Side-to-Side 3D Coverage Path Planning Approach for Agricultural Robots to Minimize Skip/Overlap Areas between Swaths

Full text

Robotics and Autonomous Systems 76 (2016) 36–45
Contents lists available at ScienceDirect
Robotics and Autonomous Systems
journal homepage: www.elsevier.com/locate/robot
Side-to-side 3D coverage path planning approach for agricultural
robots to minimize skip/overlap areas between swaths
I.A. Hameeda,∗,A. la Cour-Harbob,O.L. Osena
aNorwegian University of Science and Technology, Faculty of Engineering and Natural Sciences, Department of Automation Engineering, Larsgårdsvegen
2, 6009 Ålesund, Norway
bAalborg University, Faculty of Engineering and Science, Department of Electronic Systems, Section of Automation and Control, Fredrik Bajers Vej 7C, 9220
Aalborg, Denmark
highlights
•We developed a more efficient 3D field coverage approach compared to existing approaches.
•We developed a numerical approach to examine the efficiency of 3D coverage algorithms in terms of skip/overlap areas.
•We developed side-to-side 3D field coverage approach, which ensure 100% coverage regardless of the topographical nature of the field surface.
•Simulation and real field experiments are conducted to prove the efficiency and superiority of the developed approaches.
article info
Article history:
Received 7 January 2015
Received in revised form
10 November 2015
Accepted 16 November 2015
Available online 3 December 2015
Keywords:
Area coverage planning
Coverage efficiency
Side-to-side 3D coverage planning
Robotics
Optimization
abstract
Automated path planning is an important tool for the automation and optimization of field operations.
It can provide the waypoints required for guidance, navigation and control of agricultural robots and
autonomous tractors throughout the execution of these field operations. Typical field operations are
repetitively required nearly every cropping season and therefore it should be carried out in a manner that
maximizes the yield and minimizes operational cost, time and environmental impact taking into account
the topographic land features. Current 3D terrain field coverage path planning algorithms are simply 2D
coverage path planning projected into 3D through field terrain represented by the field’s Digital Elevation
Model (DEM). When projecting 2D coverage plan into its 3D counterpart, the actual distance between
adjacent paths on the topographic surface either increases or decreases, and consequently there might be
skips or overlaps between adjacent paths on the slopes. In addition, when the machine rolls on slopes the
effective width of the implement decreases by a similar amount to double this error and complicates the
problem. Skips and overlaps can lead to an inefficient use of land and resources. In this paper, a numerical
approach to estimate the total skip/overlap areas is developed and applied to determine the optimum-
driving angle that minimizes this impact. Also, a novel side-to-side 3D coverage path planning approach,
which ensures zero skips/overlaps regardless of the topographical nature of the field terrain, is developed.
The approaches developed in this paper are tested and validated using a hypothetical test field of a tailored
terrain and a real experimental field of uneven terrain nature. The proposed approaches illustrated that
a significant percentage of uncovered area could be saved if appropriate driving angle is chosen and if a
side-to-side 3D coverage is used.
©2015 Published by Elsevier B.V.
1. Introduction
Robots, for long decades, have played a fundamental role in in-
creasing the efficiency and reducing the cost of many industries
∗Corresponding author.
E-mail address: ibib@ntnu.no (I.A. Hameed).
and products. Robots are used for tasks when there are concerns
over human safety, or when the task is repetitive and can be done
more productively by a robot working longer hours than humans
and offer a precision that humans cannot provide. The agricul-
tural industry is no different in this regard. In the last two decades,
a similar trend has started to take place in agriculture, which is
suffering from shortage of skilled and unskilled labor workforce.
With GPS- and vision-based self-guided tractors and harvesters
already being available commercially, farmers have started to
http://dx.doi.org/10.1016/j.robot.2015.11.009
0921-8890/©2015 Published by Elsevier B.V.

I.A. Hameed et al. / Robotics and Autonomous Systems 76 (2016) 36–45 37
(a) Illustration of roll effect on effective
width; ais the reduction of effective
boom width while bis the lateral
translation of implement [12].
(b) Conceptual diagram of overlap and skip areas
between two adjacent swaths caused by variation of
slope from pass to pass [17].
Fig. 1. Effect of roll on machine coverage.
experiment with autonomous systems that automate typical field
operations such as harvesting, mowing, spraying, and weed re-
moval [1]. Automated path planning is an important tool for au-
tomation and optimization of field operations. It is used to provide
a complete trajectory for guidance, navigation and control of agri-
cultural robots and autonomous tractors throughout the execution
of these field operations [2,3].
