An Adaptive Path Tracking Controller with Dynamic Look-Ahead Distance Optimization for Crawler Orchard Sprayers

Abstract

Based on the characteristics of small agricultural machinery in terms of flexibility and high efficiency when operating in small plots of hilly and mountainous areas, as well as the demand for improving the automation and intelligence levels of agricultural machinery, this paper conducted research on the path tracking control of the automatic navigation operation of a crawler sprayer. Based on the principles of the kinematic model and the position prediction model of the agricultural machinery chassis, a pure pursuit controller based on adaptive look-ahead distance was designed for the tracked motion chassis. Using a lightweight crawler sprayer as the research platform, integrating onboard industrial control computers, sensors, communication modules, and other hardware, an automatic navigation operation system was constructed, achieving precise control of the crawler sprayer during the path tracking process. Simulation test results show that the path tracking control method based on adaptive look-ahead distance has the characteristics of smooth control and small steady-state error. Field tests indicate that the crawler sprayer exhibits small deviations during path tracking, with an average absolute error of 2.15 cm and a maximum deviation of 4.08 cm when operating at a speed of 0.7 m/s. In the line-following test, with initial position deviations of 0.5 m, 1.0 m, and 1.5 m, the line-following times were 7.45 s, 11.91 s, and 13.66 s, respectively, and the line-following distances were 5.21 m, 8.34 m, and 9.56 m, respectively. The maximum overshoot values were 6.4%, 10.5%, and 12.6%, respectively. The autonomous navigation experiments showed a maximum deviation of 5.78 cm and a mean absolute error of 2.69 cm. The proportion of path deviations within ±5 cm and ±10 cm was 97.32% and 100%, respectively, confirming the feasibility of the proposed path tracking control method. This significantly enhanced the path tracking performance of the crawler sprayer while meeting the requirements for autonomous plant protection spraying operations.

1. Introduction

Field management is a key step for the healthy growth and high yield of crops [1]. However, in fruit tree orchards in hilly and mountainous areas, the small and dispersed land parcels, as well as the rugged and irregular transition roads, present certain difficulties for conventional wheeled agricultural machinery to enter and operate [2,3]. In addition, drones also face issues such as inconvenient movement, complex operation, and insufficient load capacity [4,5]. Due to the advantages of tracked chassis agricultural machinery, including easy operation, strong terrain adaptability, excellent climbing and obstacle-crossing capabilities, a large ground contact area, low soil pressure, a small turning radius, and a higher load capacity, it is considered a suitable solution for such environments [6,7,8]. Therefore, lightweight and user-friendly crawler sprayers have become the preferred crop protection equipment in these regions. During spraying operations, challenges such as repetitive tasks, operational oversights, and high physical demands on operators highlight the need for automatic navigation technology. This technology would improve operational quality and efficiency while reducing labor intensity. Consequently, research on automatic navigation control for crawler sprayers is essential, as it can significantly reduce crop protection operation costs, improve operational quality, and enhance the intelligence level of agricultural machinery [9,10].

The automatic navigation operation system of agricultural machinery consists of a navigation controller and an automatic operation control strategy. Agricultural machinery equipped with this automatic navigation system can perform field operations with minimal human intervention [11,12]. Scholars both domestically and internationally have conducted relevant research on automatic navigation operation systems based on different equipment used in various operational stages, including seeding, fertilization, and harvesting operations [13,14,15,16,17]. These studies mainly focus on sensor integration, control algorithms, and specific application scenarios such as paddy field environments and wet soil conditions [18]. In research on the navigation controller for tracked agricultural machinery, Kurita et al. proposed an automatic harvesting framework for tracked rice harvesters. This system enables automated rice harvesting and automatic grain unloading when the storage is full in an unmanned farm. By integrating sensors such as vision systems, it reduces the navigation tracking error to the centimeter level [19]. Jia et al. designed an automatic driving system for the NF-752 tracked tractor and proposed a heading estimation model controller [20]. Guan et al. focused on the path tracking control method for tracked harvesters in paddy field environments, using a tracked combine harvester as the research subject. They established a kinematic model for the turning motion of tracked vehicles, providing theoretical references for the design of path tracking algorithms for tracked harvesters in wet soil conditions [21]. Ding et al. utilized electromagnets as actuators and combined BeiDou navigation with electronic compasses to design a path tracking control method based on immune PID control, which reduced the maximum tracking error by 18.1% and the average tracking error by 32.6% compared to traditional path tracking control methods [22]. Although significant progress has been made in the research of automatic navigation systems for large agricultural machinery, there is relatively little research on small crawler machinery. This may be due to factors such as high algorithm complexity, low market demand, and cost limitations [23].

