Optimal design and experimental verification of a four-claw seedling pick-up mechanism using the hybrid PSO-SA algorithm

Funding agencies/institutions	Project / Grant
National Natural Science Foundation of China	61763042/62163032

MATERIAL AND METHODS

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Design requirements of the seedling pick-up mechanism

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The functions of the seedling pick-up device are to extract seedlings from the pot, transfer them, and feed them into the transplanting unit (Brewer, 1994). The seedling pick-up mechanism should steadily perform seedling pick-up without damaging the seedlings and the substrate (Han et al., 2015a). The lower part of the seedling substrate is usually more robust than the upper part, so clamping it from the lower part helps to reduce damage to it (Han et al., 2013a). Besides, the best opening of pick-up pins was 2-3 mm lower than the pot width (Choi et al., 2002b). With the increase in the number of pick-up pins, the stability of picking up seedlings also increases (Li et al., 2017).

In conclusion, the optimal trajectory of pick-up pins should meet the following requirements: (i) inserting into the lower part of the substrate; (ii) keeping a safe distance from the inner wall and bottom of the cell; (iii) clamping the substrate with more pick-up pins.

Development of seedling pick-up mechanism

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Structure of seedling pick-up mechanism

The seedling pick-up mechanism consists of the mounting plate, a servo motor, driving and connecting links, and pick-up pins. As shown in Fig. 1, the Servo motor is connected to Driving link 2 through a connecting screw rod. Driving link 2 meshes with Driving link 1, with Driving link 2 is also connected to Driving link 3 with a sleeve flange. The servo motor rotates clockwise at a constant speed, and Driving link 2 is steered by the Connecting screw rod. The meshing of Driving link 2 and 1 achieves the clockwise rotation of Driving link 2 and 3 and the counterclockwise rotation of Driving link 1. As the Driving link moves inward, the pick-up pins approach the substrate in the cell and insert it. After the Pick-up pins clamp the seedling, the pick-up mechanism is lifted by lifting devices, and the seedling is extracted from the cell. Then the horizontal slider transfers the seedling pick-up mechanism to a specific position for releasing the seedling.

Figure 1. Structure of the seedling pick-up mechanism: exterior structure (a); interior structure (b). 1) mounting plate 1; 2) screw; 3) sleeve flange; 4) driving link 3; 5) driving link 2; 6) mounting plate 2; 7) driving link 1 8) small shaft; 9) interlocking screw; 10) pick-up pins; 11) servo motor; 12) connecting screw rod; 13) circlip; 14) connecting link; 15) bearing.

Working principle of seedling pick-up mechanism

Initially, the pick-up pins open and the pick-up mechanism move down with the slider. Then, the pick-up pins gradually approach the surface of the substrate (Fig. 2b). As the driving link rotates inward, the pins insert into the substrate. Until the substrate is clamped completely (Fig. 2c). As shown in Fig. 2d, the seedling is extracted with the upward movement of the slider. The pick-up pins are opened at the discharge point, then the driving link rotates outward, and the seedling is released.

Figure 2. Working process of the seedling pick-up device for picking up seedlings: descending (a), picking up seedlings (b), clamp seedlings (c), extract seedlings (d). 1) slider; 2) seedling pick-up mechanism; 3) plug tray; 4) seedling; 5) guide rail.

Determination of structural parameters

Fig. 3 shows that O and O’ are the rotation center of the driving link OA and O’A’, respectively. C and C’ is the rotation center of the connecting link BC and B’C’ individually. L₁ is the distance between point O and O’, L₂ is the length of the driving link OA, and φ is the angle of the y axis intersected with the line OC.

Figure 3. Motion diagram of the seedling pick-up mechanism.

The curve e-f-g-h is the planned trajectory for picking up seedlings. The pick-up pins should insert into the substrate along the curve f-g-h for seedling extraction. Point g is the completion position of picking up seedlings, and points f and h are the releasing positions. When picking up seedlings, the seedling pick-up mechanism should meet the conditions in Eq. (1).