Currently, most coverage path planning algorithms are only ca-
pable of dealing with fields on 2D terrain [4–6]. Optimization algo-
rithms have been developed to optimally select driving angle and
sequence of tracks of these 2D driving patterns so that field oper-
ations can be carried out in a manner that reduces maneuvering
over the field surface and total operational time and in turn re-
duces soil compaction, fuel consumption and henceenvironmental
impact [7–10]. 2D coverage path planning algorithms are based
on the assumption that most agricultural fields are flat and hence
ignore elevation changes. It has been observed that important in-
formation is lost when elevation changes are ignored which de-
teriorates the optimization process and thus gives inferior design
of the coverage paths [11]. The terrain characteristics have signifi-
cant influence on the design and optimization of the coverage path
planning. A great proportion of farms have rolling terrains, which
have considerable influences on the design of coverage paths, for
example, 47% of cropland in the United States is no less than 2%
slopes; 48% of the cropland is on slopes between 2% and 10% [12].
Koostra et al. [13] showed that the error between planimetric and
topographic surface area could be as much as 5% in typical farm
fields. Dilon et al. [14] demonstrated that these area discrepan-
cies are economically significant, especially when considered over
multiple field operations. Therefore, a new coverage path planning
considering the terrain characteristics is expected to have a great
potential to further optimize field operations.
Despite its importance in the optimization of field operations
and accurate navigation of agricultural robots and autonomous
tractors, 3D terrain field coverage path planning did not attract
the expected attention from researchers. Only limited research
on developing area coverage planning for 3D terrain has been
reported. For example, Jin and Tang [15] developed an optimized
3D terrain field coverage path planning algorithm that classifies
the field terrain into flat and sloppy areas and then applies
the most appropriate path planning strategy to each region in
terms of minimized headland turning cost, soil erosion cost, and
skip/overlap area cost. Hameed et al. [8,9] developed a simple
and effective approach for 3D terrain path planning where the
2D path planning was first generated and then projected through
the field’s DEM. Based on this approach, Hameed [16] developed
an optimization algorithm which can optimize the driving angle
and sequence of tracks over 3D terrain so that field operations
can be carried out in a manner which reduces operational time,
fuel consumption, and non-productive traveled distance and
maneuvering over the field surface.
The objective of this paper is to develop an approach to estimate
the total skipped/overlapped areas between field rows when
projecting 2D coverage path into 3D coverage path through DEMs.
This approach will be used to find the optimal driving angle that
minimizes the skipped/overlapped areas and hence reduces its
economical impact. In addition, a new 3D coverage approach is
proposed which can provide full coverage regardless of the terrain
structure of the field. The developed approaches are applied to
typical (synthesized) field terrain and two real fields.
The paper is organized as follows; initially, a simple 2D coverage
approach is introduced in Section 2.1. Next, a 3D terrain modeling
and interpolation is presented in Section 2.2. The impact of
projecting 2D planning into its 3D counterpart is then presented
in Section 2.3. In Section 2.4, a complete side-to-side 3D coverage
approach that ensures full coverage regardless of the terrain
structure is introduced. In Section 3, a number of experiments
are performed to test and validate the developed approaches.
Finally, a brief concluding remarks and future work are presented
in Section 4.
2. Methodology
2.1. Background
The basic assumption that most agriculture fields are flat and
ignoring elevation changes across the field has lead to some
problems not only with 2D path planning but also with 3D path
planning obtained from projecting the resultant 2D path planning
through the field terrain. When projecting 2D planning result to
3D terrain, the actual distance between paths on the topographic
surface either increases or decreases, consequently, there will be
skip and/or overlap areas between adjacent paths on the slopes,
as it isshown in Fig. 1(a). Former researchers figured out that this
area discrepancy between planimetric and topographic models is
significant and might result in economic impacts, especially when
considered over multiple field operations [13,14]. Topography can
have an impact on machine travel patterns in the field, which
in turn will affect the application coverage [12]. This impact
becomes evident if the machine is utilizing some form of GPS-
based guidance system, which is not considering the vertical
(i.e., elevation) component of position. This will have several
impacts on the effective coverage of the machine. If the machine is
experiencing some roll (sideways tilt), its planimetric or effective
width decreases which makes the problem even worse as it is
obvious in Fig. 1(b). Similarly for a given swath spacing, the actual
distance between paths on the topographic surface increases.
The spacing increase is the same as the machine width decrease
essentially doubling the error. The result is that there will be skips
on steeper side slopes and vice versa [12]. Further complicating the
effect of machine roll is the fact that the GPS antenna is mounted
on the top middle of the machine. As the machine rolls, if there is

38 I.A. Hameed et al. / Robotics and Autonomous Systems 76 (2016) 36–45
Fig. 2. An illustrative example of the 2D geometrical field representation: (a) satellite image of a field of an area of around 5.54 (ha) located in [+54°57′8.28′′ N,
+9°46′49.31′′E], (b) driving pattern for a driving angle of 4.5°, working width of 9 m and two headland polygons, and (c) driving pattern for two headland paths at
both sides of the field tracks where field tracks are clustered into blocks [8,9].
no measurement and compensation of roll in the GPS position, the
guidance system will attempt to keep the antenna on the desired
path instead of the centerline of the machine. This will cause the
machine implement (e.g., spray boom, planter or tillage tool) to
actually translate to the side of the desired path.
