# Study and Experiment on a Wheat Precision Seeding Robot

Authors: Lin Haibo; Dong Shuliang; Liu Zunmin; Yi Chuijie
Journal: Journal of Robotics
 (2015)

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## Abstract

The wheat precision seeding technology provided an advanced agricultural support for the high yield of wheat. But the lack of effective agricultural machine made this technique difficult to apply widely. In this paper a wheel mobile robot to achieve the wheat precision seeding technology was designed. The kinematic model of the robot was built and simulated. And experimental study was taken under different operating conditions. Because of multiple effort factors, a quadratic orthogonal rotation combination design method was applied in the experiments, identifying the main factors by analysis. Then the field test was carried out according to the main factors. The experiment results showed that the qualified rates of seeding exceed 93% in different sowing speed. That reached the agronomic requirements of wheat precision seeding.


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## Body

## 1. Introduction

With the development of agriculture in China, the traditional intensive and meticulous farming had been unable to meet the requirements of current agriculture and agronomy development. Using agricultural machinery instead of the traditional manpower had become a major trend in the world [1, 2]. And the agricultural robot had become an important target in research and development of agricultural machinery engineering [3, 4]. In agricultural robotics research, Japan, the United States, and other countries were in the lead [5, 6]. In China it started in these years, and there was a certain gap in technology comparing with the developed countries [7, 8].Wheat is one of major food crops in China. China’s wheat acreage was 24 million hectares in 2013. Increase of wheat production was of great significance for China’s food security. Academician Songlie from Shandong Agricultural University proposed the wheat precision seeding agronomic techniques to improve wheat yield. Using Lumai-5 as experimental wheat seed, the experiments results showed that the yield of the precision seeding techniques was greater by 7.5% to 22.3% than that of the traditional seeding techniques [9]. However, due to the special characteristics of the wheat seed grain geometry, now the mechanization for the wheat precision seeding techniques was still in research stage. Automatic agricultural vehicles had received attentions from the 1920s [10]. Especially in the recent 20 years, with the development of computer and sensor technologies, numerous researches on this subject, particularly agricultural robots, had been reported [11–15]. In this paper, a wheel mobile robot was designed and developed for the wheat precision seeding. A kinematic model was built for the four-wheel drive robot, and some experiments were taken using this machine. It provided a reference for the design and product of wheat precision seeding robot.


## 2. Design of the Precision Seeding Robot

According to the working environment of the robot and the agronomic requirements of the wheat precision seeding techniques, this robot was designed with four-wheel drive, the drive system using servo motor, and the steering system using stepper motor [16]. To ensure the robot’s load-bearing capacity and robustness, the frame was welded by rectangular steel together, seen in Figure 1. Figure 2 was the system block diagram of the wheat precision seeding robot. The robot was mainly divided into three parts: the robot mobile body, the control system, and the sensor system. And, the robot mobile body was divided into the mobile platform and the precision seeding mechanism. The control system was the core of the robot, seen in Figure 2. It could process the sensor signal and the information received in the working time. By adjusting the coherent drive motors, the control system could precisely control the movement of the robot, the picking up and seed of the wheat, and the adjustment of the pressure of the vacuum chamber, realizing the agronomic requirements of the wheat precision seeding.Figure 1
Wheat precision seeding robot.Figure 2
System block diagram of the robot.


