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C0356 Martin A.F. Jensen, Claus G. Sørensen, Dionysis Bochtis. ” Assessment of track
sequence optimization based on recorded field operations”. EFITA-WCCA-CIGR Conference
“Sustainable Agriculture through ICT Innovation”, Turin, Italy, 24-27 June 2013.
The authors are solely responsible for the content of this technical presentation. The technical
presentation does not necessarily reflect the official position of the Internation Commission of
Agricultural and Biosystems Engineering (CIGR) and of the EFITA association, and its printing
and distribution does not constitute an endorsement of views which may be expressed.
Technical presentations are not subject to the formal peer review process by CIGR editorial
committees; therefore, they are not to be presented as refereed publications.
Assessment of Track Sequence Optimization
based on Recorded Field Operations
Martin A. F. Jensen
1,2,*
, Claus G. Sørensen
1
, Dionysis Bochtis
1
1
Aarhus University, Faculty of Science and Technology, Department of Engineering,
Blichers Alle 20, DK-8830 Tjele, Denmark
2
CLAAS Agrosystems Gmbh, Danish Branch, Møllevej 11, 2990 Nivå, Denmark
*Corresponding author. E-mail: martinf.jensen@agrsci.dk
ABSTRACT
The sequence of working the parallel lines in agricultural field area coverage operations
can be optimized to minimize the total non-productive time. The amount of savings
achieved in using the optimized sequence, denoted the B-pattern, compared to the
conventional sequence varies considerably depending on the operation’s features. This
work presents a method for estimating the savings of using B-patterns and is applied on
a specific problem instance consisting of a specific tractor, implement and field, based
on a recording of a “conventional” operation.
The savings assessment method consists of fitting a turn model using data from the
recording, generating the Traveling Salesman Problem (TSP) cost matrix with turn
model, solving the TSP and finally using parts of the recording to estimate the savings.
The specific problem instance was a harrow operation with an estimated savings of
3.3% in total operation time.
Keywords: B-patterns, track sequence optimization, monitoring, Dubins curves,
Traveling Salesman Problem, Denmark
1. INTRODUCTION
In the majority of agricultural field operations, a machine treatment covers the entire
field by following parallel tracks and turning between them in the headland. As it has
been shown, for “neutral material flow” field operations, the optimal sequence of
working the tracks minimizing time can be modeled with a Traveling Salesman
Problem (Bochtis 2008; Bochtis & Sørensen 2009). The optimal track sequence
depends on the problem instance data, including the geometric layout of tracks, the
machine kinematics, the working width, and the desired start and ending locations of the
operation. The task time savings of using the optimal track sequence, denoted the “B-
pattern” instead of a “conventional” sequence, was studied by simulating a series of
different problem instances where the turning radius and working width was varied
(Vougioukas et al 2010). This specific study showed task time savings in the range 8.4-
C0356 Martin A.F. Jensen, Claus G. Sørensen, Dionysis Bochtis. ” Assessment of track
sequence optimization based on recorded field operations”. EFITA-WCCA-CIGR
Conference “Sustainable Agriculture through ICT Innovation”, Turin, Italy, 24-27 June
2013.
17%. As the survey showed, the task time savings varies significantly depending on the
specific problem instance and the already used sequence, so it can be difficult for the
farm manager to know what the actual level of savings would be by applying B-
patterns.
This work presents a procedure for the estimation of the expected task time savings
derived from the optimization of the track sequence that is based on the analysis of the
GPS-recordings of the operation.
2. ASSESMENT METHOD
The time savings of using an optimized sequence can be computed as:
Duration of normal operation - Duration
of optimize operation
savings Duration of normal sequence
=
The time working a field consists of a working part where the soil (or the crop) is
treated and a non-working part where the machine makes maneuvers like the turnings
and other travel where the soil (or the crop) is not treated.
The working part, denoted
w
t
, is constant (in terms of the travelled time), but the non-
working part varies depending on the sequence of working the tracks. We denote the
non-productive time as a function
n
t ( )
s
of the sequence of working the tracks, s. The
sequence observed in the recording is denoted
r
s
and the optimal sequence is denoted
*
s
. The savings is then computed as:
(
)
r *
r *
n w n w n n
r r
n w n w
t ( )+t - t ( )+t
t ( )-t ( )
savings
t ( )+t t ( )+t
s s
s s
s s
= =
(E.g. 1)
The time of the non-working part
r
n
t ( )
s
and the working part
w
t
can be measured
from the recorded path. The remaining unknown is the time of the non-working part
using an optimal sequence
*
n
t ( )
s
. The optimal sequence and the time of it, can be found
if a model of the function
n
t ( )
s
is known.
It is however impossible to estimate the “summed-time-of-all-turns” function
n
t ( )
s
using the recording of a single operation. Instead it can be shown that it is enough to
estimate the “time-of-an-individual-turn” function
turn i f
t ( , )
c c
, where
i
c
and
f
c
is
some representation of the vehicle state at the beginning and end of a turn. From the
recordings we can extract many turns needed for the model fitting of this function.