\{\binom{W_{1} < n}{D_{1} cos φ < H}

(1)

When the seedling pick-up mechanism is ready to move upward, the force analysis is shown in Fig. 2b. F_L is the resistant force for extracting plug seedlings, which is determined by the mass of the plug seedlings, the adhesion between the substrate and the pot (Miao et al., 2013). F_J1 and F_J2 are the clamping forces of the seedling pick-up mechanism on the seedling, which is determined by the substrate’s deformation and compressive properties (Han et al., 2013b). F_S1 and F_S2 are the frictions between the pick-up pins and the substrate, which are mainly composed of the slip friction force F_f and the sliding resistance F_fa. Considering the homogeneity of the substrate, F_S1 = F_S2 = F_f + F_fa = µ (F_J1+P_s), where µ is the friction factor between the substrate and the pick-up pins, and s is the contact area. Given the small contact area between the substrate and the pick-up pins, F_fa can be ignored, so F_S1 = F_S2 = µF_J1 (Hu, 2011). The mechanical balance equation is shown in Eq. (2).

\{\binom{F_{S2} sin α + F_{J1} cos α = F_{S1} sin α + F_{J2} cos α}{(F_{J1} + F_{J2}) sin α + (F_{S1} + F_{S2}) cos α \geq F_{L}}

(2)

Assuming that the substrate is a homogeneous material, then F_J1 and F_J2 have the same effect, Eq. (3) can be obtained:

F_{J1} = F_{J2} \geq \frac{F_{L}}{2 (sin α + μ cos α)}

(3)

Because the clamping force on the substrate is generated by the motor, the force of the motor on the pick-up pins is F_T1 and F_T2. When the pick-up pins grasp the substrate and start to move upward, analyzing the force of pick-up pins, Eq. (4) can be obtained:

F_{T1} = \frac{F_{J1}}{sin β}

(4)

Therefore, to extract the seedling successfully, the force generated by the motor must meet the constraint conditions in Eq. (5).

F_{T1} \geq \frac{F_{L}}{2 sin β (sin α + μ cos α)}

(5)

where F_L is the resistant force determined by the agronomic conditions for seedling raising (Miao et al., 2013) and is the clamping angle of the seedling pick-up mechanism.

It can be found from Eq. (4) that the clamping force decreases with the increase of the clamping angle. However, if the clamping angle is too large, the insertion depth of the pick-up pins will be affected. Choi et al. (2002a) found that the pick-up pins were inserted into the substrate with a gap of 2-3 mm lower than the pot wall and that inserting the substrate as deep as possible contributed to the seedling extraction. In order to ensure the maximum clamping angle and meet the specifications of the plug tray at 128 holes and 72 holes in Table 1, the clamping angle was designed to be 18° theoretically. Consequently, the pick-up pins and the pot wall can maintain a 2-3 mm insertion gap to have an initial opening of 28-35 mm and a maximum insertion depth of 37 mm. The separation force of cucumber, tomato, and other plug seedlings from the pot has been measured as 0.97-2.93 N (Han, 2014). The static friction factor of the substrate and pick-up pins is 0.49-0.54 (Han et al., 2013b). Therefore, according to Eqs. (2) - (5), it was estimated that the motor torque needed to overcome the maximum separation force of seedlings from its pot was 0.64 N∙m.

Table 1. Specifications of plug tray.

Specification	Size (L*W), mm²	Central distance of hole (d), mm	Depth of hole (h), mm	Upper caliber (a*b), mm	Lower caliber (c*c), mm
12*6	280*540	45	45	40*40	20*20
16*8	280*540	32.5	42	32*32	14*14

In order to satisfy the requirements for picking up and releasing seedlings, avoiding mechanical interference, and not causing damage to the seedlings, the initial value of each parameter is (Eq. (6):

(L_{1} L_{2} L_{3} φ) = (846026516)

(6)

where L₃ is the length of pick-up pins, and φ is the angle of the y axis intersected with the line OC.

