Adaptive Sliding Mode Path Tracking Control of Unmanned Rice Transplanter

Abstract

To decrease the impact of uncertainty disturbance such as sideslip from the field environment on the path tracking control accuracy of an unmanned rice transplanter, a path tracking method for an autonomous rice transplanter based on an adaptive sliding mode variable structure control was proposed. A radial basis function (RBF) neural network, which can precisely approximate arbitrary nonlinear function, was used for parameter auto-tuning on-line. The sliding surface was built by a combination of parameter auto-tuning and the power approach law, and thereafter an adaptive sliding controller was designed. Based on theoretical and simulation analysis, the performance of the proposed method was evaluated by field tests. After the appropriate hardware modification, the high-speed transplanter FLW 2ZG-6DM was adapted as a test platform in this study. The contribution of this study is providing an adaptive sliding mode path tracking control strategy in the face of the uncertainty influenced by the changeable slippery paddy soil environment in the actual operation process of the unmanned transplanter. The experimental results demonstrated that: compared to traditional sliding control methods, the maximum lateral deviation was degraded from 17.5 cm to 9.3 cm and the average of absolute lateral deviation was degraded from 9.1 cm to 3.2 cm. The maximum heading deviation was dropped from 46.7° to 3.1°, and the average absolute heading deviation from 10.7° to 1.3°. The proposed control method not only alleviated the system chattering caused by uncertain terms and environmental interference but also improved the path tracking performance of the autonomous rice transplanter. The results show that the designed control system provided good stability and reliability under the actual rice field conditions.

1. Introduction

Due to the high labor cost, the shortage of rural labor force, and the poor straightness accuracy of the seedling row, unmanned transplanters have gradually become a significantly sought-after in promoting the mechanized transplanting of rice in China. The path tracking control performance is the key to determining the straightness of transplanting [1,2,3].

Scholars, both domestically and abroad, have carried out relevant studies on path tracking control algorithms based on fuzzy control [4,5], the pure tracking model [2,6,7,8], sliding mode control [9,10], and other methods. A fuzzy adaptive pure tracking algorithm for agricultural machinery was proposed [11] which improved the tracking accuracy of the model path. However, the control laws were difficult to establish and thus increased the control difficulty. To enhance the adaptability of the navigation control system, a pure tracking control method for tractor navigation was developed based on the SVR reverse model; it was difficult to make real-time and dynamic adjustments for the tracking error because of complex model construction and sample training [12]. An improved Stanley controller was proposed to improve the path tracking the performance of autonomous tractors and the parameters of the controller were optimized based on a multiple-population genetic algorithm [13]. The effectiveness and advantages were evaluated by simulation. A control strategy based on nonsingular fast terminal sliding mode control with a finite time disturbance observer was presented to improve the trajectory tracking ability of the autonomous agricultural tractor [14]. However, the effectiveness of the designed control algorithm was not verified by field tests. Some of the state-of-the-art deep learning models have been used in agricultural applications. Deep learning methods were used in uncrewed vehicles to detect fruits [15,16,17]. A modified YOLOv3 model, called YOLO-Tomato models, was established to detect tomatoes in challenging environmental conditions [16]. The real-time growth stage detection model for a high degree of occultation was developed based on DenseNet-fused YOLOv4 [17]. The deep learning can be used for parameter optimization of control systems. In order to improve the trajectory tracking performance of autonomous orchard vehicles, a model-based control algorithm was presented for wheel slip compensation [18]. The model predictive control algorithm was designed to improve trajectory tracking performance, and nonlinear least squares frequency domain system identification was applied to identify the yaw dynamics [19].

Sliding mode control (SMC) has the advantages of fast response, insensitivity to parameter changes and disturbances, no online system identification, and simple physical implementation, which has widely concerned by scholars from all over the world. However, the chattering problem of sliding mode control in practical systems is a prominent obstacle. A robust controller based on backstepping sliding mode control for a 4WS/4WD agricultural robotic vehicle was designed against system uncertainties [20]. A layered multi-loop powerful control architecture is presented for an electro-hydraulic coupling system, and a sliding mode controller was applied to consider the parameter uncertainties and disturbances from the system [21]. Although an adaptive steering control strategy was proposed for varying yaw rate properties of a farm tractor, the performance is hardly validated by experimental tests. To weaken chattering and improve the dynamic performance of approaching movement by adopting various reaching laws, a significant number of studies was carried out. A path tracking control strategy for the tracked robot was proposed based on a sliding mode variable structure algorithm [22], and a good control effect on path tracking was demonstrated by simulation. A fuzzy sliding mode control algorithm was designed based on inverse control and good robustness was verified by simulation results [23]. However, these two sliding mode control methods have not taken into account the influence of uncertain disturbance such as sideslip caused by the variation of the working environment and have not been verified by actual field tests. Moreover, although widespread applications of sliding mode control algorithms including improved algorithms have been found, most research has been limited to computer simulations and constrained real-time in practical working processes.