The design of the navigation controller is a key technology in the automatic navigation system for agricultural machinery operations [24,25,26]. For the navigation control of tracked chassis agricultural machinery, Li et al. studied the interaction between the tracked chassis and soil underneath and developed a dynamics model to propose a path tracking control algorithm for a tracked robot based on sliding mode variable structure [27]. Zhang et al. designed a fuzzy adaptive tracking navigation control method and developed an automatic navigation controller for a tracked oilseed rape seeder [28]. He et al. improved the PID path tracking algorithm for a tracked peanut harvester based on the virtual steering angle and proposed a dual PID path tracking control method based on pure pursuit look-ahead waypoints. The path tracking control of the tracked peanut harvester was achieved using a pulse width modulator [29]. Xiong et al. designed an automatic operation control system for a tracked orchard sprayer based on the pure pursuit path tracking algorithm. Currently, there is a significant amount of research on navigation controllers for tracked agricultural machinery, but there are fewer studies on navigation controllers that can achieve high navigation accuracy and adapt to changes in speed [30]. Although there is considerable research on the navigation controllers of crawler agricultural machinery, there is relatively less research on achieving high navigation accuracy and adaptive variations.

The pure pursuit algorithm is widely used in the automatic navigation control of low-speed agricultural machinery due to its high stability, simplicity, and low computational requirements. In low-speed operational scenarios, this algorithm can be easily deployed to achieve autonomous path tracking control for agricultural machines, meeting the practical needs of agricultural operations. However, in the traditional approach of this algorithm, the process of determining the look-ahead distance parameter is cumbersome and difficult to adapt to the complex and variable field conditions [31,32,33]. To address this, this paper proposes a pure pursuit algorithm based on dynamic look-ahead distance, which searches for the optimal look-ahead distance within the look-ahead area by constructing an evaluation function system, thereby reducing the need for manual parameter tuning and improving path tracking accuracy.

This study selects a lightweight crawler sprayer as the research platform due to its superior maneuverability in orchard and garden terrains, combined with the stringent path tracking accuracy required for uniform chemical spraying. Despite these practical demands, research on automatic navigation for small crawler sprayers remains scarce. To address this gap, the work is structured as follows: (1) A kinematic model of the sprayer is established, and tracking control is implemented using the pure pursuit algorithm; (2) An adaptive look-ahead distance mechanism is designed to optimize path tracking; (3) Simulations and field experiments validate the algorithm’s effectiveness. Results demonstrate high tracking accuracy and adaptability in lightweight crawler machinery, offering a novel solution for precision agriculture in complex terrains.

2. Materials and Methods

2.1. The Platform for Crawler-Type Sprayers

2.1.1. The Overall Mechanical Structure

A plant protection operations platform of a crawler-type sprayer is designed to track an operation path in the field. Based on this platform, a path tracking controller is studied to achieve autonomous navigation capabilities. The overall mechanical structure of the crawler-type sprayer studied in this article mainly consists of the tracked chassis, driving system, power system, control system, and working device, as shown in Figure 1. The tracked chassis is equipped with double-wheeled rubber tracks; the driving system connects the drive wheels to the tracked chassis through a reducer and a brushless DC motor for propulsion. The power system consists of a range-extended power platform made up of a generator and batteries, which allows the generator to provide continuous power when the battery is low. The control system mainly includes the control end and the execution end, composed of an industrial computer that supports the Linux system and a motor driver. The working device is a crucial component for the sprayer’s field application, primarily consisting of a spray system with six sets of nozzles and a water tank. It is capable of being efficiently applied to orchard plant protection, and the basic parameters of the crawler-type sprayer are shown in

Table 1. Main parameters of the crawler-type sprayer.

Parameters	Unit	Value
External dimensions	mm	2150 × 1100 × 1400
Weight	kg	450
Wheelbase	mm	910
Maximum working slope	°	30
Operating tank capacity	L	200
Spray width	m	1.5–4.5
Minimum turning radius	m	0
Maximum travel speed	m/s	1.25

.

2.1.2. The Framework of the Control System

The control system framework for the autonomous navigation of the crawler sprayer is illustrated in Figure 2 and is organized into a three-level layered architecture: information, control decision, and execution. The control decision layer features a navigation management system that oversees decision-making processes for the motion control of the agricultural machinery, employing an embedded ARM industrial control computer to make real-time decisions based on the current state of the machinery. The information layer mainly consists of the BeiDou equipment, which is composed of two satellite antennas and an RTK mobile station. The BeiDou receiving antenna is fixed at the top of the crawler sprayer and provides high-precision real-time differential positioning information for the sprayer through the RTK differential principle, and the data are transmitted via RS232 protocol at a frequency of 10 Hz. Finally, the execution layer includes the actuator unit of the agricultural machinery, consisting of the chassis walking system, tracked chassis steering system, and spraying operation system. The vehicle control unit communicates with the driver through a CAN bus at a rate of 500 Kbps, allowing for real-time monitoring of wheel hub motor speeds and control signals for the motor driver. This layered architecture collectively facilitates efficient navigation and operation of the crawler-type sprayer, enhancing its autonomous capabilities in agricultural applications.