## 3. Kinematic Model and Simulation

For the mobile robot, the model reflected the relationship between the state variables and control parameters of the robot. So, It was essential to build the model to design an effective tracing control law for small error or no error robot trajectory tracking. In this paper, the precision seeding robot’s platform was designed with 4-wheel drive and 4-wheel steering. Rotation and steering of the four wheels are controlled independently, there were four servomotors to control each wheel for rotation, and there were also four step motors to steer. A central controller coordinated the eight motors to work well together. Theoretically, the four-wheel steering scheme has all the degrees of freedom in the plane [17]. But, there were many forms that were not practical in actual application. Figure 3 shows some basic operation mode. Considering the characteristics and the actual situation of the working in the field, mode (c) was selected in the design of the wheat precision seeding robot.Figure 3
Some basic operation mode. (a) Four-wheel same direction steering, (b) front wheel steering, (c) four-wheel opposite steering, (d) differential speed mode, (e) slide steering mode, (f) zero radius steering mode, and (g) braking mode.
(a)
(b)
(c)
(d)
(e)
(f)
(g)Two assumptions were made in this paper for the kinematic model of the robot: (1) the platform of the robot was considered as a rigid body and the wheel was considered as a rigid wheel; it was that the elastic deformation of the wheel and the ground was ignored; (2) the robot did not consider the vertical and pitching motion, excluding the impact of roll.In this paper, we discussed the kinematic model of mobile robot when front and rear wheels are steering in the opposite direction, showing in Figure3(c). Through analyzing the four-wheel opposite steering mode, there were some certain relationships in the steering angle between the rear wheels and the front wheels and the speed between the left wheels and the right wheels.Figure4 was the schematic diagram of four-wheel steering mode. O3 was the instantaneous center of the mobile robot platform; PX′Y′ was the coordinate system of the mobile robot; O2 is the rear wheels’ axis center; O1 was an intersection point of the line through the point O3 perpendicular to the body axis and the extended line of the wheels axis; P is the reference point for precision seeding meter. ϕfl was the steering angle of the front-left wheel; ϕbl was the steering angle of the rear-left wheel; vfl was the speed of the front-left wheel; vbl was the velocity of the rear-left wheel; vp was the velocity of the reference point P; vo3 was the velocity of O3; x0 was the distance between O3 and the front wheels axis.Figure 4