This translation will not affect coverage if the roll is constant
from one path to the next since translation on each pass will be
the same amount in the same direction. The translation becomes
critical as the slope varies from pass to pass, for example, at a
translation from higher flat area to a downward slope, adjacent
swaths could overlap. Likewise, a skip could be produced on a
translation from a slope to a lower flat, as it is shown in Fig. 1(b).
Stombaugh et al. [12] pointed out that manufactures of guidance
and automated steering systems are attempting to compensate
for translational effect caused by topography by incorporating roll
measurement and compensation devices into their equipment.
However, the problem remains as long as the resultant path
is obtained through simple projection through DEMs without
incorporating the topographical effect in the coverage path design.
Therefore, the objective here is to incorporate the topographical
effect of the field terrain in the design of the 3D coverage path
to minimize the skips between adjacent swaths. Two algorithms
are proposed. First, an algorithm to numerically evaluate the total
skips in current conventional 3D coverage algorithms, which is
based on projection through field terrain and provides farmers
with the optimum driving angle that minimizes the total skips
and/or overlaps. Second, an enhanced 3D side-to-side coverage
algorithm is proposed in which spaces between adjacent swaths
are kept equal taking into account the topographical nature of the
field.
2.2. 2D coverage path planning
Field coverage is the process in which a driving pattern is gen-
erated to guide an autonomous tractor or a robot to cover a crop
field in a systematic way and in a manner which reduces opera-
tional time, maneuvering over the field surface, soil compaction,
fuel consumption, etc. These patterns can be represented by a set
of waypoints representing field tracks and headland polygons par-
allel to a predefined driving direction and within a certain operat-
ing width between its swaths. In recent years, many field coverage
approaches have been developed [18,4–6,19,7].
The inputs to such methods are; (1) the field outer boundaries
as a set of coordinates, (2) driving angle (basically the driving
direction as a compass direction in degrees), and (3) the number
of headland paths (i.e., chosen based on the operating width and
minimum turning radius of the vehicle). The outputs are; (1) a set
of waypoints representing field tracks, and (2) a set of waypoints
representing headland paths or polygons (as it is shown in Fig. 2).
Headland paths could be in the form of closed polygons adjacent
to field outer boundaries and permanent obstacles, as it is shown
in Fig. 2(b), and this type requires more computational time to
provide more smoothed polygons. Alternatively, headland paths
could be generated at both sides of the field tracks, as it is shown
in Fig. 2(c) and this approach provides headland paths similar to
what human drivers used to do when they drive in the field and
this approach is three times faster than generating headland paths
as closed polygons because it does not require smoothing which is
computationally exhaustive [8,9].
2.3. Rapid 2D/3D path planning
In 2D coverage path planning approaches, each field track/swath
is defined by two waypoints, namely, starting and ending way-
points. To map the 2D coverage path into its 3D counterpart, the
track line is sampled to generate intermediate waypoints at dis-
tance less than the grid cell size. These points are then mapped
through the field terrain to find the elevation of each intermediate
point. Terrain’s surfaces are represented in 3D using digital eleva-
tion model (DEM), which is a grid of squares representing eleva-
tions. DEMs are commonly built using data collected using remote
sensing techniques, but they may also be built from land surveying.
This process is carried out track-by-track and hence time consum-
ing and not practical for optimization algorithms such as Genetic
algorithms (GAs) and does not ensure full coverage [8,9].
In this paper, a new 2D/3D field coverage approach is
developed, in which field tracks are generated and mapped
directly. In this approach, the minimum bounding box (MBB),
which is the smallest enclosing box of the set of points representing
the field’s boundaries, is first determined. MBB is then extended by
a distance (e.g., half the circumradius of the field’s outer polygon
or the field’s MBB) to ensure full coverage when the grid is rotated
to match the required driving angle. The EMBB is then divided
along its X- and Y-axes into cells, so that each cell within the
grid is a rectangle of length land width win meters. Cell length,
l, is used to define the precision of the resultant 3D tracks while
cell width, w, is used to define the operating width of the vehicle
or implement or the effective distance between swaths, as it is
shown in Fig. 3(a). Cell length, l, is usually chosen as a trade-off
between resolution and computational complexity. Fig. 3(b) shows
the coordinate grid of an EMBB of a real field for a driving angle
θ=90°,l=0.1 m, w =10 m. Driving angle is defined as
the angle between the horizontal axis, X-axis, and the required
driving direction. The vertical grid lines (blue lines) shown in
Fig. 3(b) which are represented as a set of points at distance, l, are
considered as potential field tracks.