2.2. Mathematical Model of the Crawler Sprayer

2.2.1. Kinematic Model of Tracked Chassis

To achieve automatic navigation of a crawler sprayer, the navigation controller must meet high precision requirements, with an accurate kinematic model being essential. Based on the tracked chassis’ walking mechanism and the vehicle’s motion characteristics, the motion control relies mainly on the speed difference between the two tracks. By simplifying and abstracting the system, a kinematic model can be developed. Additionally, since autonomous plant protection spraying is typically performed on flat surfaces at low speeds, most dynamic factors can be ignored. Thus, the kinematic model is established under the following assumptions:

• The agricultural machinery is a rigid body;
• Rolling and pitching motion are ignored;
• Lateral slip is ignored.

And the motion diagram of the tracked chassis walking mechanism is shown in Figure 3.

Based on the geometric relationships depicted in Figure 3, derive the following equations:

$$\left\{\begin{array}{c}{v}_c={\displaystyle \frac{v_L+v_R}{2}}\\ R={\displaystyle \frac{D\left(v_L+v_R\right)}{2\left(v_L-v_R\right)}}\\ {\omega }_C={\displaystyle \frac{v_L-v_R}{D}}\end{array}\right..$$

(1)

For the tracked chassis, let the rotational speeds of the left and right drive wheels be denoted as $n_r$ and $n_l$, respectively, and let the radius of the drive wheels be $r$. Therefore, based on the conversion relationship between track speed and the rotational speed of the drive wheels, the forward kinematic model of the tracked chassis can be derived. The kinematic relationships of the tracked chassis can then be expressed using the following matrix:

$$\left[\begin{array}{c}{v}_c\\ {\omega }_c\end{array}\right]=\left[\begin{array}{cc}\pi r& \pi r\\ -{\displaystyle \frac{2\pi r}{D}}& {\displaystyle \frac{2\pi r}{D}}\end{array}\right]\left[\begin{array}{c}{n}_r\\ n_l\end{array}\right].$$

(2)

At the same time, the inverse kinematic model of the control quantities for the rotational speeds of the left and right drive wheels can be obtained from the linear velocity and angular velocity of the tracked chassis as follows:

$$\left[\begin{array}{c}{n}_r\\ n_l\end{array}\right]=\left[\begin{array}{cc}{\displaystyle \frac{1}{2\pi r}}& -{\displaystyle \frac{D}{4\pi r}}\\ {\displaystyle \frac{1}{2\pi r}}& {\displaystyle \frac{D}{4\pi r}}\end{array}\right]\left[\begin{array}{c}{v}_c\\ {\omega }_c\end{array}\right].$$

(3)

Using the differential drive control principle and established kinematic models, the motion control system processes input and output parameters at the decision layer, improving efficiency and accuracy. This approach optimizes motion control and provides a strong foundation for more advanced autonomous navigation systems that can adapt to different agricultural environments. As a result, the pose information during the motion of the tracked chassis can be represented as follows: $P={\left[\begin{array}{ccc}X& Y& \phi \end{array}\right]}^T$. By combining the above formulas, the expression for $Q={\left[\begin{array}{cc}{v}_C& {\omega }_C\end{array}\right]}^T$ and the motion pose equation expression for the tracked sprayer chassis can be established as follows:

$$\stackrel{·}{P}=\left[\begin{array}{c}\stackrel{·}{X}\\ \stackrel{·}{Y}\\ \stackrel{·}{\phi }\end{array}\right]=\left[\begin{array}{cc}\cos \phi & 0\\ \sin \phi & 0\\ 0& 1\end{array}\right]\times Q=\left[\begin{array}{cc}\pi r\cos \phi & \pi r\cos \phi \\ \pi r\sin \phi & \pi r\sin \phi \\ -{\displaystyle \frac{2\pi r}{B}}& {\displaystyle \frac{2\pi r}{B}}\end{array}\right]\left[\begin{array}{c}{n}_r\\ n_l\end{array}\right].$$

(4)

2.2.2. Pure Pursuit Algorithm

The pure pursuit algorithm is a motion control method that simulates driver behavior and is widely used in path tracking control for mobile robots, particularly suitable for automatic navigation of agricultural machinery operating at relatively low speeds. In this study, we assume that the slip between the tracks and the ground is negligible [29], and we establish the pure pursuit model under the condition that the centroid of the track traveling mechanism coincides with its geometric center, as shown in Figure 4. In Figure 4, XOY represents the world coordinate system, which is a fixed reference frame in the global environment, while XCY denotes the vehicle coordinate system, which is a dynamic reference frame attached to the vehicle body and moves along with it. Based on the heading angle and odometry, there exists a transformation relationship between the two coordinate systems.