Schematic diagram of four-wheel steering mode.Givenϕfl, the steering angle of front-left wheel, and ϕbl, the steering angle of rear-left wheel, the following relationship could be obtained from the triangle:(1)x0=2l·tan⁡ϕfltan⁡ϕfl+tan⁡ϕbl.By the velocity of rear-left wheel, the robot’s angular velocity around the instantaneous center could be obtained as(2)ω=vfl·sin⁡ϕflx0=vfl2lsin⁡ϕfl+cos⁡ϕfl·tan⁡ϕbl.As O1O3=x0/tan⁡ϕfl+b, the velocity of O3 was(3)vo3=ω·O1O3=vfl·cos⁡ϕfl+bx0·vfl·sin⁡ϕfl.The kinematic model of the system could be established with O3 for reference points as(4)x˙o3=vfl·cos⁡ϕfl+bx0·vfl·sin⁡ϕfl·cos⁡θ,y˙o3=vfl·cos⁡ϕfl+bx0·vfl·sin⁡ϕfl·sin⁡θ,θ˙o3=vfl·sin⁡ϕflx0.From the relationship of points O3 and P, (5) could be derived:(5)xp=xo3-m+2l-x0·cos⁡θ,yp=yo3-m+2l-x0·sin⁡θ,θp=θ-α.By taking derivation on both sides of (5), the kinematics model with p for reference point was(6)x˙p=vo3·cos⁡θ+m+2l-x0·sin⁡θ·ω,y˙p=vo3·sin⁡θ-m+2l-x0·cos⁡θ·ω,θ˙p=ω.It was(7)x˙py˙pθ˙p=cos⁡θsin⁡θ0m+2l-x0sin⁡θ-m+2l-x0cos⁡θ1·vo3ω.In (7), vo3, x0, and ω could be obtained from ϕfl and ϕbl. And the relationship of the left wheels and the right wheels was(8)ϕfr=arctan⁡x0tan⁡ϕflx0+2btan⁡ϕfl,ϕbr=arctan⁡2l-x0tan⁡ϕflx0+2btan⁡ϕfl.From these equations, when ϕbl=0, the front wheel steering kinematic model of the robot could be obtained.Based on the kinematic model, a trajectory tracking controller was built and simulation was taken on the control law. The error differential equation of the wheat precision seeding robot was(9)x˙e=-k1xe+yeωr+k2vrye2+k3vryesin⁡θe,y˙e=-xeωr-k2vrxeye-k3vrxesin⁡θe+vrsin⁡θe,θ˙e=-k2vrye-k3vrsin⁡θe.First, straight line trajectory tracking was simulated. Set the linear equation as follows:(10)xt=t,yt=t+1.In straight line motion, ωr=0, the velocity was constant, and set vr=1, k1,k2,k3T=5,5,5T. So the differential equation of the robot was as follows:(11)x˙e=-5xe+5ye2+5yesin⁡θe,y˙e=-5xeye-5xesin⁡θe+sin⁡θe,θ˙e=-5ye-5sin⁡θe.The initial location of the robot was P(0)=0,0,0T, the initial location of the desired trajectory was R(0)=0,1,-π/4T, and Figure 5 was the error curve of straight line tracking. Figure 6 was the actual movement of the robot tracking a straight line.Figure 5
Diagram of error curve of straight line tracking.Figure 6
Diagram of the movement of straight line tracking.From the simulation, the errors ofx and y and the angle became 0 after 3.5 s. The actual path and expected path were overlapped after 3 s.Then, circular trajectory tracking was simulated. The circle equation was(12)xt=sin⁡2πt,yt=cos⁡2πt,θt=2πt.The robot’s initial position was p(0)=-0.5,0.5,π/2T and the initial position of expected path was R(0)=0,1,0T. The expected linear velocity and angular velocity were vr,ωrT=π/12,π/6T. The controller parameter was k1,k2,k3T=20,20,10T. The differential equation for the location of the robot was as follows:(13)x˙e=-20xe+π12ye+10π3ye2+5π3yesin⁡θe,y˙e=-π12xe-10π3xeye-5π3xesin⁡θe+π6sin⁡θe,θ˙e=-10π3ye-5π3sin⁡θe.Figures 7 and 8 showed the result of simulation.Figure 7
Diagram of error curve of circular tracking.Figure 8
Diagram of the movement of circular tracking.From the diagram, the errors ofx and y and angle became 0 after 3 s. In the movement diagram, the path turned 2 circles before the actual curve to coincide with expected path, so the error in y-axis should better be improved.