Because of powerful approximation properties, neural networks (NN) and fuzzy systems were applied to modeling the uncertainties and external disturbances in the system or approaching the switching part of the controller by making discontinuous control signals continuous and thus effectively reducing chattering. A novel neural network sliding mode control method is proposed. The neural network is used to estimate the nonlinear part, the uncertain part, and the unknown disturbance of the linear system. An equivalent control based on a neural network is realized, and chattering is effectively eliminated [24]. Two neural networks are used to approximate the equivalent sliding mode control part and the switching sliding mode control part, respectively. The chattering of the controller is eliminated effectively without an object model [25]. Compared with BP-NN, RBF-NN has good generalization ability and a simple network structure, which can avoid unnecessary and lengthy calculations and approximate any nonlinear function in a compact set at arbitrary precision. Using the approximation ability of NN, a sliding mode controller based on an RBF-NN is proposed. The switching function s is used as the network input, and the controller is entirely realized by the continuous RBF (radius basis function) function, which eliminates the switching term and chattering [26].

To make up for the shortcomings of the above algorithms and realize the precise control of the expected rotation angle and the travel speed, an adaptive sliding mode variable structure path tracking control algorithm based on the power approach law and an RBF-NN was proposed in this study, aiming at overcoming the influence of uncertainty from the changeable slippery paddy soil environment in the actual operation process of the unmanned transplanter. The reliability of the model and the feasibility of the method are verified by the theoretical analysis, model simulation, and field tests.

2. System Hardware Modification

2.1. Steering Control

The hydraulic power steering device of the existing FLW 2ZG-6DM high-speed transplanter is installed as a whole, and its automatic steering was achieved by a parallel oil circuit [27,28]. The automatic steering control only can be realized by adding an electric steering wheel to the original steering mechanism and controlling the motor to simulate the manual operation of the steering wheel. The AF300 electric steering wheel, as shown in Figure 1, was adopted (Shanghai LIANSHI Navigation Co., Shanghai, China). The specific parameters of the electric steering wheel are shown in Table 1.

To ensure accuracy, long-term operation stability, and reliable performance during driving operation, the fixed bracket (Figure 2) is designed and installed under the front axle arm of the rice transplanter. The connecting rod and the front wheel steering shaft constituted a parallel four-bar mechanism, and the angle sensor was installed at the wheel steering trapezoid, which provided accurate angle data for the steering control of the transplanter. Considering the cost performance, volume, and other factors, the DWQT-RS485-G/J angle sensor (Beijing Tianhai Technology Co., Beijing, China) was selected, and the specific parameters are shown in Table 2.

2.2. Travel Speed Control

As one of the essential control units of the traveling speed control, the accelerator pedal mechanism is the key to ensuring the stability of the operating speed. The original mechanical accelerator pedal of the rice transplanter is transformed into an electric push rod pull accelerator pedal. The corresponding relationship between displacement and velocity is established through the real-time displacement information of the electric push rod. According to measurements, the actual pulling force of the accelerator pedal is about 50 N, and the displacement of the stay wire is 95 mm. Considering the water-resistance of the operating equipment under the paddy field environment, a DC electric push rod with position feedback (Taiwan, China, LD3-12-20-50-IP65-POT) was selected. Its structure and installation are shown in Figure 3, and the main performance parameters are shown in Table 3.

2.3. Location Information Collection

During transplanting operations, to achieve continuous and accurate navigation, reduce accumulated positioning error, and ensure the stability of the positioning system, the combined navigation of BEIDOU and INS (inertial navigation system) [29] was adopted. A HUA XIN full band antenna, supporting C201 receiver, and a navigation reference station were selected as the navigation module. The RTK horizontal positioning accuracy is ±2 cm, and the data update rate is set at 5 Hz. The attitude sensor is a micro inertial sensor MTI-30 model manufactured by the XENS company of the Netherlands. The navigation reference station and attitude sensor are shown in Figure 4, and the performance parameters of the attitude sensor are shown in Table 4.

2.4. Main Controller

The main board of the series STM32F103 is used as the central controller to realize the functions of position information collection, angle information collection, electric steering wheel control, and travel control. The controller has 64KB SRAM, 512KB FLASH, five serial ports, and 112 general I/O ports. It can meet the data processing requirements of the intelligent control system. The system block diagram is shown in Figure 5. The navigation module and angle transducer are attached to the master controller by two groups of the RS485 interface. The navigation module provides position and gesture data such as lateral deviation, heading deviation, and vehicle speed for the master controller at a 10 Hz frequency. An angle transducer is employed to sense the front steering wheel angle in real-time. The master controller is connected to the attitude sensor by RS485 interface, which manages the yaw angle, pitch, and roll angles from the attitude sensor at a 10 Hz frequency. The electric steering wheel is attached to the controller through the RS232 interface and is used to drive the front wheel of the rice transplanter. A linear actuator with displacement sensor, attached to the controller by A/D and digital output interfaces and assembled in the controller, is employed to adjust vehicle speed. Moreover, the touch screen, which connects to the controller by the RS232 interface, is applied to display data, and set control parameters.

