The trichogramma balls delivery system is built using a quad-rotor unmanned plant protection aircraft (EFT E410S) and a flight control system (JIYI K++). The structure is shown in Figure 2 . The drone has a maximum operating height of 50m, a maximum speed of 10m/s, and a maximum takeoff weight of 25kg. The main frame is made of carbon fibre material. The folding arms are symmetrically mounted on the two diagonal lines of the frame using injection molding technology. A motor is installed at the end of the arm(Zhan et al., 2021; Ji et al., 2022).

The ground control system includes BeiDou mobile station, base station, and upper computer to obtain real-time information on flight altitude, speed and trajectory parameters of the drone during operation, as well as the actual landing point location information of the trichogramma balls. The structural diagram is shown in Figure 3 . The core module of the system is the BeiDou board card (ComNav K705), with detailed technical parameters shown in Table 1 . A data transmission module (Microhard P900) is used as the Beidou data wireless transmission device.

The trichogramma ball is made of degradable composite material using injection moulding technology. The trichogramma eggs are loaded inside the trichogramma ball, which can avoid the trichogramma from being exposed to the outside world before eclosion. The shape of the trichogramma ball is like a cylinder, with a diameter of 18 mm and a height of 18 mm, the edges of both ends are rounded with a radius of 5 mm, and the maximum diameter length is 20.5 mm, this structure can prevent the trichogramma ball from rolling too far after falling to the ground. There are eight breathable holes on both ends with a diameter of 0.5 mm, preventing natural enemies from swallowing insect eggs while ensuring a certain degree of breathability. The structure of the trichogramma ball is shown in Figure 4 .

The delivery device mainly includes a base, material bucket, balls distribution plate, stirring connecting piece, stirring sphere, and steering engine, as shown in Figure 5 . The base matches the bottom of the material bucket, the four pits in the inner circle correspond to the protrusions around the bottom hole of the material bucket, two circular tracks are designed on the base, then the entering balls can slide along the tracks, ensuring that the balls can fall into the balls distribution plate at any posture. After the steering engine is installed on the base, the steering plate is sequentially connected with the balls distribution plate, the stirring connecting piece and the stirring sphere through bolts.

The circuit part of the control system of the trichogramma balls delivery device is composed of three parts: the power module (LM2596HVS step-down module), the control module (STM32F103C8T6), and the output module (DS3230 360° metal digital rudder). These components are directly connected to the UAV flight control system to realize the matching of the UAV flight speed and the trichogramma balls delivery speed. That is, the distance between trichogramma balls released at any flight speed is always a fixed value, so as to avoid the problem of uneven delivery of the balls in the field and achieve the linkage effect. The steering engine rotates when the PWM signal is input, so the speed of the steering engine is tested under different PWM input signals, and the functional relationship between the PWM signal value x ₁(μs) (input to the steering engine and the steering engine speed n(r/min) obtained by fitting is shown in Equation 1, the determination coefficient R ² = 0.9968.

The steering engine rotates 1/3 of a turn to drop a trichogramma ball and the UAV is required to put the trichogramma balls at equal intervals l(m), the UAV flight speed v(m/s) and the steering engine speed n(r/min) meet the Equation 2:

Therefore, the relationship between the PWM signal value x ₁(μs) input to the steering engine and the UAV flight speed v(m/s) can be expressed as follows:

Through flight test, the relationship between PWM value x ₂(μs) of flight controller output and UAV flight speed v(m/s) can be obtained as follows:

Then the PWM value x ₂(μs) of flight controller output and the PWM signal value x ₁(μs) input to the steering engine should meet the following relationship:

In the actual field operations of UAVs, the mechanical structure stability and control system accuracy of the trichogramma balls delivery system will directly affect the quality of field operations of the system. Therefore, experiments were conducted on system stability and release accuracy.