C0356 Martin A.F. Jensen, Claus G. Sørensen, Dionysis Bochtis. ” Assessment of track
sequence optimization based on recorded field operations”. EFITA-WCCA-CIGR
Conference “Sustainable Agriculture through ICT Innovation”, Turin, Italy, 24-27 June
2013.
2.2 Turn Model
The turn model is based on Dubins curves because of the low computational time and
memory requirements while it still models the minimal turning radius present in most
agricultural machinery steering systems (Dubins 1957). The input to the shortest Dubins
curve function is the initial and final pose, and the minimum turning radius of the
vehicle. The output is the determination of the shortest path connecting the initial and
final poses using straight and circular arcs, and its corresponding length.
To achieve a model outputting time, the path length is divided with a speed.
Furthermore it is beneficial to add a constant or offset to the length of the path.
The turn time model becomes:
i i i f f f
turn i i i f f f
d( , , , , , , R ) o
t ( , , , , , )
v
x y x y
x y x y
θ θ
θ θ
+
=
The model parameters are the minimal turning radius, R, the offset, o, in meters and the
speed, v, in m s
-1
. The function
d( )
⋅
is the path length in meters of the Dubins curve. The
model input is the initial pose,
i i i
{ , , }
x y
θ
, and final pose
f f f
{ , , }
x y
θ
.
A version of the model which returns the distance is also used:
turn i i i f f f i i i f f f
d ( , , , , , ) d( , , , , , , R) o
x y x y x y x y
θ θ θ θ
= +
Computing the shortest Dubins curve is done by taking the shortest of all eight
possibilities (See Shkel & Lumelsky 2001 for more details on computing the various
possible paths).
2.3 Aspects in fitting turn model to data
The model fitting process consists of finding the parameter values which minimize the
sum of the residuals, i.e. the differences between the measured turn and the modeled
turn. Each turn is a data point in model fitting terminology and we must find these in
the recorded path of the machine. Standard least squares fitting were used.
It was desirable to fit both time and distance in the fitting process. However in this
multi-objective fitting, the two different types of residuals must be weighted in order to
equalize their importance. The distance is included to gain some regularization to the fit
to prevent overfitting. Overfitting means that the best fit can be achieved with many
different sets of parameter values.
We characterize the turns in relation to how many tracks are skipped when driving from
an initial pose to the final pose. For example the turn from a track to another track
directly adjacent to it, is denoted a skip zero turn, and the turn from a track to another
track where the adjacent track is skipped, is denoted a skip one turn.
C0356 Martin A.F. Jensen, Claus G. Sørensen, Dionysis Bochtis. ” Assessment of track
sequence optimization based on recorded field operations”. EFITA-WCCA-CIGR
Conference “Sustainable Agriculture through ICT Innovation”, Turin, Italy, 24-27 June
2013.
In many cases the recording of an operation includes an uneven distribution of the count
of various skip turn types. To ensure that the model is equally accurate for the various
skip types, the residuals of each turn type must be weighted somehow in relation to the
distribution. If very few turn samples exist of a certain turn type the weighting should
not be too high to prevent the case that a single outlier of that turn type is given too
much influence.
2.4 Finding the optimal track sequence
To find the optimal sequence of working the tracks minimizing the non-working turning
time the TSP approach from Bochtis 2008 and Bochtis & Sørensen 2009 is used. The
turn time model is used to generate the cost matrix of the TSP and it is solved with the
open source LKH TSP-solver (Helsgaun 2009). It should be noted that the speed and
offset parameter of the turn time model does not affect the optimal track sequence
because they occur as constant scaling and addition in the elements of the cost matrix.
3. USE OF ASSESMENT METHOD ON EXERIMENTAL DATA
3.1 Recording operation and segmenting path
The path of a tractor harrowing two adjacent fields were recorded with 1 Hz sampling
frequency using a GPS logger placed in the window of the tractor. The field area was 21
ha and the operation took 2 hours and 20 minutes. The tractor was a belt-driven
Caterpillar Challenger and the implement was a Horsch Terrano 12 FG harrow with 12
m working width (See Figure 1).
Figure 1 - Tractor and harrow implement used in recorded operation. GPS logger was
placed in the window of the tractor.
The recorded path is segmented into working parts: tracks and headland and non-
working parts: turns and “field exit travel”. The identification of the point on the
trajectory that separates a turn and a track is arbitrary to some extent. The separated
turns are used in the fitting of the turn model, so the offset parameter will compensate
for the choice of separation point. It is thus important to be consistent, for example by
C0356 Martin A.F. Jensen, Claus G. Sørensen, Dionysis Bochtis. ” Assessment of track
sequence optimization based on recorded field operations”. EFITA-WCCA-CIGR
Conference “Sustainable Agriculture through ICT Innovation”, Turin, Italy, 24-27 June
2013.
choosing a point which is closest to the path of the innermost headland pass (See the left
insert in Figure 2).
Some parts might seem to fit neither of the grouping types, however they can usually be
included as part of a track. The path around the obstacle in the lower field is included as
part of the associated track, as is the odd eight-digit-shaped path in the upper field.