## 4. Design of Seeding Experiments

During the working, for the robot, the main factors affecting the quality of seeding were three: the pore size of planting tray, the pressure (negative) of vacuum chamber, and the speed of the planting tray [18]. The pressure of vacuum chamber and the pore size of the planting tray had a direct impact on the leakage rate and reseeding rate. The smaller size needed the bigger pressure, and if the pore size was too small, it would cause the absorbing force which was too weak to pick up the seed, resulting in leakage phenomenon. If the pressure was too big, it would cause the increase of the reseeding. Meanwhile in the seeding process, if the speed of planting tray exceeded a certain limit, there was no adequate filling time, likely to cause serious leakage phenomenon [19–21].Due to the fact that the impact of these factors on the qualified rate was not a simple linear relationship, the quadratic orthogonal rotation combination design method was taken in this paper to arrange the experiments. The regression analysis was used to analyze the connection between the factors and determine the relation of primary and secondary between them.According to the quadratic orthogonal rotation combination design method, the test points were composed of 3 types of combination [22, 23]; it was(14)n=mc+mr+m0.And mc was the test number of factor point, mr was the test number of star point, and m0 was the test number of zero level center point. The number of factors was 3, so all the test numbers were 23.According to the test and experience, the best combination of factors was selected as the zero level of the experiments, the pore size of the planting tray was 2.4 mm, the speed of the planting tray was 30 r/min, and the pressure of the vacuum chamber was −2.3 kPa. The values and code table of each level of the 3 factors were determined according to the zero level, as shown in Tables1 and 2.Table 1
Code variable design level and the value.
Level
-
r
-
1
0
1
r
Value
x
0
i
-
Δ
i
×
r
x
0
i
-
Δ
i
x
0
i
x
0
i
+
Δ
i
x
0
i
+
Δ
i
×
rTable 2
Level code table of tests factors.
Levelzj
Pore sizex1/mm
Speedx2/(r/min)
Pressurex3/kPa
-
1.682
2.0
20
-
1.8
-
1
2.16
24
-
2.0
0
2.4
30
-
2.3
1
2.64
36
-
2.6
1.682
2.8
40
-
2.8Table3 was the orthogonal rotation design structure matrix and calculation table of the seeding qualified rate.Table 3
Orthogonal rotation design structure matrix and calculation.
Number
z
0
z
1
z
2
z
3
z
1
z
2
z
1
z
3
z
2
z
3
z
1
′
z
2
′
z
3
′
y
i
1
1
1
1
1
1
1
1
0.406
0.406
0.406
85.780
2
1
1
1
−1
1
−1
−1
0.406
0.406
0.406
82.370
3
1
1
−1
1
−1
1
−1
0.406
0.406
0.406
94.650
4
1
1
−1
−1
−1
−1
1
0.406
0.406
0.406
93.270
5
1
−1
1
1
−1
−1
1
0.406
0.406
0.406
87.560
6
1
−1
1
−1
−1
1
−1
0.406
0.406
0.406
80.350
7
1
−1
−1
1
1
−1
−1
0.406
0.406
0.406
93.420
8
1
−1
−1
−1
1
1
1
0.406
0.406
0.406
83.380
9
1
1.682
0
0
0
0
0
2.234
−0.594
−0.594
92.830
10
1
−1.682
0
0
0
0
0
2.234
−0.594
−0.594
84.620
11
1
0
1.682
0
0
0
0
−0.594
2.234
−0.594
85.220
12
1
0
−1.682
0
0
0
0
−0.594
2.234
−0.594
95.360
13
1
0
0
1.682
0
0
0
−0.594
−0.594
2.234
93.830
14
1
0
0
−1.682
0
0
0
−0.594
−0.594
2.234
90.430
15
1
0
0
0
0
0
0
−0.594
−0.594
−0.594
94.600
16
1
0
0
0
0
0
0
−0.594
−0.594
−0.594
92.140
17
1
0
0
0
0
0
0
−0.594
−0.594
−0.594
90.230
18
1
0
0
0
0
0
0
−0.594
−0.594
−0.594
92.600
19
1
0
0
0
0
0
0
−0.594
−0.594
−0.594
95.120
20
1
0
0
0
0
0
0
−0.594
−0.594
−0.594
92.460
21
1
0
0
0
0
0
0
−0.594
−0.594
−0.594
94.340
22
1
0
0
0
0
0
0
−0.594
−0.594
−0.594
93.280
23
1
0
0
0
0
0
0
−0.594
−0.594
−0.594
95.640
B
i
=
∑
z
y
2083.48
25.169
−45.715
27.759
−10.880
−12.460
−0.800
−34.979
−26.127
−15.720
d
i
=
∑
z
2
23.000
13.660
13.660
13.660
8.000
8.000
8.000
15.890
15.890
15.890
b
i
=
B
i
d
i
90.586
1.843
−3.347
2.032
−1.360
−1.558
−0.100
−2.201
−1.644
−0.989
S
S
i
=
b
i
B
i
46.376
152.995
56.409
14.797
19.406
0.080
76.998
42.959
15.552Because the design factors were the function of the norms variablez confirmed by a dimensionless linear coding, these bi among the first term regression coefficients and bi and the interaction terms were not relevant. Therefore, the affection to seeding qualified rate was directly judged by comparing the absolute values of the norms variable regression coefficient bi. So the influence order within a certain range was x2>x3>x1. Among them, the speed x2 was the biggest effect on the seeding performance, the pressure x3 was less, and the pore size x1 was the smallest.Based on the above analysis, the conditions for the seeding experiments of the robot were listed in Table4. The experiments were taken under different speeds to verify the performance of the robot.Table 4
Experiment parameters list.
Item
Value
Unit
Pore size
2.5
mm
Pressure
−2.4
kPa
Seed space
6
cm
Speed
0.7, 0.9, 1.1
m/s