The test site was located at the Qilin District Sports Ground of South China Agricultural University (23.15°N 113.35°E). The test was conducted under the conditions of sunny weather, no wind, and 28°C temperature. Each time, 200 balls were placed in the material bucket, and five steering speeds of 6 m/s, 9 m/s, 12 m/s, 15 m/s and 18 m/s are set up through the delivery device control system. Three repeated releasing experiments are conducted respectively, and the number of balls released and the number of blocked and missed balls within two minutes were recorded, as shown in Table 2 .

As can be seen from Table 2 , when the steering speed is 6 r/min, 9 r/min, 12 r/min, 15 r/min and 18 r/min, the device’s accuracy rate for releasing within 2 minutes reaches over 97.69%. Moreover, under these five speeds, all loaded balls are released without any issues of stuck balls or missed releases, indicating that the mechanical structure of this device is stable and reliable in releasing balls.

The trials conducted for the accuracy of system deployment in flight linkage mode includes two flight trajectories, each 80m long and 10m apart, with the UAV flight altitude set at 5m, UAV speeds are set to 3 m/s, 5 m/s, 7 m/s, and 9 m/s (Zhan et al., 2021). After each trial was completed, a tape measure was used to manually measure the distance between two adjacent balls on the same flight route (excluding acceleration and deceleration intervals). The actual landing site spacing data of the trichogramma balls under the four UAV flight speeds were recorded, and A One-way ANOVA (α = 0.05) was conducted using IBM SPSS (26.0) software. This study explored the impact of changes in UAV flight speed on the distance between the actual deployments of trichogramma balls, obtaining data in Table 3 (Ding et al., 2021; Fang et al., 2022; Wang et al., 2022).

As can be seen from Table 3 , when the test level is α = 0.05, the F test falls in the acceptance range, sig. = 0.874 > 0.05, which indicates that the change in UAV flight speed do not have a significant impact on the actual landing site spacing between adjacent balls. Moreover, as shown in Table 3 , the average spacing between adjacent balls is between 10.0 m and 10.5 m at the above four flight speeds. This proves that UAV’s flight control can accurately coordinate with the delivery device to drop balls at the set spacing, and the release process is accurate and reliable.

The natural crop fields in our country often present complex boundaries, as shown in Figure 6 . If the red lines are used to indicate the shape of the complex boundary of the field in the figure, and the yellow lines are used to indicate the basic polygons in the field, it can be seen that except for the largest rectangular field in the center of the field, any irregular field at the boundary position can be deconstructed from rectangular, trapezoidal, and stepped fields. The operational quality at the boundary position is an important factor affecting the overall operational quality of the entire field.

To explore the influence of rectangular, trapezoidal and stepped boundary fields on the overall field operational quality, a field operation test of the trichogramma balls delivery system was carried out, as shown in Figure 7 . The test site was located in a pineapple field at Guangken Agricultural Machinery in Zhanjiang, Guangdong (21.3°N 110.3°E). The rectangular, trapezoidal, and stepped fields with an area of approximately 8 acres were selected. The actual field area and boundary size of the three test plots were measured and marked on Figure 8 , where the white line frame represented the boundary of the operational area, the red line represented the flight route of the UAV, the green circle marked with S represented the starting point of the UAV for releasing the balls, and the red circle marked with F represented the ending point of the UAV (Cao et al., 2020).

A trichogramma ball stores approximately 2000 trichogramma eggs, and the range of protection after the hatching of the contained trichogramma eggs is a circle with a diameter of 14.9 m centred on the trichogramma ball, as shown in the green circle in Figure 9 . To achieve full coverage of the UAV operational area, the spacing L of the released balls should be less than or equal to 10.5 m , ( d / 2 ) as shown in Figure 9 , so the flight path spacing is set to 10.5 m. The flight speed is set to 7 m/s. After the test flight is completed, the mobile station is removed from the UAV and installed on a handheld fixture to make a ball landing point data sampler. The locations of the dropped balls were sampled one by one in the pineapple field, as shown in Figure 10 .