The ending of each track is given a unique identifier and the sequence of visiting them
in the working of the tracks defines
r
s
.
Figure 2 - Plot of the segmented recorded path of the tractor. The left insert shows how
turns are defined as starting at the innermost headland pass. The dotted pink path in the
right insert is an example of a turn outlier which should not be included in the turn
model fitting.
C0356 Martin A.F. Jensen, Claus G. Sørensen, Dionysis Bochtis. ” Assessment of track
sequence optimization based on recorded field operations”. EFITA-WCCA-CIGR
Conference “Sustainable Agriculture through ICT Innovation”, Turin, Italy, 24-27 June
2013.
3.2 Fitting the Turn Model to data
From each turn we collect the initial pose, final pose, time and distance. The initial and
final pose are inputted in the turn model to achieve a modeled time and distance. In
order to do the multi-objective fitting, the time is weighted according to the ratio
between the mean of the times and the mean of the distances which is around 3.65.
Most of the turns are skip zero turns, however to achieve a good model we need more
samples of the other types: skip one, skip two etc. These were collected from other fields
that the machine was working the same day.
In order to achieve equal influence on the model, the various skip types are weighted
according to their count. The skip three and four types gets a lower weighting because
there are very few data points in those groups and an eventual outlier will have too
much influence. The weightings for skip zero, one, two, three and four are respectively
30%, 30%, 30%, 5% and 5%.
The collected turns and the resulting fitted turn model using least squares fitting is
shown in Figure 3. Notice that the turning time of the fitted model is lowest for skip one
turns. The fitted model has a turning radius of 7.7 m, speed of 3.6 m/s and offset of 20
m.
Figure 3: Collected turns and the fitted turn model. Turns are collected from the
recording seen in Figure 2 and from some other recordings of the same machine and
working conditions.
C0356 Martin A.F. Jensen, Claus G. Sørensen, Dionysis Bochtis. ” Assessment of track
sequence optimization based on recorded field operations”. EFITA-WCCA-CIGR
Conference “Sustainable Agriculture through ICT Innovation”, Turin, Italy, 24-27 June
2013.
3.3 Finding optimal sequence and estimated savings
We use the fitted turn model to generate the TSP cost matrix. As said in section 2.4, the
speed and offset has no influence on the optimal sequence itself, only on the time of the
optimal sequence.
The LKH TSP-solver returns an optimal TSP solution which is used to generate the
optimal sequence of working the tracks
*
s
. The modeled optimized turning time
*
n
t ( )
s
is computed using the fitted turn model.
The difference in sequence between the recorded and the optimized sequences is
illustrated in Figure 4 of the upper field. As can be seen more of turn type skip one are
present in the optimized sequence as is expected when skip one turn is a minimizer of
the turn model as seen in Figure 3.
Figure 4 – The left plot shows the recorded sequence with modeled turns. The right plot
shows the optimized sequence with modeled turns.
The time spent in working tracks, headlands and the non-working turns and field exit
path for the recorded operation and the optimized operation are shown in Figure 5. The
absolute savings is 4.3 minutes and the relative savings are 3.3 %.
5. CONCLUSION
This work presents a method for estimating the savings of implementing an optimized
field area coverage planning, in the particular case the B-patterns. The method was
applied on a specific problem instance consisting of a specific tractor, implement and
field, based on a recording of the corresponding “conventional” operation.
A turn model was fitted to turn collected from the recording and the found model
seemed to fit the data well.
C0356 Martin A.F. Jensen, Claus G. Sørensen, Dionysis Bochtis. ” Assessment of track
sequence optimization based on recorded field operations”. EFITA-WCCA-CIGR
Conference “Sustainable Agriculture through ICT Innovation”, Turin, Italy, 24-27 June
2013.
Figure 5: Absolute savings are 4.3 minutes and relative savings are 3.3 %.
6. ACKNOWLEDGEMENTS
We thank the employees at Bregentved Gods in Denmark for their help in obtaining the
recorded operation.
7. REFERENCES
Bochtis, D. 2008. Minimising the non-working distance travelled by machines operating
in a headland field pattern. Biosystems Engineering.
Bochtis, D. and Sørensen, C. G. 2009. The vehicle routing problem in field logistics
part I. Biosystems Engineering.
Dubins, L. E. 1957. On curves of minimal length with a constraint on average curvature,
and with prescribed initial and terminal positions and tangents. American Journal of
mathematics 79.3 (1957): 497-516.
Helsgaun, K. 2009. General k-opt submoves for the Lin–Kernighan TSP heuristic.
Mathematical Programming Computation.
Shkel, A. M., and Lumelsky, V. 2001. Classification of the Dubins set. Robotics and
Autonomous Systems.
Vougioukas, G. S. et al. 2010. FutureFarm: Integration of Farm Management
Information Systems to support real-time management decisions and compliance of
management standards. Seventh Framework Programme report. Project no. 212117.
0
50
100
150
Recorded (total
time = 139)
Recorded with
modeled turns
(total time =
129)
Optimized with
modeled turns
(total time =
125)
Minutes
Comparing operations times
Field exit travel
Turns
Working headlands
Working tracks