3. Algorithm of Path Tracking Control System

3.1. Kinematic Modeling and Theoretical Analysis of Rice Transplanter

Take the transplanter as the controlled object and establish the relative kinematic model between the transplanter and the path as shown in Figure 6. The kinematic model can be expressed as [30].

(1)$\{\begin{array}{l}\dot{l}=\frac{vcos\rho }{1-c\left(l\right)d}\\ \dot{d}=vsin\rho \\ \dot{\rho }=v\left(\frac{tan\theta }{D_L}-\frac{c\left(l\right)cos\rho }{1-c\left(l\right)d}\right)\end{array}$

where $d$, $D_L$ and $l$ denote lateral deviation, wheel base of transplanter and path tracking curvature, respectively; $\rho ={\phi }_c-\phi$, $\theta$ denotes the heading deviation and steering wheel angle, respectively; $c(l)$ and $v$ are the path arc length and speed of the rice transplanter, respectively.

Let $z=\left[z_1,z_2{]}^T=\right[d,\rho {]}^T$ and calculate the derivative of $z$ respect to $l$, the Equation (1) can be rewritten as

(2)$\dot{z}=f\left(z\right)+g\left(z\right)\frac{\mathit{tan}\theta }{D_L}$

where

$$\begin{gathered} f\left(z\right)=\left[\begin{array}{c}tan{z}_2\left(1-z_{1}c\left(l\right)\right)\\ -c\left(l\right)\end{array}\right] \\ g\left(z\right)=\left[\begin{array}{c}0\\ sec{z}_2\left(1-z_{1}c\left(l\right)\right)\end{array}\right] \end{gathered}$$

To ensure nonsingular of Equation (4), the following two conditions must be met:

$1-c\left(l\right)z_1\ne 0, z_2\ne k\pi +\frac{\pi }{2}\left(k=0,1,2\cdots \right)$

The path curvature tracked by rice transplanters is generally not very large, $1/c\left(l\right)\gg z_1$; during operation, the rice transplanter travels along the direction of the path and thus $z_2<\frac{\pi }{2}.$ Therefore, the above conditions are easily met in the actual transplanting process.

Thus, Equation (2) can be expressed by the matrix form

(3)$\dot{z}=\left[\begin{array}{c}\dot{d}\\ \dot{\rho }\end{array}\right]=\left[\begin{array}{l}v\mathit{sin}\rho \\ -\dot{l}c\left(l\right)+v\frac{\mathit{tan}\theta }{D_L}\end{array}\right]$

According to dynamic feedback linearization theory, Equation (4) can be obtained by applying state transformation and input transformation to Equation (3) [31],

(4)$\{\begin{array}{l}{e}_1=z_1\\ e_2=\nabla e_{1}f\left(z\right)=\left(1-z_{1}c\left(l\right)\right)\mathit{tan}{z}_2\\ u=\phi \left(z,\frac{\mathit{tan}\theta }{D_L}\right)={\mathit{sec}}^3{e}_2{(1-z_{1}c\left(l\right))}^2\frac{\mathit{tan}\theta }{D_L}\\ +\left(z_{1}c\left(l\right)-1\right)c\left(l\right)\left({\mathit{tan}}^2{z}_2+{\mathit{sec}}^2{z}_2\right)\end{array}$

According to Equations (3) and (4), the controllable standard type can be expressed as

(5)$\left[\begin{array}{c}{\dot{e}}_1\\ {\dot{e}}_2\end{array}\right]=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]\left[\begin{array}{c}{e}_1\\ e_2\end{array}\right]+\left[\begin{array}{c}0\\ 1\end{array}\right]u$

The complexity and spatial variability of the operating environment brings great uncertainty to the steady-state performance of the vehicle yaw rate [32]. The interference term $\left|\gamma \right|\le T$ ($T$) is introduced to represent this uncertain disturbance. Thus, the Equation (5) can be rewritten as

(6)$\left[\begin{array}{c}{\dot{e}}_1\\ {\dot{e}}_2\end{array}\right]=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]\left[\begin{array}{c}{e}_1\\ e_2\end{array}\right]+\left[\begin{array}{c}0\\ 1\end{array}\right]u+\left[\begin{array}{c}0\\ 1\end{array}\right]\Delta \eta$

where

$\mathsf{\Delta }\eta =\frac{{(1-dc\left(l\right))}^3}{v{\mathit{cos}}^3(\rho )}\gamma$

It can be seen from Equations (5) and (6) that the path tracking ability of the model under the conditions of uncertain interference is effectively improved by eliminating the influence of time and speed on the system.

However, under the conditions of uncertain disturbance, the path tracking error of the controlled object will change with an amplitude of $\mathsf{\Delta }\eta$. If the control of the influence of uncertain disturbances such as sideslip are realized, system chattering will occur in the process of path tracking, which will affect the control of the system. Therefore, to decrease or eliminate system chatting, sliding mode control is used to improve the convergence speed of the system, and, then, the RBF neural network is used to approach the disturbance adaptively and ensure the stability and convergence of the system.