In order to evaluate the actual field operational quality of the trichogramma balls UAV delivery system in linkage mode, an actual landing map was drawn based on the actual operational route and the landing point position, that is, the actual operational status was drawn in Auto CAD (2022). The target area S ₀, effective coverage area S ₁, uncovered area S ₂, ineffective coverage area S ₃, repetitive covered area S ₄, and total coverage area S_n are defined as shown in Figure 11 , and the operational performance indicators, effective coverage rate η ₁, uncovered rate η ₂, ineffective coverage rate η₃, utilization rate of balls η ₄, and repetition rate of balls η ₅, are also defined as follows.

The effective coverage rate η ₁ meets Equation 6:

The uncover rate η ₂ meets Equation 7:

The ineffective coverage rate η ₃ meets Equation 8:

The utilization rate of balls η ₄ meets Equation 9:

The repetition rate of balls η ₅ meets Equation 10:

The system operational indicators η ₁,η ₂,η ₃,η ₄,η ₅, all affect the overall operational quality of the system, but the influence degrees of each are different, so the influence of each indicator needs to be reflected by weights. The entropy weight method is an objective weighting method for determining the weights of evaluation indicators. This method is based on the current sample data to obtain the weight of the indicators by statistics, avoiding deviations caused by human factors. The process of evaluating the overall operational quality using the entropy weight method is as follows (Qin et al., 2023):

1) Construct an evaluation indicator matrix X = ( x i j ) m n , i = 1 , 2 , ⋯ , m ; j = 1 , 2 , ⋯ , n . where x_ij represents the value of j-th indicator of the i-th sample. m represents the number of field types, and n represents the number of indicators.

2) Standardize the indicators. If the indicator has a positive effect (the larger, the better), the standardization method is as follows.

If the indicator has a negative effect (the smaller, the better), the standardization method is as follows.

Where x i j ' is the standardized indicator value and represents the j-th standard indicator value of the i-th sample.

3) Use the translation method to handle special situations that may occur after standardization.

4) Calculate the proportion matrix P = (p_ij ) _mn , where p_ij represents the proportion of the j-th indicator value of the i-th sample, and take it as the probability when calculating the information entropy.

5) Calculate the information entropy matrix of the evaluation indicators E = (e_j ). e_j represents the information entropy of the j-th indicator.

Where I i j = − l n p i j represents the information of the j-th indicator value of the i-th sample. The larger p_ij is, the smaller the uncertainty is, and the less information it contains. The maximum value of ∑ i = 1 m p i j I i j is lnm, so dividing ∑ i = 1 m p i j I i j by a constant lnm to make e_j falls between [0,1].

6) Calculate the evaluation matrix W = (w_j ). w_j represents the weight of the j-th indicator.

Where g j = 1 − e j represents the information utility of the j-th indicator value. The larger the information entropy of the indicator, the less information it carries, and the smaller the information utility.

7) According to the objective weights obtained using the entropy weight method, the comprehensive score is calculated using the linear weighting method for overall operational quality evaluation.

In the ideal operational state, without considering factors such as flight route deviation, the ideal landing point diagram of the trichogramma ball is obtained. Using the center of the trichogramma ball’s ideal landing point as the center of a circle d = 14.9 m, a schematic diagram of the coverage of the balls in three types of fields is drawn as shown in Figures 12A, C, E . The data is analyzed to obtain the ideal operational data in Table 4 .

In the actual experimental field, the lush foliage of pineapple branches and the small size of the trichogramma ball make it very easy for falling balls to go unnoticed, resulting in a lack of actual landing points or redundant sampling due to previous missed detection. To avoid these situations affecting the experimental data, an average spacing is used as a reference, for obvious redundant landing points along the flight path, ideal ball landing points are used as reference points for deletion. for obvious missing points, including obvious missing points at the beginning or end of the route, the data is filled at an average spacing from the nearby reference point(the nearby actual landing point). Then With the landing point as the center of the circle d = 14.9m, a schematic diagram of the effective coverage area is drawn, as shown in Figure 13 , which is simplified to Figures 12B, D, F . The actual operational parameters and performance indicators are also shown in Table 4 . In terms of the uniqueness of the test results, as can be seen from Figures 12A, C, E , to ensure full coverage of the target area in rectangular, trapezoidal, and stepped fields, the flight path and release points are unique. Therefore, in the operation, the starting point of the UAV to begin to drop the trichogramma balls needs to be marked in advance in the flight control system.

