted to planar UTM coordinates.The dataset is attributed to Seyyedhasani et al. (2019).Source: §4 · p. 5
- The tests use four headland tracks, a 3.16 m implement operating width, and a 40° critical-angle threshold.At that threshold, turns are required below 140° or above 220° vertex angles.Source: §4 · p. 5
- 36 of 101 fields have at least one specified characteristic, leaving 65 field shapes expected to be solved successfully under the chosen parameters.The implementation is tested on each of the 65 remaining field shapes.Source: §4 · p. 5
5. RESULTS
The implementation solves most of 65 field shapes, including several challenging corner configurations. It fails on five fields with closely spaced alternating convex and concave critical vertices.
5. RESULTS
- The implementation successfully plans headland tracks for most of the 65 field shapes.Three successful solutions are visualized in Fig. 7.Source: §5 · p. 5
- Fig. 7 shows successful track extensions for corners with multiple vertices, nearby corners, and curved contours.For corners with multiple vertices, only one vertex is critical; the tracks extend to the field boundary considering the others.Source: §5 · p. 5
- Five of 65 fields could not be solved because nearby alternating convex and concave critical vertices caused track extensions to intersect other tracks before reaching a boundary.The extension line can encounter another headland track before reaching the outer or inner headland boundary.Source: §5 · p. 5
6. DISCUSSION
The proposed method improves coverage compared with two adapted earlier methods, particularly at corners around 90 degrees and 240 degrees or greater. Its performance depends on field-boundary characteristics, and some cases remain unresolved.
6. DISCUSSION
- Coverage improved over two adapted earlier methods, especially at field corners around 90 degrees and 240 degrees or above, measured by gap, overlap, and boundary-crossing area.Exact values depend on the scenario.Source: §6 · pp. 5–6
- Nearby alternating convex and concave critical vertices, narrow passages, and changes in critical vertices can prevent track construction; the approach also assumes sufficiently long field sides.Some such cases remain unsolved by all examined methods and are left for future work.Source: §6 · p. 6
- The method handles corners with multiple vertices when at most one is critical and permits transitions between inner and outer headland tracks at corners requiring turns.These are cases the other methods do not explicitly address.Source: §6 · p. 6
- The authors suggest combining the three methods, selecting among them case by case according to gap, overlap, boundary crossing, and vehicle-implement limits.The critical-angle threshold can be adapted to choose the method offering the better trade-off.Source: §6 · p. 6