IJERD – International Journal of Environmental and Rural Development (2013) 4-1

Research article
erd

Guidance of a Transplanting Skid Steer Vehicle with
Variable Center of Gravity
NOE VELAZQUEZ LOPEZ*
Graduate School of Agriculture, Tokyo University of Agriculture, Tokyo, Japan
Email: noe.velazquez@gmail.com

KIYOSHI TAJIMA
Faculty of Regional Environment Science, Tokyo University of Agriculture, Tokyo, JapanHIDEYUKI TANAKA
Graduate School of Agriculture, Tokyo University of Agriculture, Tokyo, Japan

DO TUAN THANH
Graduate School of Agriculture, Tokyo University of Agriculture, Tokyo, Japan

WATARU YUKUMOTO
Graduate School of Agriculture, Tokyo University of Agriculture, Tokyo, Japan

MASATAKA JITSUNO
Graduate School of Agriculture, Tokyo University of Agriculture, Tokyo, Japan

MASAYOSHI KATO
Faculty of Agriculture, Tokyo University of Agriculture, Tokyo, JapanEIICHIRO SAKAGUCHI
Faculty of Regional Environment Science, Tokyo University of Agriculture,Tokyo, Japan

JUNYA TATSUNO
Faculty of Engineering, Kinki University, Hiroshima, JapanTADASHI ISHII
Jisedaitech L.P., Kanagawa, Japan
Received 17 December 2012

Accepted 30 January 2013(*Corresponding Author)

Abstract In this study it is proposed a photovoltaic powered farming robot system thatconsists of a delivery vehicle and a working vehicle. The proposed system is designed
based on a newly proposed farming method called shaft tillage cultivation. So, we havedeveloped two automatic vehicles, as well as a 2-D localization method for positioning ofthe working vehicle. In addition, we have developed an attachment for shaft tillage andtransplanting which is derived from commercially available transplanting machines. This
movable transplanting attachment was mounted over two rails which are disposedtransversally on the frame of the working vehicle which in turn permits transplanting
multiple rows. The working vehicle is based on a skid steer vehicle with independent left
and right motors that allow for motion direction control by turning the left- and right-side
wheels at different velocities. However, within the field, even if same turning velocities
are applied to both left- and right-side wheels a yaw angle is generated due to the sinkage
and rolling resistance. Additionally, controllability of the working vehicle is greatly
affected by variable changes of the center of gravity caused by lateral motion of thetransplanting attachment. So, this paper focused on the effect of the position of center ofgravity on the yaw angle in the working vehicle. The least square method was examined as
method to find out the instantaneous center of rotation (ICR) and its effectiveness wasconfirmed. When the position of center of gravity was on the faster wheels the turning ofⒸ ISERD75

IJERD – International Journal of Environmental and Rural Development (2013) 4-1

the skid steer vehicle was more difficult than in other positions. The ICR changed evenwhen the left- and right-side wheels were driven at the same velocities. Therefore,
considering the position of center of gravity in the skid-steer vehicle would allow arational guidance of the vehicle.
Keywords transplanting, skid steer vehicle, trajectory, variable center of gravity

INTRODUCTION
A current trend in agricultural area is the development of mobile robots and autonomous vehicle
for precision agriculture. These are usually required to travel across unpaved terrains to operate ortransport material. In this kind of terrains, the mobility and the controllability of the robot isstrongly influenced by the physical properties of the terrain (Gonzalez et al., 2009).
Authors are involved in the development of a photovoltaic powered farming robot system thatconsists of a delivery vehicle and a working vehicle (Tajima et al., 2008). The proposed system isdesigned based on a newly proposed farming method called shaft tillage cultivation method which
promotes weed and crop coexistence. Figure 1 shows an image of cross section of plants cultivatedwith the shaft tillage method. The tool has two different diameter sections as is shown in Fig. 1.
The principal characteristics of this farming method are to minimize the power required whentillage and weed control is done separately by trimming periodically (Tajima et al., 1996). Shaft
tillage cultivation method involves drilling a vertically shaped shaft with the rotary sinker that
achieves an effect of tillage and the soil is not exposed on the surface of the field (Tajima et al.,1997). As such, we have developed two automatic vehicles. Figure 2 shows the developed
photovoltaic powered farming robot system. Functions such as, transportation and positioning of
the robot system, electric power generation and storage, transportation and supply of seedling traysetc. were distributed in these two vehicles. The delivery vehicle is guided outside the field througha magnetic tape and has functions such as, positioning of the working vehicle, electric power
generation and storage as well as transport and seedlings supply. On the other hand, the working
vehicle receives control information, power and a seedling supply from the delivery vehicle, andhas function of positioning and transplanting of seedlings. Positioning of the working vehicle isbeing carried out by a 2-D localization system using a laser distance sensor (Tatsuno et al., 2005).
In addition, we have developed an attachment for shaft tillage and transplanting which is derived
from commercially available trans-planter. This movable transplanting attachment was mounted
over two rails which are disposed transversally on the frame of the working vehicle which in turn
permits transplanting multiple rows. The transplanting attachment is equipped with a tillage device
for transplanting and a seedling tray tank which also move transversally within the frame of theworking vehicle.