Once the coordinated grid is obtained, the grid can then be
rotated by an angle, θ, counter clockwise around its center point,

I.A. Hameed et al. / Robotics and Autonomous Systems 76 (2016) 36–45 39
Fig. 3. Grid based 2D/3D coverage approach. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Flowchart of the developed 2D/3D field coverage approach.
(xc,yc), using Eq. (1) where each primitive or point (x,y) is first
rotated by an angle θaround the origin and then translated in the
direction of the center point, (xc,yc) to then translated back again
to its original location.
x′
y′
1=cos (θ)−sin (θ)xc
sin (θ)cos (θ)yc
0 0 1 ·x
y
1,
xθ
yθ
1=−
cos (θ)sin (θ)−xccos (θ)−ycsin (θ)
sin (θ)cos (θ)xcsin (θ)−yccos (θ)
0 0 1 
·x′
y′
1.
(1)
The final 3D tracks can then be obtained through filtering
where points, which are not located inside the field polygon, are
discarded (this can easily done using a MatlabTM function called
inpolygon [20]). The 3D tracks are then obtained by simple projec-
tion through the DEM of the field to find elevation of each point.
The approach is described by the flowchart shown in Fig. 4.
2.4. 3D terrain interpolation
Terrain representation plays a central role in environmental
modeling and landscape visualization. The Digital Elevation Mod-
els (DEMs) contain elevation of discrete points measured at regu-
lar spaced intervals to represent the surface. DEMs of agricultural
field terrains have an accuracy of 1.6 m. The accuracy of DEMs data
has direct implications on the associated operations such as field
coverage [21,22]. Before projecting a 2D driving pattern into its 3D
counterpart, it is essential to interpolate the terrain in order to find
elevation of positions which do not exist in DEM data. Interpola-
tion is the first step toward accurate 3D coverage path planning.
Interpolating methods were applied to estimate the elevation of
any point based on the data pointsin DEMs [23].
In this paper, Bilinear Interpolation (BLI) approach is used. BI
is a resampling method that uses the distance-weighted average
of the four values of a grid cell to estimate a new value. Interpo-
lation can be used to estimate the elevation of an unknown point
in the terrain surface that does not exist in the DEM grid data us-
ing four input grid known neighboring points. The key idea behind
BI is to: (1) perform linear interpolation along each line of latitude
in the West–East direction; (2) normalize the two partial weights
for each point; and finally (3) perform a linear interpolation along
each line of longitude in the perpendicular (i.e., the South–North)
direction, as it is shown in Fig. 5. Although each step is linear in the
sampled values and in the position, the interpolation as a whole is
not linear but rather quadratic in the sample location. Suppose that
we want to find the value of the unknown function fat the point
P=(x,y)where fis the elevation at point P,xand yare the lati-
tude and longitude of the position on the surface. It is assumed that
we know the values of fat the four grid points; f(Q11)is the ele-
vation at Q11 =(x1,y1),f(Q12)is the elevation at Q12 =(x1,y2),
f(Q21)is the elevation at Q21 =(x2,y1), and f(Q22 )is the elevation
at Q22 =(x2,y2). We first do linear interpolation in the x-direction
(i.e., West–East direction). This yield:
f(R1)≈x2−x
x2−x1
f(Q11)+x−x1
x2−x1
f(Q21),
f(R2)≈x2−x
x2−x1
f(Q12)+x−x1
x2−x1
f(Q22)
(2)
where R1=(x,y1)and R2=(x,y2).

40 I.A. Hameed et al. / Robotics and Autonomous Systems 76 (2016) 36–45
Fig. 5. The four red dots; Q11,Q12 ,Q21 and Q22 show the available four data points
of a cell and the blue dot, P, is the point at which we want to interpolate to find
elevation. (For interpretation of the references to colour in this figure legend, the
reader is referred to the web version of this article.)
We then proceed by interpolating in the y-direction (i.e., the
South–North direction) to give the desired estimate of f(x,y), as
follows:
f(P)≈y2−y
y2−y1f(R1)+y−y1
y2−y1f(R2).(3)
Other methods for interpolating data points on a 2D regular
grid such as Bicubic Interpolation (BCI) where the interpolated sur-
face is smoother than the corresponding surfaces are obtained by
BLI [24].
2.5. Efficiency estimation of conventional 3D coverage planning
Agriculture constantly strives for improved efficiencies. Agri-
cultural application or swathing efficiency is one area of inter-
est given the potential of new technology in precision farming.
Tools and techniques are needed to assess application efficiency
so in-field guidance techniques can be compared and quantified.