From Figure 4, it is known that $l_d$ is the variable to be determined. The following equations are derived from the geometric relationship in Figure 4:

$$\left\{\begin{array}{l}{l}_d=\sqrt{{\left(x_i-x\right)}^2+{\left(y_i-y\right)}^2}\\ R={\displaystyle \frac{l_d}{2\sin \alpha }}\\ \sin \alpha =e_y/l_d\end{array}\right..$$

(5)

Let the coordinates of the goal point G in the XCY vehicle coordinate system be $\left(x_C,y_C\right)$; then, the following can be obtained: $e_y=y_C$. By substituting the coordinate transformation relationship and simplifying Equation (5), it is clear that

$$R={\displaystyle \frac{l_d^2}{2e_y}}={\displaystyle \frac{{\left(x_i-x\right)}^2+{\left(y_i-y\right)}^2}{2\left((y_i-y)\cos \varphi -(x_i-x)\sin \varphi \right)}}.$$

(6)

By combining with the kinematic equations, the relationship between the left and right track velocities $v_L$ and $v_R$, using the vehicle speed $v_C$ and the tracking control’s look-ahead distance $l_d$, can be obtained as follows:

$$\left\{\begin{array}{l}{v}_R=v_C\left[1-D\cdot e_y/l_d^2\right]\\ v_L=v_C\left[1+D\cdot e_y/l_d^2\right]\end{array}\right..$$

(7)

According to the above equation, the look-ahead distance is a key adjustable parameter in the pure pursuit algorithm. When the look-ahead distance is small, the lateral adjustment capability is enhanced, and the vehicle quickly approaches the target path with a larger turning radius. However, if the look-ahead distance is too small, it can lead to vehicle oscillations. Conversely, when the look-ahead distance is large, the vehicle approaches the target path more slowly with a smaller turning radius, which helps prevent oscillations but results in longer adjustment times. Therefore, the size of the look-ahead distance determines the path tracking control accuracy of the tracked chassis. As shown in Equation (6), the target point on the reference path determines the value of the look-ahead distance and also affects the turning radius during path tracking. Based on the above analysis, it can be concluded that the tracking performance of the pure pursuit algorithm is primarily determined by the selection of the target point on the reference path.

2.3. The Controller Design Based on Adaptive Look-Ahead Distance

In this section, we have designed a pure pursuit algorithm based on adaptive look-ahead distance for the path tracking motion control of the crawler sprayer. This algorithm dynamically adjusts the look-ahead distance according to the relationship between the current position of the agricultural machinery and the reference path, improving the speed and stability of the navigation controller. The controller system framework is shown in Figure 5. Firstly, based on the given path information and real-time dynamic positioning data obtained from the RTK mobile station, the look-ahead area for path tracking is determined. Secondly, using the tracked chassis pose prediction model, the path points within the look-ahead area are traversed, and the tracking error for each point is calculated. Finally, by defining an evaluation function for the tracking error, the results of the traversal are searched to find the target point with the highest evaluation metric within the range of the look-ahead area. This process allows the system to determine the look-ahead distance for pure path tracking of the tracked chassis based on the position of the optimal target point, achieving the goal of adaptively updating the look-ahead distance during reference path tracking.

2.3.1. Determine the Range of the Look-Ahead Area

The autonomous navigation control of agricultural machinery based on the pure pursuit algorithm simulates the process of a human driver controlling the vehicle by observing a section of the path ahead and attempting to minimize the path tracking error. This section of the path is called the look-ahead area, as shown in Figure 6, and the reference path is discretized into a list of reference path points.

For the look-ahead distance adaptive pure pursuit algorithm, it is necessary to determine the range of the look-ahead area. Within this range, the look-ahead distance is dynamically determined and updated, simulating the decision-making behavior of the driver, thus achieving precise path tracking and navigation control. As shown in Figure 6, by setting the minimum look-ahead distance $l_{d_{min}}$ and the maximum look-ahead distance $l_{d_{max}}$, the range of the look-ahead area can be determined. Therefore, the relationship between the target points of the reference path within the look-ahead area and the current position of the agricultural machinery can be described by the following relationship:

$$l_{d_{\min }}\le \sqrt{{\left(x_i-x\right)}^2+{\left(y_i-y\right)}^2}\le l_{d_{\max }}.$$

(8)

The above Equation (8) describes the range of look-ahead distance. At the same time, it can be summarized from the research of many scholars that when tracking a path of a certain length, under the condition of knowing the starting point of the path, the variation in coordinates between the endpoint of the tracked path and the current position of the agricultural machinery does not change the total length of the path [34,35]. Therefore, we propose to integrate the tracking path length corresponding to the look-ahead area, with $S$ representing the path length, as follows:

$$S={\displaystyle \int ds=\underset{i\to n}{\lim }}{\displaystyle \sum _1^n\sqrt{{(x_{i+1}-x_i)}^2+{(y_{i+1}-y_i)}^2}}.$$

(9)

In conjunction with the above analysis, we propose an algorithm to determine the range of the look-ahead area, with the specific steps as follows: First, a search is performed from the nearest point $p_1$ between agricultural machinery and the reference path as the starting point of the look-ahead area. Then, the distance between the current position point of agricultural machinery and this point is calculated, which is the minimum look-ahead distance $l_{d_{min}}$. Finally, starting from the point $p_1$, integration is performed along the reference path, and the accumulated integral length $S_{-}lenth$ is calculated until either of the two following conditions is satisfied: (1) The integration length $S_{-}lenth$ is longer than the maximum integration length $S_{-}{max}_{-}lenth$. (2) The distance between the current position point and the path point is larger than the maximum look-ahead distance $l_{d_{max}}$. At the same time, the point $p_2$ on the reference path that satisfies the condition is at a distance from the agricultural machinery’s current position equal to the maximum look-ahead distance. At the end of the algorithm, a list of the coordinates of the points on the reference path from the starting point $p_1$ to the endpoint $p_2$ of the look-ahead area is obtained, thus determining the range of the look-ahead area.