Fig. 1 Cross section of plant under cultivated by the shaft tillage method and the rotary
sinker for the shaft tillage cultivationⒸ ISERD

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IJERD – International Journal of Environmental and Rural Development (2013) 4-1

Photovoltaic cell
Seedlings tray handlingdeviceSeedlings tray storage
deviceSeedlings handling device
driving motor
Charger controller
Control unit
Battery

Seedlings tray storage
device driving motor

Driving unit(a) Delivery vehicle
Attachment device Attachment
Seedling
control PLC
devicetrays rack
Reflector sheet for
positioning of theattachment
Cross-feedmotor

Right wheel
Left wheel
driving motor
driving motor
Shaft tillage Transplanting
devicehandlers

Water tank

Reflector mirror for
positioning of theattachment
Reflector sheet for
positioning of theworking vehicle

Power supply
plug(b) Working vehicle
Fig. 2 Photovoltaic powered robot system
The working vehicle is based on a skid steer vehicle with independent left and right motors(Tajima et. al. 2003). As the right- and the left-side wheels are driven independently, the wheel
speed and direction of rotation determine the direction of the skid steer vehicle. Skid-steer vehicle
is capable of zero-radius, "pirouette" turning. This is very important for positioning the skid steer
vehicle when transplanting due to its facility in correcting the position in polar coordinates. In otherwords, the vehicle can turn based on a specific vertical axis within the frame. This system isdesigned to carry out multitasking. So eventually, it would be possible to perform variable cultural
practices (by changing the attachment) using a manipulator, such as disease detection and control
by image processing (Velazquez et al. 2011) creating the necessity to combine the generalcoordinates system in the field with that in the image so a more accurate positioning of the working
vehicle could be achieved.
However, within the field, even if the same turning velocities are applied to both left- andright-side wheels a yaw angle is generated due to the sinkage and rolling resistance. Additionally,mobility and controllability of the working vehicle is greatly affected by changes in the position ofcenter of gravity caused by lateral motion of the attachment. It is known that the turning
characteristics of a skid steer vehicle are highly dependent on the position of center of gravity,especially for lateral changes (Sasaki et al. 2005), though enough knowledge has not been obtained
for the development of an algorithm to guide the proposed system where the center of gravity
moves transversally while traveling.
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IJERD – International Journal of Environmental and Rural Development (2013) 4-1

OBJECTIVE
The objectives of this paper are to find out the effect of the position of center of gravity on the yaw
angle in the working vehicle and to consider a method to find out the instantaneous center ofrotation.
METHODOLOGY
In order to measure a turning circular trajectory, it takes a lot of time due to the velocity of our skid
steer vehicle is very slow, when the circular trajectory is large a wide area is needed and it isdifficult to maintain the same ground conditions. Therefore, an accurately method to find out theICR and the turning radius (R) from a small trajectory was necessary. In that respect, the leastsquared method was proposed.
Experiments were carried out inside a greenhouse using the skid steer vehicle showed in Fig.3.
This skid steer vehicle is based on the Agri-cart manufactured by Alumis Co., Ltd. Turningexperiments were carried out at very low speed. As power supply a regulated power DC supply wasused. PWM driver was used for control of the left- and right-side motors. A load of 196 N was used
for all experiments. Tires pressure was set to 196 kPa. 9 load conditions were set as is shown in Fig.
4. Driving speeds of the wheels were set as shown in Table 1. The turning direction was set tocounterclockwise. Experiments were conducted as follows: First the load on each wheel wasmeasured for each condition of the load. A mark was collocated each 90 degrees on the right-front
and left-rear wheels. Then after traveling a distance of 2 m, 8 m trajectory was plotted on theground. Plotted points were then measured in Cartesian coordinates with a tape.