3.2. Design and Analysis for Adaptive Sliding Mode Controller

The amplitude of the uncertain term $\mathsf{\Delta }\eta$ in Equation (6) varies greatly with the path tracking error. If a large interference boundary is assumed in robust controller design, the chattering amount will increased and the control results will be too conservative. In order to decrease the lateral and heading deviations and improve the adaptive ability of the control system, an adaptive sliding mode path tracking control algorithm is presented based on the power approach rate (PAR) and RBF. The adaptive estimation of $\mathsf{\Delta }\eta$ is achieved by RBF, and PAR is used to reduce or eliminate the chattering. The PAR is expressed as

(7)$\dot{\sigma }=-\epsilon |\sigma {|}^p\mathit{sgn}\sigma -k\sigma$

where

$0<p<1$, $\epsilon >0$, $k>0$

(8)$\sigma =\mu e_1+e_2$

where

$\mu >0$

By differentiation of $l$ and combining Equations (6) and (7) as

(9)$\dot{\sigma }=\mu {\dot{e}}_1+{\dot{e}}_2=\mu {\dot{e}}_1+u+\Delta \eta =-\epsilon |\sigma {|}^p\mathit{sgn}\sigma -k\sigma$

Let the control rate $\mathsf{\Delta }\eta =0$ be

(10)$u=-\mu {\dot{e}}_1-\epsilon |\sigma {|}^p\mathit{sgn}\sigma -k\sigma$

The stability analysis is carried out by using the Lyapunov function $V={\sigma }^2/2$ as

(11)$\dot{V}=\sigma \dot{\sigma }\le -\epsilon |\sigma {|}^{p+1}-k{\sigma }^2+\left|\sigma \right|\mathsf{\Phi }$

where

$\mathsf{\Phi }\ge \left|\mathsf{\Delta }\eta \right|$

According to Equation (11),

(12)$\dot{V}+k{\sigma }^2=\dot{V}+2kV\le -\epsilon |\sigma {|}^{p+1}+\left|\sigma \right|T$

If $\left|\sigma \right|\ge {(T/\epsilon )}^{\frac{1}{p}}$, $\dot{V}+k{\sigma }^2\le 0$ exists. Thus, there is an interference stability bound of ${(T/\epsilon )}^{\frac{1}{p}}$, which can make the system converge to the region $\left|\sigma \right|\le {(T/\epsilon )}^{\frac{1}{p}}$ stably in a limited distance. This implies that an interference stability bound ${(T/\epsilon )}^{\frac{1}{p}}$ exists. In order to eliminate this interference stability bound, the online estimation of $\mathsf{\Delta }\eta$ is performed by RBF (Figure 7) in this study. The corresponding input and output of RBF is $e={[e_1,e_2]}^T$ and the control rate is $\mathsf{\Delta }\eta$. The 2-5-1 neural network architecture is determined by trial and error. Mini-batch gradient descent is employed, and mini-batch size is set to 2048 by trial and error. The number of epochs is 10. To accelerate learning in the early stage of algorithm optimization and avoid large fluctuations in the later period, the learning rate is adjusted from 0.9 to 0.2. The detailed structure diagram is as follows.

The network algorithm used to eliminate the interference stability bound can be described as

(13)$h_j=\mathit{exp}(\frac{-|\left|e-c_j\right|{|}^2}{2b_j^2})$

where, $h_j$ denotes the jth neuron output of the network hidden layer, j is the jth node of the network hidden layer (j = 1, 2…5). $c_j$ is the center vector value of the jth hidden layer and $b_j$ is the base width parameter of the j hidden layer.

(14)$\mathsf{\Delta }\eta =w^{*}{}^{T}H$

where $w^{*}$ denotes the ideal weight, $H={[h_j]}^T$ is the output of the Gaussian basis function. The estimation value of $\mathsf{\Delta }\eta$ can be written as

(15)$\mathsf{\Delta }\widehat{\eta }={\widehat{w}}^{T}H$

where $\widehat{w}$ is the actual weight of the network.

(16)$\mathsf{\Delta }\eta -\mathsf{\Delta }\widehat{\eta }=w^{*}{}^{T}H-{\widehat{w}}^{T}H=-{\tilde{w}}^{T}H$

where $\tilde{w}=\widehat{w}-w^{*}$. Substituting $\Delta \widehat{\eta }$ for $\Delta \eta$, the developed control rate can be presented as

(17)$u=-\mu {\dot{e}}_1-\epsilon |\sigma {|}^p\mathit{sgn}\sigma -k\sigma -{\widehat{w}}^{T}H$

Lyapunov function is defined as $V=\frac{1}{2}{\sigma }^2+\frac{1}{2\lambda }{\tilde{w}}^T\tilde{w}$ and λ is adjustment parameter and $\lambda >0$.