From Table 4 , it can be seen that in actual delivery operations, only the number of balls dropped in trapezoidal fields (50) reaches the ideal number of delivery operations (50), while rectangular (45) and stepped (37) fields do not achieve the same ideal number of delivery operations (50, 44), which will have an impact on the operational effect. In actual operations, the coverage rate of balls dropped can reach 97%, and the delivery area per unit time can reach 4158 m²/min.

From the data in Table 4 , the comparison chart of the five indicators obtained from three different boundary fields under ideal and actual operating conditions is shown in Figures 14 and 15 , respectively. From Figures 14 and 15 , it can be seen that in terms of the effective coverage rate η ₁, in ideal situations, rectangle η ₁ > trapezoidal η ₁ > stepped η ₁; in actual situations, trapezoidal η ₁ > rectangle η ₁ > stepped η ₁, stepped η ₁ is always the smallest. The main reason is that the height of the ladder at the step is not up to the height standard of two trichogramma balls, when planning the path, it can only be covered by one trichogramma balls delivery route, and the number of pitches is minimum, which leads to the increase of the uncovered area of the operation and the decrease of the effective coverage rate η ₁. For rectangular and trapezoidal fields, under ideal operational conditions, all four sides of the rectangular field are regular right-angled sides (90°), the positioning of the pitch points is planned so that the trichogramma balls can cover all routes and also cover all target area. For the trapezoidal field, at its hypotenuse, although the planned pitch point can cover all routes, it does not consider the difficult-to-cover gaps between upper and lower flight routes caused by the oblique edges, therefore, in the ideal situations, rectangle η ₁ > trapezoidal η ₁. In actual situations, trapezoidal η ₁ > rectangle η ₁, and compared to the ideal situations, the overall η ₁ declined. The main reason for this is that during actual operations, deviations in drone flight paths and the landing positions of the trichogramma balls lead to a decline in the overall coverage effects. It is also found that during actual operations, the largest uncovered area is at the edges and corners of the field.

Theoretically, the relationship between the field edge angle θ and the uncovered area S at the edge corners satisfies Equation 18, and its relationship curve is shown in Figure 16 (when R=1). The schematic diagram is shown in Figure 17 .

As shown in Figure 16 , with the increase of θ, the uncovered area decreases, and the circular area covered by the ball increasingly matches the edge boundaries. Relatively speaking, when θ > 90° ( Figure 17A ), the circular area covered by the ball is more fit with the boundary. The larger θ is, the higher the fit and the smaller the uncovered area are. When θ = 90° ( Figure 17B ), the circular area covered by the ball is difficult to fit with the boundary, and the uncovered area is larger than that when θ > 90°. When θ < 90° ( Figure 17C ), the circular area covered by the ball is the most difficult to fit with the boundary, and the uncovered area is larger than that when θ = 90°. Since the extension of the circular area covered by the balls beyond the field boundary does not bring about any damage similar to that after pesticide spraying, it only leads to an increase in the ineffective coverage area of the trichogramma balls.

Therefore, considering that the distance between the balls release point and the vertex of the edge and corner should be equal to that between the balls release point and vertex of edge and corner in Figure 17A ), both are L ( Figures 17A, D ), so as to reduce the large uncovered area caused in Figure 17C . Therefore, in actual operations, this system can easily achieve a higher effective coverage rate η ₁ in fields with θ > 90°, and the effective coverage rate η ₁ is the lowest in stepped fields due to they have more right-angle edges.

Due to the fact that the sum of effective coverage rate η ₁ and uncover rate η ₂ is 1, the changes of η ₁ and η ₂ in the three types of fields exhibit an inverse synchronization relationship. Therefore, when quantifying the effectiveness of the operation, one of the changes is selected as an evaluation indicator. In this operational quality evaluation system, the effective coverage rate η ₁ is chosen as the system operational effect evaluation indicator.