Fig. 3 Skid steer vehicle

12

3

4

56

789Fig. 4 Load conditions (Top view)

Table 1 Driving setting speed of the wheels
Speed setting
123Left-side angular Speed ωl (rad/s)
00.64
1.20

Right side Speed ωr (rad/s)
1.24
1.24
1.24

Least square method
The turning radius and ICR were calculated using the least square method. Eq. (1) represents theequation for a circle. This method is based on minimizing the mean square distance from the circle
to the data points(1)
Whererepresents the center of the circle andrepresents the radius. The
residual obtained from the circle trend line and data points, xi and yi, obtained from the trajectoryof the skid steer vehicle are expressed by Eq. (2).
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Then the squares of the residuals
are summed and A, B and C are determined so that thesum is minimized as shown in Eq. (3). Here, A=-2a; B=-2b and C=a2+c2-r2.
(3)
Particularly, the estimated values of A, B and C can be obtained by partial differentiation andequating to zero.
RESULTS AND DISCUSSION
Figure 5 shows the load on wheels under the 9 load conditions (Fig. 4). The load was distributed
symmetrically for load condition 5 on the left-and right-sides of the vehicle with values from 201249N. The load moved to right-side for condition 6 and to left-side for condition 4 confirming thatthe center of gravity moved along with the load. Fitting the circle equation to plotted data points
with the least square method allowed calculating the ICR and turning radius, from a small
trajectory in a short time, confirming the effectiveness of the method.
142

5

3

6

Left front
wheel

Right front
Loadwheel
Condition

Left rear
wheel

Right rearwheel

300-325N
78

9250-300N
201-249N
0-200N

Fig. 5 Load on wheels

Fig. 7 Relationship between ωl/ωrand 1/R for
Speed setting 2

Fig. 6 Relationship between ωl/ωr and 1/R forSpeed setting 3

Fig. 8 Relationship between ωl/ωr and 1/R forSpeed setting 1

Figures 6, 7 and 8 show the relationship between the ratios of ωl/ωr and 1/R. R represents theturning  radius  and  ωl and  ωr are the left- and right-side wheels angular speed, respectively. As it
can be observed in each figure the turning radius varied for each load condition even whenexperiments were carried out under the same speed and ground setting conditions. When the load
was on the faster wheel (right-side), braking effort on the slower wheel (left-side) reduced as aresult of wheels sinkage and rolling resistance making the turn more difficult. On the other hand,when the load was over the slower wheel (left-side) the braking effort increased facilitating the turn.
In other words, when the load is over the faster side the vehicle tends to travel straight and when
the load is over the slower side the vehicle tends to tight turn.
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IJERD – International Journal of Environmental and Rural Development (2013) 4-1CONCLUSION
The least square method fitting the circle equation was proposed and examined as a method to findout the turning radius and the ICR of the vehicle from plotted point data obtained from a short
trajectory and its effectiveness was confirmed. The ICR changed even when the left- and right-side
wheels were driven at the same speed. Considering the position of center of gravity in the skidsteer vehicle would allow for a rational guidance of the vehicle. Hence, analytical studies arenecessary in order to achieve a more accurate control for positioning of the skid steer vehicle. In
other words, mathematical modeling (equations of motion) and simulation of the working vehicle
taking into account changes in the position of the center of gravity are required. As a result,velocities for the left- and right-side wheels as well as the appropriate position of the center ofgravity could be obtained. Finally, in order to evaluate the accuracy of the mathematical model,
comparison between experimentally obtained data and those obtained by simulation is required.
ACKNOWLEDGEMENTS
We wish to acknowledge the support of Yuki Watanabe, Toshihiko Nishitani and Yuki Takeishi,
undergraduate students of the Laboratory of Farm Robotics at Tokyo University of Agriculture.
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