(18)$\begin{array}{ll}\dot{V}& =\sigma \dot{\sigma }+\frac{1}{\lambda }{\tilde{w}}^T\tilde{w}=\sigma \left(\Delta \eta -\Delta \widehat{\eta }-\epsilon |\sigma {|}^{p}sgn\sigma -k\sigma \right)+\frac{1}{\lambda }{\tilde{w}}^T\dot{\tilde{w}}\\ & =\sigma (-{\tilde{w}}^{T}H-\epsilon |\sigma {|}^{p}sgn\sigma -k\sigma )+\frac{1}{\lambda }{\tilde{w}}^T\dot{\tilde{w}}=-\epsilon |\sigma {|}^{p+1}-k{\sigma }^2+{\tilde{w}}^T(\frac{1}{\lambda }\dot{\tilde{w}}-\sigma H)\end{array}$

The path tracking error converges to zero when the adaptive rate of RBF is selected as $\dot{\widehat{w}}=\lambda \sigma H$ and $\dot{V}\le 0$. Supposing $\beta$ is the estimation error in the network, thus $\mathsf{\Delta }\eta =w^{*T}H+\beta$ ($\left|\beta \right|\le E$ and $E$ is the upper bound of the estimation error). Finally, the tracking error of the system converges steadily to ${(E/\epsilon )}^{\frac{1}{p}}$. From Equation (11), it can be seen that ${(E/\epsilon )}^{\frac{1}{p}}$≪${(T/\epsilon )}^{\frac{1}{p}}$, which can meet the tracking error requirements of the rice transplanter. From the above analysis, the RBF neural network has good robustness to approach the interference stability bound. In other words, when the system is disturbed by uncertainty, the tracking path of the transplanter can still move along the sliding surface towards the balance point, and the system is asymptotically stable.

3.3. Simulation Verification and Analysis

In order to evaluate the effectiveness of the proposed path tracking control strategy for the rice transplanter, the simulation was conducted by MATLAB software. The adaptive rate, neural network, wheelbase of the transplanter, and other relevant parameters are set. The specific information is as follows: wheelbase $D_L$ = 1040 mm, approach law coefficient $\mathit{\epsilon }$ = 1.2, $k$ = 0.8, $p$ = 0.5, linear sliding surface coefficient $\mathit{\mu }$ = 8, adaptive rate coefficient $\lambda$ = 2000, neural network coefficient $b_j$ = 2, $c_j$ = (−0.1, −0.5, 0, 0.5, 1).

In the complex nonlinear system environment, the adaptive sliding mode path tracking control is used to simulate the lateral deviation and heading deviation in the range of 10 m. The simulation results are shown in Figure 8.

From Figure 8, under real field conditions with uncertain disturbance, it can be found that the lateral error converges from a large deviation value to the zero point after about 0.6 m. Meanwhile, the heading deviation converges to the zero point after approximately 0.5 m, and the system gradually enters the steady state. When the adaptive sliding mode path tracking control method is applied to approach uncertain disturbances such as vehicle sideslip, it can effectively improve the steady-state performance of the system and reduce the influence of chattering caused by the system track reaching the switching surface on the system. That is to say, the adaptive sliding mode path tracking control method can effectively eliminate the uncertain disturbances and chattering in the actual control process under the influence of interference, which ensures the accuracy of path tracking and the stability of long-term operation.

4. Field Test and Data Analysis

4.1. Field Experiment

The performance of the proposed adaptive sliding mode path tracking control algorithm is evaluated by comparing with a traditional sliding mode control algorithm, the paddy field tests are carried out in the grain industrial park of XINGHUA City, JIANGSU Province. The test platform and field test are shown in Figure 9.

A 100 m × 30 m rectangular field was selected for the experiment. The unevenness of paddy soil was less than 5 cm. The mud foot depth in the field is about 25 cm. During paddy field experiments, the vehicle track with depth about 25 cm was generated after the vehicle travelled across the planned paths. If the vehicle runs along the same path many times, the mud foot depth will become deeper and deeper. Due to the influence of sideslip and the restriction of the driving ability of the electric steering wheel, in the next round, it will be difficult for the vehicle to escape the track generated in the previous round of testing. Hence, four groups of field tests with different paths were carried out to validate effectiveness. Considering effect of the vehicle track of the previous trial on tracking performance of the current run, the traditional sliding control and proposed control algorithms were used alternately during each group of tests. For each group of tests, the vehicle followed the same planned paths. During the group 1 and 3 tests, the traditional sliding mode control was applied first and after the proposed control algorithms in this study were run. For groups 2 and 4, the running sequence of the two control algorithms was the opposite. After four sets of tests, the lateral and heading errors were averaged and the corresponding path tracking results from the two control algorithms were presented in Figure 10 and Figure 11, respectively.