One measure of application efficiency is the occurrence of over-
lap (double application) and skips (missed application) areas be-
tween adjacent swaths in application. Many techniques have been
developed to evaluate the application efficiency in field applica-
tions [17]. These approaches were based on the assumption that
most of agricultural fields are flat and spaces between swaths are
fixed regardless of the topographical nature of the field terrain. Ig-
noring elevation change simplified the derivation process of 2D
coverage path planning used in today agriculture. However, when
simply projecting 2D coverage path into 3D through field terrain,
new problems and challenges come up.
For a given swath spacing, the actual distance between paths on
the topographic surface increases and there will be skips between
adjacent paths on the slopes. If the machine is experiencing some
roll (sideways tilt), its effective width decreases while spacing
increases essentially doubling the error. Therefore, the need arises
to develop a quantitative analysis to compare operational and
topographic surfaces in terms of skips and/or overlaps to quantify
this impact and to improve the application efficiency. Stombaugh
et al. [12] presented an analytical approach to quantify total skip
area; however, this method assumed that the entire field is in
one common slope. The objective of this paper is to develop
a numerical approach that is able to quantify the skips and/or
overlaps of any 3D coverage plan for all driving angles with high
accuracy. The approach can be potentially used to provide farmers
with the driving angle which when followed can minimize the
topographical impact on coverage efficiency. In addition, it will
raise the concern for the need for a new enhanced 3D coverage
path planning algorithm that is able to compensate for topographic
impact on swath spaces.
Numerical approach
In this approach, 3D coverage path planning is quantified for
skip (i.e., due to missed application) and/or overlap areas (i.e., due
to double application). A coverage path planning consists of a
number of headland paths/polygons and a number of parallel field
tracks, as it is shown in Fig. 5(a), for a hypothesized testing field
terrain of 200 m2flat area with a half cylinder of radius 10 m on its
center to provide a simple terrain with varying sloping. The plan is
generated for an effective operating width w=1 m and the driving
angle θ=90°. Each field track consists of a number of segments,
each of length lchosen in a way to give sufficient accuracy when
represented in 3D. To numerically measure the distance between
tracks in 3D, a 3D cylinder of radius equal to the vehicle’s operating
width, w, is generated around each segment, as it is shown in
Fig. 5(b). Then a fine grid is generated and projected into the field
terrain. Finally, the total number of points which are located inside
the 3D cylinder, N, is determined and divided by the total number
of points located in the entire field, Nf, and used as an estimate of
the coverage efficiency, given by Eq. (4).
covef =
cy
N/Nf.(4)
Covered area can then be obtained by multiplying the field
surface area by the coverage efficiency. When the approach is
applied to the 3D driving path of the field shown in Fig. 6(a), a huge
number of tiny 3D cylinders of radius, w, are generated around
each segment as it is shown in Fig. 6(c). Fig. 6(d) shows the field
from 2D point of view where skips cannot be noticed. By comparing
Fig. 6(c) and (d), it becomes obvious that the topographical nature
of the field increased spaces between swaths and large areas are
missing covering. In this example and for this driving angle around
16% of the field area is missing covering which can cause financial
losses to farmers.
2.6. Side-by-side 3D coverage approach
The cylindrical approach for coverage efficiency assessment
presented in Section 2.5 can be used to assess the application
efficiency for all possible driving angles and provide farmers
with the angle that minimizes the impact of the topographical
nature of the field terrain and hence maximizes the coverage
efficiency and yield. This process will definitely improve the land
use, however, it might conflict with the optimization criterion
such as maneuvering over the field surface, operational time, fuel
consumption, and soil compaction. Therefore, the need arises for
an approach that can achieve 100% coverage regardless of the
topographical nature of the field terrain. Here, a new 3D coverage
algorithm is proposed in which distance between adjacent swaths
are kept equal regardless of the topographical nature of the
field. The developed approach simply generates tracks side-by-
side directly in the 3D representation of the field without gaps
between neighboring tracks. This technique overcomes skip areas
between field tracks when projecting 2D coverage plan into its 3D
counterpart.
The process starts by generating a starting curve (i.e., seed
curve) in the middle of the field. Once a seed curve is found, it
can be offset sideways on the topographic surface of the field for
generating the subsequent paths, and this process continues until
the whole field surface is fully covered. A 3D cylinder is generated
around the seed curve. Two neighboring tracks are obtained as the

I.A. Hameed et al. / Robotics and Autonomous Systems 76 (2016) 36–45 41
(a) 3D driving path for driving angle θ=90°. (b) 3D cylinder of radius wand
length l.
(c) Skip areas between swaths in 3D are obvious. (d) Ignoring elevation suppresses skips.
Fig. 6. Cylindrical approach to assess application efficiency.
Fig. 7. Flowchart of side-by-side 3D field coverage approach.
intersection between the cylinder and the field surface. The process
continues until the entire field is fully covered. A flowchart of the
proposed approach is shown in Fig. 7.