In terms of the invalid coverage rate η ₃, it is clear that the lower the η ₃, the better the operation. From Figures 14 and 15 , it can be seen that ideally, the stepped η ₃< rectangle η ₃< trapezoidal η ₃. Actually, rectangle η ₃<stepped η ₃< trapezoidal η ₃,with the trapezoid always being the largest, This is mainly due to that in order to improve the effective coverage area, the trapezoidal field adds the dropping point of the balls at the hypotenuse, thereby increasing the ineffective coverage area outside the target area. In ideal situations, stepped η ₃ < rectangle η ₃, mainly because the stepped field’s step height is less than the height required to put two balls, therefore, only one row of delivery points is planned, so that the invalid coverage area S₃ is reduced. In actual situations, the rectangle η ₃ < stepped η ₃, mainly due to the deviation of the route and the position of the landing point at the right angle turning point, and at the right angle corners, this deviation is more pronounced, such as the stepped shape has multiple right angle corners, resulting in a greater pitch deviation and resulting in a smaller effective coverage area and a larger ineffective coverage area. However, ineffective coverage for the balls delivery operation does not lead to pesticide drift into invalid coverage areas as when spraying pesticides, so the influence of η ₃ can be weakened or even not considered in the evaluation process. The effectiveness of ineffective coverage is indirectly reflected by the utilization rate η ₄, obviously, the higher the better. Under ideal and actual operating conditions, all are rectangular η ₄ > trapezoidal η ₄ > stepped η ₄, but in terms of the balls repetition rate η ₅, obviously the lower the better. Under ideal and actual operating conditions, all are stepped η ₅ < trapezoidal η ₅ < rectangular η ₅, so it is difficult to simply judge which type of field is the best from the trichogramma balls utilization effect.

To quantify the differences in operational quality among three shapes of fields in ideal and actual delivery operations, we set up a comprehensive evaluation system for operational quality, It quantitatively analyzes from two aspects: the effectiveness of field operation U ₁ and the utilization effect of trichogramma balls U ₂. The aforementioned evaluation indicators are divided into two levels. The effective coverage rate η ₁ reflects the system operational effect U ₁, while the balls utilization rate η ₄ and repetition rate η ₅ reflect the trichogramma balls utilization effect U ₂. The specific grading is shown in Table 5 .

Firstly, the entropy weight method is used to determine the secondary indicator weights of η ₄ and η ₅ to evaluate the utilization effect of trichogramma balls. The trichogramma balls utilization rate η ₄ is a positive effect indicator, the larger the indicator, the better the utilization effect of balls, which can be directly standardized using Equation 8. The repetition rate of the balls η ₅ is a negative effect indicator, the larger the indicator, the worse the utilization effect of balls, which should be converted into a positive effect indicator using Equation 9 to obtain the standardized matrix X ₁. Then, after translation processing using Equation 10, the proportion matrix P ₁ of η ₄, η ₅ is calculated according to Equation 11 for evaluating different fields, and the information entropy matrix E ₁ of η ₄, η ₅ is calculated according to Equation 12, the weight matrix W ₁ of η ₄, η ₅ is calculated according to Equation 13. The linear weighting method of Equation 14 is used to calculate the data of trichogramma balls utilization effect U ₂, and then the same method is used to determine the X ₂, P ₂, E ₂, and W ₂ of the two primary indicators U ₁, U ₂,The specific data obtained under ideal and actual conditions are as follows, and the indicator weights are shown in Table 5 . The comprehensive field operational scores of three types of field blocks under ideal and actual conditions are obtained by using the linear weighting method with weights and standardized sample values, and the data are shown in Figure 18 .

From Figure 18 , it can be seen that from the perspective of system field comprehensive operational quality evaluation, under ideal operational conditions, the comprehensive operational quality score F of rectangular fields is the highest, reaching 1.000, while under actual operational conditions, the comprehensive operational quality score F of trapezoidal fields is the highest, at 0.8866. This indicates that in actual operations, if any complex boundary natural fields are decomposed into several rectangular, trapezoidal, or stepped small fields, the more trapezoidal small fields, the higher the comprehensive operational quality of this complex boundary field.