The four longitude and latitude coordinates of the field vertices were collected by the navigation module and transformed into the current field coordinates. According to the operation width of the rice transplanter, the field operation path was independently planned and autonomously generated. Once the transplanter starts to work along the starting position of the long side, the real-time data of lateral deviation and heading deviation were collected through the RS485 serial port of the navigation module. It can be seen from Figure 10 that the lateral deviation obviously increases at about 93 m where the rice transplanter suffered a sudden side slip, which causes the electric steering wheel to rotate beyond the maximum range towards the planned path. In order to prevent the vehicle from rolling over and ensure driving safety, only a small turning angle can be used to approach the planned path step by step. This means that the robustness and adaptive ability of the traditional sliding mode control algorithm is poor when the rice transplanter suffers from uncertain interference such as sideslip or a bumpy road. Moreover, large fluctuations of lateral and heading deviations can be observed, which perhaps are caused by a large stability bound of the control algorithm.

The small fluctuation amplitude of lateral deviation and heading deviation is observed in Figure 11. This indicates that the proposed control algorithm is robust and has good adaptive ability to uncertain inference.

4.2. Data Analysis

In order to verify the performance of the adaptive sliding mode path tracking control method, it is compared with the traditional sliding mode path tracking control method. The compared results are shown in Table 5.

It can be seen from Table 5 and Figure 10 and Figure 11 that system chattering is obvious when using the traditional sliding mode control; the maximum lateral deviation and the average lateral deviation of path tracking are 17.5 cm and 9.1 cm, respectively. However, the lateral deviation and the average lateral deviation from the adaptive sliding mode control reduce to 7.9 cm and 3.2 cm, respectively. Furthermore, the maximum heading deviation drops from 19.3° to 2.7°, and the mean value of the heading deviation decreases from 8.5° to 1.3°. This phenomenon implies that the control quantity from the controller changes smoothly by adopting the proposed control algorithm and chattering is effectively eliminated, which shows that the proposed path tracking control method is better than the traditional sliding mode path tracking control method.

5. Conclusions

In view of the chattering problem of the system, which is easily caused by external interference and uncertainty in the process of path tracking of the unmanned transplanter, an adaptive sliding mode path tracking control algorithm was proposed. The proposed control algorithm integrated an RBF neural network and sliding mode control which improved the adaptability of the transplanter to the complex and uncertain environment and reduced the lateral deviation and heading deviation.

Based on modified FLW 2ZG-6DM high-speed transplanter, the vehicle kinematic model was established. The simulation tests demonstrated that the position tracking distance approximated from a large deviation distance to near the zero point within about 0.6 m, the direction tracking angle converged to the zero point within 0.5 m, and the system gradually entered the steady state. The model can effectively improve the steady-state performance of the system, reduce the impact of chattering on the system when the system track reaches the switching surface, and ensure the path tracking accuracy and long-term operation stability in the process of driving operation.

The field test results demonstrated that the maximum value and the average value of the lateral deviation were 7.9 cm and 3.2 cm, respectively. The corresponding maximum angle and average value of the heading deviation were 2.7° and 1.3°, respectively. The experimental results implied that the proposed control strategy can meet the automatic driving requirements of rice transplanter in the field.

Author Contributions

Conceptualization, J.L. and R.L.; methodology, Z.S.; software, Z.S.; validation, J.L.; formal analysis, Z.S.; investigation, J.L.; resources, J.L.; data curation, R.L.; writing—original draft preparation, R.L.; writing—review and editing, B.C.; visualization, B.C.; supervision, J.L.; project administration, J.L. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

No new data were created or analyzed in this study. Data sharing is not applicable to this article.

Conflicts of Interest

The authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Tables

Figure 1. Installation schematic diagram of steering wheel-like motor. (a) Structure diagram. (b) Installation drawing: 1. Steering wheel; 2. Tight set; 3. Barrel motor; 4. Fixed axle support; 5. Locking bolt; 6. Fixed shaft.

Figure 2. Installation schematic diagram of angle sensor. (a) Structure diagram; (b) installation drawing: 1. Steering shaft; 2. Trellis bar; 3. Angle sensor; 4. Fixed bracket; 5. Fixed link; 6. Ball tie rod.

Figure 3. Installation schematic diagram of the electric push rod. (a) Structure diagram; (b) installation drawing: 1. Accelerator pedal; 2. Linear actuator; 3. Support plate; 4. Transplanter chassis; 5. Steel strand core; 6. Stay sleeve.

Figure 4. Diagram of inertia sensor and navigation system. (a) Navigation reference station; (b) posture sensor.

Figure 5. Construction diagram of the system.

Figure 6. Kinematic model.

Figure 7. RBF neural network architecture diagram.

Figure 8. Path tracking error simulation results. (a) Lateral deviation; (b) heading deviation.

Figure 9. Experimental platform and Path tracking test. (a) Test platform; (b) field experiment.

Figure 10. Path tracking error using traditional sliding mode. (a) Lateral deviation; (b) heading deviation.

Figure 11. Path tracking error using proposed control algorithm. (a) Lateral deviation; (b) heading deviation.

Table 1

Parameters of steering wheel-like motor.

Type	Parameter
Rated voltage/V	12
Rated torque/(N*m)	15
Output mode	RS232
Speed/rmp	100

Table 2

Parameters of angle sensor.