## 5. Result Analysis

For the three speeds, 100 adjacent seed spaces as a sample were selected from each speed experiment. Tables5–7 were the selected data at the speeds of 0.7 m/s, 0.9 m/s, and 1.1 m/s. Figures 9–11 were the statistical chart of the measured seed space under each speed.Table 5
Measured data at speed of 0.7 m/s.
100 adjacent seed spaces at speed of 0.7 m/s (cm)
6.1
7.7
7.9
6.8
5.9
5.8
3.9
7.2
6.0
7.0
6.5
6.1
14.8
5.9
5.6
4.8
5.0
6.4
5.6
4.8
5.0
5.7
7.4
5.6
5.6
3.0
6.8
8.0
0.5
3.0
4.9
5.8
6.1
7.2
4.8
6.2
15.9
8.7
6.8
8.0
6.5
6.2
5.5
6.0
6.4
7.3
7.6
8.9
5.4
6.8
6.7
7.0
5.9
8.1
6.5
8.5
8.4
6.4
9.0
3.9
5.0
6.4
7.4
9.2
6.0
6.3
8.0
5.8
8.4
6.5
4.4
6.0
4.6
8.4
7.2
6.4
7.4
6.0
8.9
5.4
6.8
9.3
5.2
6.0
8.1
6.0
4.6
6.5
7.2
6.0
6.0
9.0
3.9
5.4
5.4
9.3
5.2
7.5
8.6
5.4Table 6
Measured data at speed of 0.9 m/s.
100 adjacent seed spaces at speed of 0.9 m/s (cm)
6.4
8.4
6.5
6.6
7.6
6.8
5.8
7.9
5.0
6.6
6.2
8.9
5.4
6.8
5.7
6.0
6.4
6.5
4.0
6.8
6.2
7.2
6.0
8.0
3.8
7.4
9.2
7.2
7.0
6.0
6.3
5.9
5.8
7.5
6.5
4.6
8.4
5.9
7.3
8.1
7.0
6.0
7.6
7.3
7.1
16.7
6.5
6.0
4.5
7.9
7.3
1.0
5.1
8.4
8.4
9.0
7.6
8.5
8.1
5.6
4.5
7.9
6.3
9.1
6.3
8.0
5.1
7.9
5.1
8.4
8.1
5.6
4.8
7.0
5.1
5.5
6.3
8.1
6.3
9.0
7.5
6.1
2.0
6.8
3.5
5.9
4.8
5.9
6.7
7.8
6.5
8.0
5.9
8.4
6.1
7.4
6.0
6.9
6.1
6.8Table 7
Measured data at speed of 1.1 m/s.
100 adjacent seed spaces at speed of 1.1 m/s (cm)
6.0
5.7
6.9
6.9
8.9
8.3
7.5
8.4
7.2
6.0
6.0
6.0
8.0
7.9
6.0
9.0
5.8
6.0
8.1
7.4
5.4
6.8
9.2
9.4
7.0
8.0
4.6
5.4
5.4
5.4
4.9
6.3
5.4
5.6
7.5
6.1
6.7
6.5
7.0
6.6
7.3
5.1
5.0
6.0
6.8
6.4
5.0
3.4
8.4
6.8
6.5
8.0
5.8
4.7
6.0
8.1
6.0
4.6
6.5
7.6
7.8
7.4
6.0
9.8
5.4
5.4
16.3
5.2
7.5
7.6
7.2
4.6
6.5
1.2
6.6
7.6
6.8
5.8
15.5
5.2
5.2
5.2
7.5
6.0
6.9
8.6
6.0
8.0
5.4
6.8
6.2
5.8
8.1
5.4
5.4
5.4
5.6
6.3
6.2
7.0Figure 9
Statistical chart at 0.7 m/s.Figure 10
Statistical chart at 0.9 m/s.Figure 11
Statistical chart under 1.1 m/s.According to the standard GB/T6973-2005 (testing methods of single seed drills (precision drills)), the leakage was that the seed space was greater than 1.5 times the set distance. And the reseed was that the seed space was smaller than 0.5 times the set distance. So, the seed space was divided into several ranges:[0,0.5x], (0.5x,1.5x], (1.5x,2.5x], (2.5x,3.5x], and (3.5x,+∞]; x was the set seed space. Consider(15)n1′=∑nini∈0,0.5x,n2′=∑nini∈0.5x,1.5x,n3′=∑nini∈1.5x,2.5x,n4′=∑nini∈2.5x,3.5x,n5′=∑nini∈3.5x,+∞,N=n1′+n2′+n3′+n4′+n5′.Define the leakage number n0, the qualified number n1, the reseed number n2, and the interval number N as follows:(16)n0=n3′+2n4′+3n5′,n1=N′-2n2,n2=n1′,N=n2′+2n3′+3n4′+4n5′.The following were the formulas to calculate the reseed rate D, leakage rate M, and qualified rate A:(17)D=n2N×100,M=n0N×100,A=n1N×100.Table 8 was the calculation result of the rates under different speed.Table 8
Results under different speed.
Speed (m/s)
Qualified rate (%)
Reseed rate (%)
Leakage rate (%)
0.7
94.81
0.96
4.80
0.9
95.15
0.97
3.88
1.1
93.33
0.95
5.71From Table8, it could be concluded that the qualified rates under different speed were all greater than 93%.


## 6. Summary

Through the above experiments, the results could verify the performance of the wheat precision seeding robot in the actual work environment. But there were differences under the different speed. And the speed was the main factor in the wheat precision seeding.



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*Source: 696301-2015-11-24.xml*