Design of control system

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Hardware design of control system

The hardware of the control system includes three sections: the sensor used for signal obtaining, the controller used for processing the signal, and the driving unit to perform specific actions (Yang et al., 2020).

Selection of programmable controller

We adopted Arduino as the controller of the seedling pick-up mechanism and transferring device. The flow chart of the control system and the control system’s communication are shown in Figs. 4a, and 4b, respectively. In this control system, Arduino was used for receiving the input signal from the sensor, processing the signal, and delivering the signal to the servo motor. Several key parameters must be considered in the controller selection, such as the processing speed and accuracy, the number of communication ports etc. Therefore, Arduino UNO was selected as the controller of our seedling pick-up mechanism.

Figure 4. Main control system: flow chart of control system (a) and communication of control system (b).

Design of control system hardware circuit

The hardware circuit of the seedling pick-up mechanism and transplanting device is shown in Fig. 5: 1 is the angle sensor of the seedling pick-up mechanism; 2, 3 and 4 are the photoelectric sensors of transferring and the lifting devices, respectively; 5 and 6 are the servo motor of transferring devices; and 7 is the servo motor of the lifting device. A 24-V DC power supply powered the servo motor, and the angle sensor and photoelectric sensor were connected to the input pin of Arduino. The output pin of Arduino was connected to the A and B pins of the servo motor. The VCC (voltage-to-current converter) and GND (ground) pins of the servo motor were connected to the positive and negative terminals of the power supply, respectively. This control system is based on RS-485 communication.

Figure 5. The hardware circuit of control system.

Design of control system software

Arduino IDE 1.8.13 was used as the core programming software. The photoelectric sensor was used to detect the position of the slider retained on transferring and lifting devices. The angle sensor measures the current angle of pick-up pins. When the seedling pick-up mechanism was transferred to the seedling picking position by the slider, the photoelectric sensor received and inputted the signal into the Arduino. Thus, the servo motors of transferring devices stop and then the seedling pick-up mechanism starts to pick up seedlings. When the current angle measured by the angle sensor reaches the predetermined value, the servo motor stops, and the seedling is clamped. Then the seedling is extracted from the pot by lifting devices and transferred to the releasing position.

Kinematic model of seedling pick-up mechanism

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As shown in Fig. 6, the position of the driving link is AB when pick-up pins start to approach the cell. When the pick-up pins clamp the substrate completely, the position of the driving link is AB´, and the rotation angle of the driving link is δ during this process. Since the seedling pick-up mechanism is symmetrical structurally, half of it is analyzed.

Figure 6. Kinematic model of the seedling pick-mechanism.

The coordinates of points A, B and D at initial position were as follows:

(\binom{X_{A} X_{B} X_{D}}{Y_{A} Y_{B} Y_{D}}) = (\binom{\frac{L_{1}}{2} \frac{L_{1}}{2} + L_{2}}{00} \binom{\frac{L_{1}}{2} + L_{2} - L_{3} sinφ}{- L_{3} cosφ})

(7)

The coordinates of point D´ can be expressed as Eq. (8):

\{\binom{X_{D'} = \frac{L_{1}}{2} + L_{2} cosω t - L_{3} sinφ}{Y_{D'} = L_{2} sinω t - L_{3} cosφ}

(8)

Therefore, the trajectory equation of position D is shown in Eq. (9).

y = \sqrt{L_{2}^{2} - {(x - \frac{L_{1}}{2} + L_{3} sinφ)}^{2}} - L_{3} cosφ

(9)

In this coordinate system, the position of the cell was assumed constant, so the equation of the inside wall of the pot is shown in Eq. (10):

y_{1} = 3.98x - 338.5

(10)

The velocity of point D is expressed in Eq. (11).

v = v_{x} y + v_{y} j = ẋi + ẏj = (- ω L_{2} sinωt) i + (- ω L_{2} cosωt) j

(11)