Type	Parameter
Rated voltage/V	8–24
Range/°	0–360
Output mode	RS485
Accuracy/°	0.1

Table 3

Parameters of the electric push rod.

Type	Parameter
Rated voltage/V	12
Load/N	200
Trip/mm	100
Speed/(mm*s−1)	24

Table 4

Parameters of inertia sensor.

Type	Parameter
Rated voltage/V	5
Sampling frequency/kHz	10
Output mode	RS485
Rated power/mW	480–570

Table 5

Results of experiment.

Type	Traditional Sliding Mode	Adaptive Sliding Mode
Maximum lateral deviation/cm	17.5	7.9
Average of lateral deviation/cm	9.1	3.2
Maximum heading deviation/°	19.3	2.7
Mean of heading deviation/°	8.5	1.3

References

1. Yang, F.X. Improved design of rice transplanter based on intelligent vision. China South. Agric. Mach.; 2018; 49, pp. 26-29.

2. Kondoh, T.; Nagasaka, Y.; Kato, A.; Shindo, H.; Yaji, Y. Reduction of nitrogen, phosphorus, and suspended solids effluent loads from paddy fields by transplanting into retained ponding water using a GNSS-controlled rice transplanter. Paddy. Water Environ.; 2019; 17, pp. 15-23. [DOI: https://dx.doi.org/10.1007/s10333-019-00714-5]

3. Wang, H.; Wang, G.M.; Luo, X.W.; Zhang, Z.G.; Gao, Y.; He, J.; Yue, B.B. Path tracking control method of agricultural machine navigation based on aiming pursuit mode. Trans. Chin. Soc. Agric. Eng.; 2019; 35, pp. 11-19.

4. Aldair, A.A.; Rashid, A.T.; Rashid, M.T.; Alsaedee, E.B. Adaptive fuzzy control applied to seven-link biped robot using ant colony optimization algorithm. Iran. J. Sci. Technol. Trans. Electr. Eng.; 2019; 43, pp. 797-811. [DOI: https://dx.doi.org/10.1007/s40998-019-00201-x]

5. Li, S.C.; Xu, H.Z.; Ji, Y.H.; Cao, R.Y.; Zhang, M.; Li, H. Development of a following agricultural machinery automatic navigation system. Comput. Electron. Agric.; 2019; 158, pp. 335-344. [DOI: https://dx.doi.org/10.1016/j.compag.2019.02.019]

6. Li, T.C.; Hu, J.T.; Gao, L.; Liu, X.G.; Bai, X.P. Agricultural machine path tracking method based on fuzzy adaptive pure pursuit model. Trans. Chin. Soc. Agric. Mach.; 2013; 44, pp. 205-210.

7. Ye, Y.; He, L.; Zhang, Q. Steering control strategies for a four-wheel-independent-steering bin managing robot. IFAC-PapersOnLine; 2016; 49, pp. 39-44. [DOI: https://dx.doi.org/10.1016/j.ifacol.2016.10.008]

8. Xiong, Z.H.; Hak, J.K.; Joon, Y.K.; Sang, Y.Y.; Hee, C.M.; Jung, H.K.; Young, J.K. Path-tracking simulation and field tests for an auto-guidance tillage tractor for a paddy field. Comput. Electron. Agric.; 2015; 112, pp. 161-171.

9. Huang, C.; Naghdy, F.; Du, H. Fault tolerant sliding mode predictive control for uncertain steer-by-wire system. IEEE. Trans. Cybern.; 2019; 49, pp. 261-272. [DOI: https://dx.doi.org/10.1109/TCYB.2017.2771497]

10. Wu, X.; Jin, P.; Zou, T.; Qi, Z.; Xiao, H.; Lou, P. Backstepping trajectory tracking based on fuzzy sliding mode control for differential mobile robots. J. Intell. Robot. Syst.; 2019; 96, pp. 109-121. [DOI: https://dx.doi.org/10.1007/s10846-019-00980-9]

11. Wu, H.M.; Karkoub, M.; Hwang, C.L. Mixed fuzzy sliding-mode tracking with backstepping formation control for multi-nonholonomic mobile robots subject to uncertainties. J. Intell. Robot. Syst.; 2015; 79, pp. 73-86. [DOI: https://dx.doi.org/10.1007/s10846-014-0131-9]

12. Zhang, W.Y.; Ding, Y.C.; Wang, X.L.; Zhang, X.; Cai, X.; Liao, Q.X. Pure pursuit control method based on SVR inverse-model for tractor navigation. Trans. Chin. Soc. Agric. Mach.; 2016; 47, pp. 29-36.