2.3.2. The Pose Prediction Model of the Crawler Sprayer

Based on the requirements of agronomy for spray uniformity in plant protection operations, during the operation of the crawler sprayer, a motion control strategy that combines operational control with agronomy is adopted. This approach fully considers the complexity of the operating environment and task characteristics and requires the use of a relatively constant speed motion control strategy. Therefore, during path tracking of the tracked chassis, since its kinematic model uses linear velocity $v_C$ and angular velocity ${\omega }_C$ as input control variables. In addition, $∆t$ can be set as the time interval for updating the agricultural machinery’s position. The integral of Equation (6) can be obtained as follows:

$$\left\{\begin{array}{l}x\left(t+\Delta t\right)=x\left(t\right)+{\displaystyle {\int }_t^{t+\Delta t}{v}_C\cdot \cos \varphi \cdot d_t}\\ y\left(t+\Delta t\right)=y\left(t\right)+{\displaystyle {\int }_t^{t+\Delta t}{v}_C\cdot \sin \varphi \cdot d_t}\\ \varphi \left(t+\Delta t\right)=\varphi \left(t\right)+{\displaystyle {\int }_t^{t+\Delta t}{\omega }_C\cdot d_t}\end{array}\right..$$

(10)

In the above equation, the current pose of the tracked chassis is $\left(\begin{array}{ccc}x\left(t\right)& y\left(t\right)& \phi \left(t\right)\end{array}\right)$ and the predicted pose of the tracked chassis is $\left(\begin{array}{ccc}x(t+∆t)& y(t+∆t)& \phi (t+∆t)\end{array}\right)$ after the time duration of $∆t$. The crawler sprayer achieves real-time pose data updates by leveraging high-precision differential satellite signals, ensuring dynamic positioning accuracy during operation. It can be assumed that the speed remains constant during the time interval $\Delta t$. Therefore, Equation (10) can be approximated as follows:

$$\left\{\begin{array}{l}x\left(t+\Delta t\right)=x\left(t\right)+v_C\times \cos \varphi \times \Delta t\\ y\left(t+\Delta t\right)=y\left(t\right)+v_C\times \sin \varphi \times \Delta t\\ \varphi \left(t+\Delta t\right)=\varphi \left(t\right)+{\omega }_C\times \Delta t\end{array}\right..$$

(11)

The equations mentioned above construct a pose prediction model for the crawler sprayer, which can describe the expected position the equipment will reach after a short time interval $\Delta t$. This model considers the current state of the crawler sprayer, including its speed, direction, and potential external influences, and predicts the continuous pose changes over time by simplifying the integral equations. Later sections approximate the prediction of the crawler sprayer position based on a specific speed input by this model for the calculation of the evaluation function.

2.3.3. Establish Evaluation Indicators

In the process of the autonomous navigation operation of the crawler sprayer, to ensure optimal tracking performance of the operation path at any position, it is necessary to adaptively select the look-ahead distance of the pure tracking algorithm based on the current position variation between the tracked chassis and the path. In this study, the relationship between the look-ahead distance and the reference path target point is described by Equation (6). The value of the look-ahead distance can be determined based on the selected target point to be tracked. Therefore, by traversing the set of all path points within the look-ahead area as potential target points, the predicted position after tracking each target point is obtained. The overall error (lateral error, heading error) between the tracked chassis’s predicted position and the reference path is then quantified. By constructing an error evaluation function, the target point that maximizes the evaluation indicator is sought, thereby obtaining the corresponding look-ahead distance value.

Based on the target point set within the look-ahead area and using the position prediction model of the tracked chassis, the mathematical equation for the overall path tracking error is established as follows:

$$J_i=w_1{e}_{y_i}^2+w_2{e}_{{\theta }_i}^2.$$

(12)

In the above formula, where $e_{y_i}$ and $e_{{\theta }_i}$ represent the lateral error and heading error corresponding to the target point set based on the prediction model, $w_1$ and $w_2$ are the weight coefficients of the errors, and $w_1+w_2=1$. In summary, the evaluation function is established as follows:

$$M_i=\left(w_1+w_2\right)/J_i.$$

(13)

In this study, an overall error evaluation system for path tracking based on a position prediction model is established by constructing an evaluation function for the target point set within the look-ahead region. Each goal $\left(x_i,y_i\right)$ point in the look-ahead region corresponds to a return value $M_i$. By substituting all target path points into the evaluation function, the maximum value $M_{max}$ will be obtained from the set of return values, which is then set as the optimal metric for tracking error evaluation. Using an enumeration method, the optimal evaluation metric corresponding to a target path point in the look-ahead region can be obtained. In this way, the crawler sprayer can adaptively determine the look-ahead distance during the path tracking process, thereby achieving the goal of autonomous navigation and motion control based on the adaptive look-ahead distance of the pure pursuit algorithm.