The acceleration of point D is shown in Eq. (12).

a = a_{x} i + a_{y} j = ẍi + ÿj = (- ω^{2} L_{2} cosωt) i + (ω^{2} L_{2} sinωt) j

(12)

Parameter optimization of seedling pick-up mechanism

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Design variables

Considering that the trajectory of point D is related to L₁, L₃ and φ, the design variables were selected as follows:

x = (L_{1} L_{BD} φ) = (x_{1} x_{2} x_{3})

(13)

Objective function

According to the requirements of the seedling picking trajectory, when pick-up pins approach the top of the cell, the deviation between the trajectory curve of point D and the predetermined trajectory curve should be minimized. So, the objective function is defined in Eq. (14).

f = \sqrt{3600 - (14 - \frac{x_{1}}{2} + x_{2} \sin x_{3})^{2}} - x_{2} \cos x_{3} + 274.8

(14)

Constraint condition

Given design requirements, the assembly restrictions, and non-interference mechanically, the size of each part should meet constraints in Eq. (15):

\{\binom{3600 - {(14 - \frac{x_{1}}{2} + x_{2} \sin x_{3})}^{2} \geq 0}{\frac{x_{1}}{2} - x_{2} \sin x_{3} + 60 > 16}

(15)

The upper and lower bounds of each decision variable are shown in Eq. (16):

(\binom{lb}{ub}) = (\binom{7525514}{9030020})

(16)

Hybrid PSO-SA optimization

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Principle of the PSO algorithm

Particle swarm optimization (PSO), as a kind of swarm intelligence, simulates the biological behavior of a bird flock seeking food and searching for the optimal value in the search space through individual cognitive and social cognitive (Eberhart & Kennedy, 1995; Kennedy & Eberhart, 1995; Shi & Eberhart, 1998). The PSO algorithm treats each individual in the population as a particle without volume or weight in the search space, representing a possible solution. The particle flies at a certain speed in the search space, and the best position experienced by the particle is the optimum solution found by the particle itself. The flight speed of the particle is dynamically adjusted by the flight experience of the particle and the group, and the optimal solution is obtained iteratively.

In the beginning, a group of particles are created in the search space S∈Rⁿ and X_kⁱ={x₁ⁱ, x₂ⁱ, ···, x_nⁱ}^Tis considered as the current position of particle k. Following this, the best value of the particle k P_k^b={P₁^b,P₂^b, ···, P_n^b}^T and the global optimal value P^g={P₁^g,P₂^g, ···, P_n^g}^T in iteration i are calculated. Then, the velocity and position of the particle are updated using Eqs. (17) and (18). The loop terminates until the convergence condition is satisfied.

{v_{k}}^{i + 1} = {ωv}_{k}^{i} + c_{1} R_{1} \cdot ({P_{k}}^{b} - {x_{k}}^{i}) + c_{2} R_{2} \cdot (P^{g} - {x_{k}}^{i})

(17)

{X_{k}}^{i + 1} = {X_{k}}^{i} + {v_{k}}^{i + 1}

(18)

where v_k is the velocity of the particle k,R₁ and R₂ are random numbers which are generated between 0 and 1, C₁ and C₂ are learning rate.

The PSO algorithm has a faster convergence speed and better global search capability than the other optimization algorithm. However, it has the problem of premature convergence and poor local search ability (Angeline, 1998).

Principle of the SA algorithm

Simulated Annealing (SA), inspired by the physical annealing process of solids, is a popular intelligent optimization algorithm. According to Metropolis et al. (1953) and Genovese et al. (2005), the probability of the atom reaching equilibrium at temperature T is e^-ΔE/(kT), E is the energy at temperature T, ΔE is the E change, k is the Boltzmann constant. The optimization problem is simulated by solid annealing, and energy E is regarded as objective function f and temperature T as the control parameter. During the iteration of the algorithm, Eq. (19) was used to decide whether to accept the new solution.

p = \{\binom{1 if f (X_{i+1}) ⩽ f (X_{i})}{e^{- \frac{Δ f}{T}} Otherwise}

(19)

where f is the fitness function, Δf = f(X_i+1)-f(X_i), and T is the controlling parameter. The acceptance probability decreases with decreasing temperature, and the Eq. (20) is usually used as a temperature decrement method.