3. Results
In this section, the approaches presented in this paper are
applied to a hypothetical test with a tailored terrain surface, shown
in Fig. 6(a), and then to a real field of an uneven terrain nature to
test and validate the developed approaches.
3.1. Hypothetical test field
The field, shown in Fig. 6(a) and again 8(a), is used to demon-
strate the functionality of the developed approaches. The field has
a flat area of 200 m2and a known surface area of 257.08 m2and
therefore it can be used to validate the approach. The 2D coverage
path of the field is generated using the grid approach presented in
Section 2.3 for a driving angle of 45°, as it is shown in Fig. 8(b). The
2D coverage path is then projected through the field terrain where
bilinear interpolation (BLI) is used to generate smoother 3D cover-
age path, as it is shown in Fig. 8(c).
The application efficiency of the 3D coverage paths is evaluated
for all possible driving angles θwhere 0°≤θ < 180°using the
3D cylindrical approach presented in Section 2.5. The estimated
covered area for each driving angle is shown in Fig. 9, from which,
it is obvious that full field coverage can be achieved for a driving
angle of 0°where field tracks are perpendicular to the sloppy
surface of the field so the topography nature does not have any
impact on the spaces between swaths, as it is shown in Fig. 10(a).
Coverage efficiency dramatically decreases to 84% for a driving
angle of 90°where field slope increases the space between swaths,
as it is shown in Fig. 10(b). Fig. 6(d) shows the 2D coverage plan for
this hypothetical test field for a driving angle of 90°. Although the
2D plan provides full field coverage, the projected 3D plan shows
large skipped areas between rows, in the range of 16% of its total
surface area that is a significant misuse of the available farmland.
Therefore, the need arises for a more efficient and enhanced 3D
approach able to provide full coverage regardless of the terrain
structure of the field.
In an attempt to eliminate the topographical impact of the
field terrain on the spaces between swaths on slopes and in order
to achieve full coverage for any driving angle, a side-to-side 3D
coverage approach is applied to the above field for a driving angle
of 90°. It results in the 3D coverage plan shown in Fig. 11(a)
where spaces between adjacent swaths become equal regardless
of the terrain nature. The 2D view of the resultant side-to-side
3D coverage plan is shown in Fig. 11(b) where distances between
tracks appear to be less in sloppy areas in order to compensate
for the terrain impact. By applying the cylindrical approach for
estimating coverage efficiency to the side-to-side 3D coverage plan
shown in Fig. 11(a) reveal that 100% efficiency can be achieved for
any driving angle.

42 I.A. Hameed et al. / Robotics and Autonomous Systems 76 (2016) 36–45
a
bc
Fig. 8. (a) Artificial field based on a plan with a half cylinder of radius 5 m, and (b) 3D field plan for a driving angle of 45°and 1 m operating width.
Fig. 9. Covered area (covered area =covering efficiency ×surface area) for driving
angle 0°≤θ < 180°.
3.2. Experimental test field
A real experimental field, shown in Fig. 12, is used for
demonstrating the functionality of the developed approaches.
Fig. 12(a) shows the satellite image of the field located at
(+56°30′48.10′′ N,+9°34′15.61′′ E) which has an area of
21.22 ha. The minimum, maximum, and average elevations on
this field are 18.68 m, 42.96 m, and 35.77 m, respectively. The 3D
surface view and the contour view of the field’s DEM are shown in
Fig. 12(b) and (c). Two elevation profiles of the field; from West-
to-East and from North-to-South are shown in Fig. 11(d) and (e).
The application efficiency of the 3D coverage plans, obtained
using the rapid approach presented in this paper, is evaluated for
all possible driving angles θwhere 0°≤θ < 180°using the
3D cylindrical approach presented in Section 2.5, as it is shown
in Fig. 13(a). From which it is obvious that the best field coverage
(99.53%) was achieved at a driving angle of 90°while lowest field
coverage (97.44%) was obtained at a driving angle of 69°. The 3D
coverage plan of this field for a driving angle of 90°and 10 m op-
erating width is shown in Fig. 13(b).
To test the capability of the side-to-side 3D coverage algo-
rithm in achieving a full coverage regardless of both the ter-
rain nature and the selected driving angle, the algorithm is ap-
plied to the above field for a driving angle of 69°and 10 m
operating width. The resultant side-to-side 3D coverage plan is
shown in Fig. 14(a) while its 2D view is shown in Fig. 14(b). It
might not be very obvious from Fig. 14 that the spaces between
Fig. 10. (a) 3D coverage plan for a driving angle of 0°(100% coverage efficiency), and (b) 3D coverage plan for a driving angle of 90°(84% coverage efficiency).

I.A. Hameed et al. / Robotics and Autonomous Systems 76 (2016) 36–45 43
Fig. 11. Side-to-side 3D coverage plan of a field with artificial terrain for an operating width of 1 m and a driving angle of 90°: (a) 3D coverage plan with equal spaces
between adjacent swaths, and (b) 2D view of the side-to-side 3D coverage plan.