3. Results and Discussion

3.1. Simulation Tests

For the path tracking algorithm proposed in this paper, we designed simulation tests in the Matlab environment, comparing the pure pursuit algorithm with fixed look-ahead distance and adaptive look-ahead distance. At the same time, based on the straight and curved operational trajectories required by the shuttle operation mode of the crawler sprayer, perform the simulation of straight and curved path tracking using the pure pursuit control based on adaptive look-ahead distance.

3.1.1. Comparison Simulation

To verify the control performance of the proposed adaptive look-ahead distance pure pursuit controller for the crawler sprayer, we conducted a simulation comparison experiment. The initial conditions were set with a lateral offset of 1.5 m, a speed of 1.0 m/s, and a heading deviation of 45.0°. A series of experiments were performed to determine an appropriate look-ahead distance as the input parameter for the pure pursuit controller. To ensure that the system’s adjustment time is minimized and the path tracking is smoother during autonomous navigation, a fixed look-ahead distance pure pursuit controller was selected. The look-ahead distance parameter was adjusted through trial and error during the experiments, and the optimal look-ahead distance was found to be 2.0 m after multiple trials. Based on this, we set up a simulation experiment where a fluctuation was applied to the reference path point at 2.0 s to simulate the performance of different controllers. The simulation results are shown in Figure 7. The results indicate that the adaptive look-ahead distance pure pursuit controller has a shorter rise time, improving by approximately 0.21 s, compared to the fixed look-ahead distance pure pursuit controller. Additionally, this controller demonstrated stronger anti-interference capabilities and smoother performance when subjected to fluctuations in the reference path point.

Further analysis revealed that the adaptive look-ahead distance effectively reduced the system’s dynamic response time, and this improvement directly translated to enhanced tracking accuracy. The simulation results conclusively demonstrate that the dynamic adjustment of look-ahead distance in the pure pursuit controller not only improves the system’s responsiveness but also enhances its robustness against external disturbances. This validation confirms that the adaptive approach is particularly effective in complex operational environments and under dynamic path variations, offering superior control performance for crawler sprayer applications.

3.1.2. Path Tracking Simulation

The field travel of agricultural machinery primarily consists of straight and curved lines. Based on the specific conditions of agricultural machinery performance parameters and field parameters, different types of agricultural machinery follow different operational process routes for various tasks. In this context, an adaptive look-ahead distance pure pursuit algorithm is applied for path tracking simulation using MATLAB(R2023b). The tracking performance is verified by setting up an S-path, where the curve radius of the S-path is set to 5.0 m, the driving velocity is set to 1.0 m/s, and the sampling time is set to 0.1 s. The initial tracking position is set to be 2.0 m from the starting point of the reference path. The path tracking simulation is shown in Figure 8.

According to Figure 8a, it can be seen that the adaptive look-ahead distance pure pursuit controller has a smooth on-line performance and a small steady-state error. It demonstrates good trajectory-fitting capability and can achieve precise tracking of the reference path. Meanwhile, the look-ahead distance of the proposed algorithm was recorded during the simulation experiments, as shown in Figure 8b. It can be observed that the look-ahead distance varies significantly when tracking the reference path from the initial position; however, it stabilizes within a certain range when the reference path is being tracked steadily. Therefore, during the path tracking process, the look-ahead distance adapts based on the positional relationship with the reference path.

3.2. Tracking Tests

In order to further validate the control accuracy and performance of the adaptive preview distance pure tracking controller designed for the tracked sprayer during path tracking, this study selected the Hou Bai Farm in Jurong City, Jiangsu Province, as the testing base and conducted multiple path tracking experiments. Additionally, based on prior test results on the spray coverage uniformity of the tracked sprayer during orchard plant protection operations, the optimal working speed was determined to be 0.7 m/s. So as to ensure that the experimental conditions closely reflect real-world applications, a control speed of 0.7 m/s was chosen for the tracked sprayer during the experiments. The latitude and longitude of the test site were (Lon): 119.210025, (Lat): 31.805154.