13. Wang, L.; Zhai, Z.Q.; Zhu, Z.X.; Mao, E.R. Path racking control of an autonomous tractor using improved Stanley controller optimized with multiple-population genetic algorithm. Actuators; 2022; 11, 22. [DOI: https://dx.doi.org/10.3390/act11010022]

14. Zhang, T.; Jiao, X.H.; Lin, Z.M. Finite time trajectory tracking control of autonomous agricultural tractor integrated nonsingular fast terminal sliding mode and disturbance observer. Biosyst. Eng.; 2022; 219, pp. 153-164. [DOI: https://dx.doi.org/10.1016/j.biosystemseng.2022.04.020]

15. Xiong, J.T.; Liu, Z.; Chen, S.M.; Liu, B.L.; Zheng, Z.H.; Zhong, Z.; Yang, Z.G.; Peng, H.X. Visual detection of green mangoes by an unmanned aerial vehicle in orchards based on a deep learning method. Biosyst. Eng.; 2020; 194, pp. 261-272. [DOI: https://dx.doi.org/10.1016/j.biosystemseng.2020.04.006]

16. Mubashiru, O.L. Tomato detection based on modifed YOLOv3 framework. Sci. Rep.; 2021; 11, 1447.

17. Arunabha, M.R.; Jayabrata, B. Real-time growth stage detection model for high degree of occultation using DenseNet-fused YOLOv4. Comput. Electron. Agric.; 2022; 193, 106694.

18. Gokhan, B.; Marcel, B.; Erhan, I.K.; Ahmet, B.K. Improving the trajectory tracking performance of autonomous orchard vehicles using wheel slip compensation. Biosyst. Eng.; 2016; 146, pp. 149-164.

19. Erkan, K.; Erdal, K.; Herman, R.; Wouter, S. Towards agrobots: Identification of the yaw dynamics and trajectory tracking of an autonomous tractor. Comput. Electron. Agric.; 2015; 115, pp. 78-87.

20. Tu, X.Y.; Gai, J.Y.; Tang, L. Robust navigation control of a 4WD/4WS agricultural robotic vehicle. Comput. Electron. Agric.; 2019; 164, 104892. [DOI: https://dx.doi.org/10.1016/j.compag.2019.104892]

21. Xu, G.F.; Chen, M.Z.; He, X.K.; Pang, H.X.; Miao, H.Q.; Cui, P.D.; Wang, W.J.; Diao, P.S. Path following control of tractor with an electro-hydraulic coupling steering system: Layered multi-loop robust control architecture. Biosyst. Eng.; 2021; 209, pp. 282-299. [DOI: https://dx.doi.org/10.1016/j.biosystemseng.2021.07.014]

22. Li, Z.Q.; Chen, L.Q.; Zheng, Q.; Dou, X.Y.; Yang, L. Control of a path following caterpillar robot based on a sliding mode variable structure algorithm. Biosystems. Eng.; 2019; 186, pp. 80-87. [DOI: https://dx.doi.org/10.1016/j.biosystemseng.2019.07.004]

23. Deng, H.; Sun, F.C.; Sun, Z.Q. Robust control of robotic manipulators using fuzzy inverse model. Acta Autom. Sin.; 2001; 27, pp. 521-529.

24. Morioka, H.; Wada, K.; Sabanovic, A.; Jezernik, K. Neural network based chattering free sliding mode control. In Proceeding of the 34th SICE Annual Conference; Hokkaido, Japan, 26–28 July 1995; pp. 1303-1308.

25. Ertugrul, M.; Kaynak, O. Neuro sliding mode control of robotic manipulators. Mechatronics; 2000; 10, pp. 239-263. [DOI: https://dx.doi.org/10.1016/S0957-4158(99)00057-4]

26. Huang, S.J.; Huang, K.C.; Chiou, K.C. Development and applications of a novel radial basis function sliding mode controller. Mechatronics; 2003; 13, pp. 313-329. [DOI: https://dx.doi.org/10.1016/S0957-4158(01)00050-2]

27. Zhu, G.Y. Study on Automatic Steering Control System of High Speed Rice Transplanter; Engineering College of Anhui Agricultural University: Hefei, China, 2018.

28. He, J.; Zhu, J.G.; Luo, X.W.; Zhang, Z.G.; Hu, L.; Gao, Y. Design of steering control system for rice transplanter equipped with steering wheel-like motor. Trans. Chin. Soc. Agric. Eng.; 2019; 35, pp. 10-17.

29. Hu, J.T.; Gao, L.; Bai, X.P.; Li, T.C.; Liu, X.G. Review of research on automatic guidance of agricultural vehicles. Trans. Chin. Soc. Agric. Eng.; 2015; 31, pp. 1-10.

30. Mohammad, R.R.; Zahra, T.S. A novel adaptive sliding mode controller design for tracking problem of an AUV in the horizontal plane. Int. J. Dyn. Control.; 2019; 7, pp. 679-689.

31. Li, T.C. Adaptive sliding mode path tracking control of agricultural wheeled mobile robots. China Mech. Eng.; 2018; 29, pp. 579-584.

32. Derrick, J.B.; Bevly, D.M. Adaptive steering control of a farm tractor with varying yaw rate properties. J. Field Robot.; 2009; 26, pp. 519-536. [DOI: https://dx.doi.org/10.1002/rob.20291]