Fig. 12. Experimental field: (a) Satellite image, (b) 3D surface view, (c) contour view based on the DEM information, (d) elevation profile from West-to-East (WE), and
(e) elevation profile from North-to-South (NS).

44 I.A. Hameed et al. / Robotics and Autonomous Systems 76 (2016) 36–45
Fig. 13. (a) Coverage efficiency of the 3D coverage plans for driving angle 0°≤θ < 180°, and (b) conventional 3D coverage plan for a driving angle of 90°and 10 m
operating width.
Fig. 14. Side-to-side 3D coverage plan applied to experimental field B for a driving angle of 69°and operating width of 1 m: (a) 3D coverage plan with equal spaces between
adjacent swaths, and (b) 2D view of the side-to-side 3D coverage plan.
swaths become equal, however, the cylindrical approach for eval-
uating coverage efficiency showed that a nearly 100% coverage
is achieved. For this field, the cylindrical approach can be used
as an evaluation tool to improve area coverage by a value in the
range of 2%–3% of the total field area. However, the side-to-side
3D coverage showed superiority in achieving a full coverage re-
gardless of the terrain nature and the driving angle.
4. Conclusions
In this paper, a new 3D coverage algorithm is presented where
2D coverage plans are projected through field terrain. A cylindrical
approach for estimating the total skip and/or overlap areas be-
tween swaths due to the topographical nature of the field is devel-
oped. The proposed approach showed that a significant amount of
skip areas could be saved and better used if an appropriate driv-
ing angle is chosen. The approach pointed out the fact that an
enhanced 3D coverage algorithm capable of eliminating the topo-
graphical impact on spaces between swaths is required. A novel
side-to-side 3D coverage approach is presented. The developed ap-
proach ensures full coverage regardless of the field terrain nature
and the chosen driving angle, leaving more freedom for optimiza-
tion of other factors. The presented approaches for the given test
fields showed that savings in the range of 2%–14% of the field sur-
face area can be achieved and better used. Consequently, signif-
icant economic benefits can be achieved, especially when these
areas are considered over multiple field operations and from year
to year. A drawback of the cylindrical approach for estimating
coverage efficiency is that it cannot differentiate between skips
and overlaps. An analytical approach in which splines are used to
smoothly represent field terrain and for generating side-to-side 3D
coverage plan is in progress. Interested readers are encouraged to
request the MatlabTM code used to implement the approaches pre-
sented in this paper from the corresponding author.
Acknowledgments
The authors gratefully acknowledge the constructive comments
of anonymous referees.
References
[1] S.M. Pedersen, S. Fountas, H. Have, B.S. Blackmore, Agricultural robots—system
analysis and economic feasibility, Precis. Agric. 7 (4) (2006) 295–308.
[2] I.A. Hameed, A. La Cour-Harbo, K.D. Hansen, Task and motion planning for
selective weed control using a team of autonomous vehicles, in: Proceedings
of 13th IEEE International Conference on Control Automation Robotics &
Vision, ICARCV, 10–12 December 2014, Singapore, 2014, pp. 1853–1857.
http://dx.doi.org/10.1109/ICARCV.2014.7064598.
[3] M.F. Jensen, M. Nørremark, P. Busato, C.G. Sørensen, D. Bochtis, Coverage
planning for capacitated field operations, Part I: Task decomposition, Biosyst.
Eng. 139 (2015) 136–148.
[4] T. Oksanen, A. Visala, Coverage path planning algorithms for agricultural field
machines, J. Field Robot. 26 (8) (2009) 651–668.
[5] I.A. Hameed, D.D. Bochtis, C.G. Sørensen, M. Nøremark, Automated generation
of guidance lines for operational field planning, Biosyst. Eng. 107 (4) (2010)
294–306.
[6] J. Jin, L. Tang, Optimal coverage path planning for arable farming on 2D
surfaces, Trans. ASABE 53 (1) (2010) 283–295.
[7] I.A. Hameed, D.D. Bochtis, C.G. Sørensen, Driving angle and track sequence
optimization for operational path planning using genetic algorithms, Appl.
Eng. Agric. 27 (6) (2011) 1077–1086.
[8] I.A. Hameed, D.D. Bochtis, C.G. Sørensen, An optimized field coverage planning
approach for navigation of agricultural robots in fields involving obstacle
areas, Int. J. Adv. Rob. Syst. 10 (231) (2013) 1–9.
[9] I.A. Hameed, D.D. Bochtis, C.G. Sørensen, A.L. Jensen, R. Larsen, Optimized
driving direction based on a three-dimensional field representation, Comput.
Electron. Agric. 91 (2013) 145–153.