3.2.1. Road Path Tracking

Under the condition of zero initial position deviation (maximum ±5 cm) and zero heading deviation (maximum ±2.0°), a straight-line path tracking experiment was conducted. High-precision real-time differential satellite positioning data were used to record the vehicle’s position and heading information at a sampling frequency of 10 Hz, and the relative deviation was calculated through multiple trials. The main experimental steps are as follows:

• First, the boundary points of the plot were obtained, and points $P_A \mathrm{and} P_B$ were selected as the start and endpoints of the straight-line tracking experiment;
• Second, the control system of the crawler sprayer was set to autonomous navigation mode, enabling it to follow a predefined path for straight-line tracking;
• Third, the operating speed of the crawler sprayer was set to 0.7 m/s, and the spraying system was adjusted to meet the requirements of plant protection operations;
• Fourth, the tracked sprayer was activated to start the straight-line tracking experiment, and the experiment was repeated multiple times;
• Fifth, the positioning data of the tracked sprayer were recorded in real-time using the onboard BeiDou positioning device, and statistical analysis was performed on the straight-line tracking characteristics.

The experimental results are shown in Figure 9. In Figure 9a, the fluctuating positional deviation indicates that to prevent continuous correction-induced oscillations, the system decomposes the process of tracking the operational path into multiple control steps, thereby enhancing the system’s stability. Figure 9b shows that the heading deviation during path tracking is kept within a certain range. The heading deviation exhibits more frequent changes during startup, and the control system of the tracked sprayer makes corresponding steering adjustments without significantly affecting positional deviation. When the positional and heading deviations accumulate to a certain extent, the system can quickly correct them to ensure precise tracking of the operational path. Statistical analysis of the tracking errors is presented in

Table 2. Statistics of position deviation for road path tracking.

Test No.	Absolute Extremum/cm	Absolute Average/cm	Standard Deviation/cm
1	3.39	1.87	1.54
2	2.97	1.12	1.02
3	4.35	2.06	1.13
4	4.56	2.44	1.27
5	5.14	3.26	0.75
Average	4.08	2.15	1.14

. Under the speed control that ensures operational quality, the absolute maximum of the positional deviation is 4.08 cm, the mean absolute error is 2.15 cm, and the standard deviation of the positional deviation is 1.14 cm. The experiment demonstrates that the pure tracking control based on adaptive look-ahead distance is suitable for the autonomous navigation of tracked sprayers. It exhibits good robustness on uneven field surfaces and improves the consistency of plant protection spraying path tracking.

3.2.2. On-Line Performance Testing

To evaluate the autonomous on-line path tracking performance of a crawler sprayer equipped with an adaptive look-ahead distance pure pursuit controller under initial position deviations of 0.5, 1.0, and 1.5 m, and to compare its effectiveness with a fixed look-ahead distance controller (set to 2.0 m), experiments were conducted. The crawler sprayer was required to maintain its position within ±5 cm of the navigation reference line and its heading deviation within ±2.0° to meet on-line operational requirements.

Figure 10 shows the experimental results. In Figure 10a, significant lateral movement occurs initially due to large position deviations, occasionally driving perpendicular to the planned path. As the position deviation decreases, the sprayer’s longitudinal velocity increases, and the system quickly corrects the direction to align with the reference path. After alignment, some lateral velocity remains, and the system enters an inertia phase, gradually stabilizing over time. In contrast, the fixed look-ahead distance controller, shown in Figure 10b, the system exhibits significant oscillations in position deviation after alignment, indicating poor dynamic response. The adaptive controller, by dynamically optimizing the look-ahead distance, significantly enhances path tracking smoothness and stability. The statistical analysis of real-time position deviation data during the crawler sprayer’s alignment test is summarized in

Table 3. Statistics of on-line performance data of different initial position deviations.

Ld-Method	Initial Deviations/m	On-Line Times/s	On-Line Distance/m	Overshoot/%
Adaptive	0.5	7.45	5.21	6.4
	1.0	11.91	8.34	10.5
	1.5	13.66	9.56	12.6
Fixed	0.5	7.93	5.55	8.6
	1.0	12.41	8.69	12.3
	1.5	14.22	9.95	14.5

. The results demonstrate that, for initial position deviations of 0.5, 1.0, and 1.5 m, the adaptive look-ahead distance pure pursuit controller achieves alignment times of 7.45 s, 11.91 s, and 13.66 s, and alignment distances of 5.21 m, 8.34 m, and 9.56 m, respectively. Additionally, the maximum overshoot values are 6.4%, 10.5%, and 12.6%, which are approximately two percentage points lower than those of the fixed look-ahead distance controller. These results indicate that the adaptive look-ahead distance pure pursuit controller significantly improves alignment performance and stability by dynamically adjusting the look-ahead distance, effectively suppressing dynamic overshoot, and shortening the adjustment period. Post-alignment, the system rapidly transitions to straight-line tracking mode, fulfilling the requirements for precision spraying tasks.

3.2.3. Automatic Navigation Operation Test

To test the stability and deviation of the crawler sprayer’s autonomous navigation operation system, a plot of land at the test base was selected for performance evaluation experiments, as shown in Figure 11. The performance of the crawler sprayer’s autonomous navigation operation control accuracy was tested.