T_{i + 1} = R_{T} T_{i}

(20)

where T₀ is the initial temperature, and R_T is a positive constant between 0.8 and 0.999. SA algorithm has been successfully applied to many fields and achieve excellent effect (Di Sciuva et al., 2003; Liu et al., 2014).

The hybrid algorithm of PSO-SA

For the past few years, many hybrid PSO-SA algorithms have been proposed, which can be divided into three categories. Accelerating the convergence of SA by adopting a good start position generated by PSO (Xia & Wu, 2006), incorporating the Metropolis et al. (1953) acceptance principles into the PSO algorithm (Shieh et al., 2011), and combining PSO cycles with the SA iterations (Costa et al., 2011).

In this paper, a hybrid PSO and SA algorithm was adopted, aiming to improve the performance of the algorithm (Javidrad & Nazari, 2017). If there are no changes during a period of PSO, a new global optimal position is generated using SA to replace the old one. Equation was used to guide the movement of particles in the search space to seek the optimal solution of an objective function. Fig. 7 shows the flow chart of the hybrid PSO-SA algorithm.

Figure 7. Flow chart of hybrid PSO-SA algorithm.

Three parameters are involved in the hybrid PSO-SA algorithm: the population size of the particle (P_s), the original temperature (T₀), and the Markov chain length (L_M). In this paper, P_s=50, T₀=100, and L_M=100 were used. The algorithm was implemented using MATLAB (R2018a). The convergence curve for the objective function is shown in Fig. 8. It can be found that the proposed hybrid PSO-SA algorithm converges to the global optimum point much faster than either PSO or SA algorithm. Moreover, the hybrid PSO-SA algorithm has better stability compared to the SA algorithm. Finally, the value of the optimized decision variable is determined, which is L₁=87.5 mm, L₂=277 mm, φ=18°.

Figure 8. Convergence behavior of objective function by the proposed hybrid PSO-SA algorithm.

Kinematic simulation validation

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A kinematic simulation analysis was conducted to validate the trajectory curve of the pick-up pins. We assumed that each part of the mechanism is made of duralumin and the weight of the seedling is negligible (Hu, 2011). A simulation cycle refers to pick-up pins moving from their initial position to clamping the seedling completely. In addition, Qi et al. (2011) found that the maximum acceleration the seedling can withstand is 45 m/s².

Firstly, the 3D model of the seedling pick-up mechanism was created using SolidWorks (3D solid modeling CAD software). Then, the 3D model was imported into the kinematic simulation software ADAMS (Automatic Dynamic Analysis of Mechanical System), the mass properties of each part were determined, and the required constraints were built. The corresponding motion was established, and then the simulation was performed. The driving function of the mechanism is shown in Eq. (21), with a simulation time of 0.03 s and a step number of 2000; the motion simulation was conducted.

step (time, 0, 0d, 0.05, 30d) + (time, 0.05, 0d, 0.08, 0) + (time, 0.08, 0d, 0.01, -30d)

(21)

Fig. 9 shows the trajectory curve of the pick-up pins, where A is the completion point of the seedling picking, and B is the initial point, indicating that when the seedling pin reaches point B, the distance between the inside wall of the cell and the pick-up pins is 2 mm. When pick-up pins clamp the seedling, the end of the pick-up pins reaches point A, which is the lower part of the cell. Therefore, the trajectory curve of pick-up pins meets the design requirements.

Figure 9. The trajectory curve of point D.