[10] M.F. Jensen, D. Bochtis, C.G. Sørensen, Coverage planning for capacitated field
operations, part II: Optimisation, Biosyst. Eng. 139 (2015) 149–164.
[11] I.A. Hameed, Intelligent Behavior of Autonomous Vehicles in Outdoor
Environment. Technical report ME-TR-2, Aarhus University, Denmark, 2012,
ISSN:2245-4594 ISBN: 978-87-92869-38-8.
[12] T.S. Stombaugh, K.B. Koostra, R.C. Dillon, T.G.T. Mueller, C.A. Pike,
in: J.V. Stafford (Ed.), Implications of Topography on Field Coverage When
Using GPS-Based Guidance, Precision agriculture ’07, Wageningen Academic
Publisher, University of Kentucky, Wageningen, 2009, pp. 425–432.
[13] B.K. Koostra, T.S. Stombaugh, T.G. Mueller, S.A. Shearer, Evaluaitng the effect
of terrain on field area measurements. Paper No. 061045, ASABE, St. Joseph,
MI, USA, 2006.
[14] R.C. Dilon, J.-M. Gandonou, B. Koostra, T. Stombaugh, G.T. Mueller, Evaluating
the economic impact of field area measurements, in: International Conference
on Precision Agriculture Poster and abstract presented at the 8th, Precision
Agriculture Center, Minneapolis, MN, USA, 2006.
[15] J. Jin, L. Tang, Coverage path planning on three-dimensional terrain for arable
farming, J. Field Robot. 28 (3) (2011) 424–440.
[16] I.A. Hameed, Intelligent coverage path planning for agricultural robots and
autonomous machines on three-dimensional terrain, J. Intell. Robot. Syst. 74
(3–4) (2014) 965–983.
[17] R. Buick, A.F. Lange, Assessing efficiency of agricultural chemical application
with differential GPS, arcview and spatial analyst, in: Proceedings of Esri
International User Conference. Available at: http://proceedings.esri.com/
library/userconf/proc98/PROCEED/TO650/PAP622/P622.HTM.

I.A. Hameed et al. / Robotics and Autonomous Systems 76 (2016) 36–45 45
[18] H. Choset, P. Pignon, Coverage path planning: The boustrophedon decompo-
sition, in: Proceedings of the International Conference on Field and Service
Robotics.
[19] T.M. Driscoll, Complete coverage path planning in an agricultural environment
(Graduate Theses and Dissertations), Iowa State University, USA, 2011.
[20] MathWorks, User’s Guide, R2015a, 2015. Retrieved August 16, 2015. From:
http://se.mathworks.com/help/matlab/ref/inpolygon.html.
[21] P.J.J. Desmet, Effects of interpolation errors on the analysis of DEMs, Earth Surf.
Process. Landf. 22 (6) (1997) 563–580.
[22] S.P. Wechsler, Digital Elevation Model (DEM) uncertainty: evaluation and
effect on topographic parameters, in: Proceedings of the 1999 ESRI User
Conference, 1999. Available at: http://gis.esri.com/library/userconf/proc99/
proceed/papers/pap262/p262.htm.
[23] A.S. Aziz, L.B. Steward, L. Tang, M. Karkee, Utilizing repeated GPS surveys from
field operations for development of agricultural field DEMs, Trans. ASABE 52
(4) (2009) 1057–1067.
[24] K.-T. Chang, Introduction to Geographic Information Systems, McGraw-Hill
Higher Education, Boston, 2006.
Ibrahim A. Hameed received the B.E. degree in Electronic
Engineering and M.Sc. degree in Control Engineering
from the Menofia University, Menofia, Egypt, in 1998
and 2005, respectively. He received Ph.D. degree in
Industrial Systems and Information Engineering from
Korea University, Seoul, South Korea and Ph.D. degree in
Mechanical Engineering from Aarhus University, Aarhus,
Denmark in 2010 and 2012, respectively. From March
2011 to December 2012, he has been working as an
Assistant Professor at Department of Industrial Electronics
and Control Engineering, Menofia University, Menofia,
Egypt. From January 2013 to July 2015, he has been working as a postdoc
at Department of Electronic Systems, Aalborg University, Denmark. Hameed is
currently an Associate Professor at Dept. of Automation Engineering, NTNU Ålesund,
Aalesund, Norway. His current research interest includes Artificial Intelligence,
Control Engineering and Field Robotics.
Anders la Cour-Harbo is an Associate Professor, UAS
group manager and Control & Automation Master program
coordinator, Aalborg University, Denmark.
Ottar L. Osen received an M.Sc. in Cybernetics from the
Norwegian University of Science and Technology (NTNU)
in 1991. He is the head of R&D at ICD Software AS and
assistant professor in automation engineering at AAUC. He
has 14 years of experience from industry and 10 years of
experience from academia. His main research interests are
artificial intelligence, cybernetics and robotics.