During the autonomous navigation operation test of the crawler sprayer, the boundary information of the test field is first collected, and the spraying operation path is automatically generated. The basic control parameters of the crawler sprayer are then set, and the navigation operation mode is initiated. Finally, once the crawler sprayer starts its spraying operation, the relevant navigation path tracking data are recorded in real-time. The real-time positioning and adaptive dynamic look-ahead distance data of the crawler sprayer during autonomous navigation are shown in Figure 12.

Under the premise of reserving a safe turning distance at the boundary of the test field, a shuttle path planning method was adopted for the crawler sprayer. This method ensures precise alignment of the agricultural machinery, effectively reducing redundant operations and minimizing missed areas. Multiple operational paths were meticulously planned, with field measurements taken to guarantee that each path was centered on the ridges. When the crawler sprayer reaches the turning point at the end of a row, it executes a smooth turn along an arc path and proceeds to the next row to continue operations. Notably, spraying operations were conducted exclusively during straight path segments. Upon entering the next row, the sprayer rapidly achieves a straight-line tracking state, maintaining stable control and high alignment accuracy, making it highly suitable for autonomous row-switching control in spraying operations, as illustrated in Figure 12a. As shown in Figure 12b, the look-ahead distance in the tracked sprayer’s autonomous navigation adapts dynamically within the predefined look-ahead region. During initialization, the sprayer quickly aligns with the operation path, with the look-ahead distance adjusting rapidly. However, during transitions between straight-line operation and turning, oscillations in the look-ahead distance occur due to the system’s rapid response to path curvature changes. This behavior reflects the adaptive adjustment of the look-ahead distance, ensuring stable path tracking control while maintaining consistent performance under varying conditions. The results highlight the inherent trade-off between response speed and smoothness in adaptive control strategies.

At the same time, relevant data recorded in real-time during the autonomous navigation operation of the crawler sprayer were statistically analyzed by randomly selecting five sets of operation rows. The results are shown in

Table 4. The test results of the automatic navigation operation.

Test No.	Maximum Deviation/cm	Absolute Average/cm	Proportion of Position Deviation Within 5 cm/%	Proportion of Position Deviation Within 10 cm/%
1	6.42	3.09	96.49	100
2	5.06	2.12	98.35	100
3	6.78	3.32	96.54	100
4	5.21	2.33	98.03	100
5	5.44	2.61	97.21	100
Average	5.78	2.69	97.32	100

. The maximum deviation during row-joining in autonomous navigation was 5.78 cm, with an average absolute error of 2.69 cm. The proportions of position deviations within ±5 cm and ±10 cm were 97.32% and 100%, respectively. Therefore, the performance of its autonomous navigation operation meets the requirements of the T/CAAMM 14-2018 General Technical Conditions for Retrofit Satellite Navigation and Automatic Driving Systems for Agricultural Machinery.

4. Conclusions

To enhance automation and intelligence in agricultural machinery for small plots in hilly and mountainous areas, this study focuses on a crawler sprayer. The design meets the requirements for scene positioning, path tracking, and autonomous navigation. An agricultural plant protection robot with a tracked chassis was developed, integrating an onboard industrial computer, sensors, a power system, and communication modules. A pure tracking motion control method based on adaptive look-ahead distance was proposed, enabling the sprayer to autonomously navigate and perform operations along planned paths with minimal human intervention.

In the research on the autonomous navigation control system for a tracked chassis, simulation results demonstrate that the control method based on adaptive look-ahead distance offers stronger anti-interference capability and more stable performance. During path tracking, the look-ahead distance adaptively adjusts according to the current position and reference path to optimize tracking parameters. Experimental results with the designed crawler sprayer show that at an operating speed of 0.7 m/s, the maximum position deviation is 4.08 cm, the average absolute error is 2.15 cm, and the standard deviation is 1.14 cm. On-line tests with initial position deviations of 0.5, 1.0, and 1.5 m resulted in on-line times of 7.45 s, 11.91 s, and 13.66 s, respectively, with corresponding on-line distances of 5.21 m, 8.34 m, and 9.56 m, and maximum overshoots of 6.4%, 10.5%, and 12.6%. In autonomous navigation tests, the maximum row-joining deviation is 5.78 cm, the average absolute error is 2.69 cm, and position deviations within ±5 cm and ±10 cm are 97.32% and 100%, respectively. The control accuracy satisfies the requirements for plant protection spraying operations.

Future work will focus on addressing the limitations of current agricultural machinery mathematical models and control strategies by implementing high-precision dynamic modeling and operational control that integrates agricultural practices with machinery. This will optimize the control accuracy of operational mechanisms and multi-machine coordination capabilities. Additionally, we plan to conduct multi-vehicle validation, full parameter space analysis, and long-term stability testing to validate and refine the research findings. Expected outcomes include high-precision dynamic models, multi-machine coordination control frameworks, agriculture-integrated control strategies, and multi-platform performance benchmarks, which will provide theoretical support and practical guidance for future agricultural machinery path tracking control design.