Seedling pick-up tests of the mechanism

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The prototype was constructed to verify the efficiency of the optimized seedling pick-up mechanism, and the performance tests were carried out in the laboratory, as shown in Fig. 10. The room temperature was 28℃, and the relative humidity 41%. A potted tray with 16×8 cells was used for the tests, with tomato seedlings 39 days old. The ratio of the main components of the matrix is shown in Table 2.

Figure 10. Performance test of the seedling pick-up mechanism.

Table 2. Ratio of the main components of the matrix.

Saturaid	Chicken litter	Husk	Soybean meal	Nitrogen	Phosphates	Potash	Ferrous sulfate
0.6	0.1	0.1	0.08	0.005	0.003	0.003	0.007

Some researchers have also found that the leave’s damage caused by the pick-up pins does not significantly affect seedling growth after transplanting. Given these factors, the success ratio in picking up seedlings is defined in Eq. (22):

T_{s} = \frac{S}{N} ✕ 100%

(22)

where S is the sum of seedlings successfully released, N is the total number of seedlings tested.

The seedling release rate and the damage rate are also important to evaluate the performance of the seedling pick-up mechanism, which can be expressed in Eqs. (23) and (24):

T_{L} = \frac{M}{N} ✕ 100%

(23)

T_{D} = \frac{M_{1} - M_{2}}{M_{1}} ✕ 100%

(24)

where M is the number of seedlings successfully released, and N is the total number of seedlings tested; M₁ is the mean mass of seedlings before transplanting, and M₂ is the mean mass after transplanting.

The success rate and release rate showed how smoothly the mechanism picked, transferred, and released seedlings. The damage rate was used to evaluate the damage to seedlings caused by the seedling pick-up mechanism. The transplanting frequency was 50, 70, and 90 plants per minute, respectively, and Table 3 provides the statistical results of the test.

Table 3. Test results of the prototype.

Seedling pick-up rate (plant/min) x₁	Moisture content (%) x₂	N (plant)	S (plant)	M (plant)	M₁ (plant)	M₂ (plant)	T_S (%)	T_L (%)	T_D (%)
50	50	128	112	108	9.86	9.33	87.50	84.38	5.38
	60	128	116	112	10.19	9.76	90.63	87.5	4.22
	70	128	109	109	9.63	9.22	85.16	85.16	4.26
70	50	128	108	101	9.37	8.86	84.38	78.91	5.44
	60	128	113	107	10.44	9.93	88.28	83.59	4.89
	70	128	103	97	9.56	9.04	80.47	75.78	5.44
90	50	128	106	102	10.71	10.14	82.81	79.69	5.32
	60	128	107	103	9.62	9.17	83.59	80.47	4.68
	70	128	99	95	9.76	9.12	77.34	74.22	6.56
Sum		1152	973	934	89.11	84.58	84.46	81.08	5.13

The Design-Expert was used to analyze the experimental results, and the regression equation between the three experimental indexes and various factors was obtained.

	Variance source	Model	x₁	x₂	x₁ x₂	x₁²	x₂²	Residual	Cor total
Success ratio, %	Sum of squares	130.6	63.7	22.89	2.45	0.033	41.53	1.89	132.49
	Mean square	26.12	63.7	101.05	36.32	3.89	0.052	65.88
	F value	41.44	101.05	36.32	3.89	0.052	65.88
	p value	0.006	0.002	0.009	0.143	0.834	0.004
Release rate, %	Sum of squares	152.49	85.58	10.19	9.77	12.23	34.72	4.77	157.27
	Mean square	30.50	85.58	10.19	9.77	12.23	34.72	1.59
	F value	19.17	53.80	6.41	6.14	7.69	21.83
	p value	0.018	0.005	0.085	0.089	0.069	0.019
Damage rate, %	Sum of squares	3.97	1.21	0.002	1.39	0.070	1.29	0.211	4.18
	Mean square	0.794	1.21	0.002	1.39	0.070	1.29	0.070
	F value	11.31	17.31	0.034	19.84	0.993	18.39
	p value	0.037	0.025	0.865	0.021	0.393	0.023

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