In modern agriculture, the integration of advanced robot technology has become a pivotal focus for enhancing efficiency, precision, and sustainability. Traditional manual operation of agricultural machinery relies heavily on the subjective experience of drivers, which can lead to inconsistencies, especially during peak farming seasons when high workloads increase operational difficulty and reduce accuracy. This often results in safety concerns and suboptimal resource utilization. To address these challenges, we have developed an autonomous driving control system for wheeled robots in agricultural machinery, leveraging cost-effective microcontroller platforms like the STM32F107. This system comprises an ARM control core, positioning data acquisition and recording modules, steering control modules, and interface circuits, enabling real-time position tracking and automated path following. By utilizing robot technology, our approach aims to minimize human intervention, improve operational precision, and contribute to the broader adoption of smart farming practices. In this article, we present a comprehensive study on path planning and tracking methodologies, incorporating mathematical models, control algorithms, and experimental validation to demonstrate the effectiveness of our autonomous navigation system.
The core of our research involves two main aspects: path planning based on two-dimensional coordinate systems and path tracking using dynamic and kinematic models. For path planning, we define operational paths within field boundaries, generating reference lines that guide the machinery during tasks such as plowing, seeding, and harvesting. This process includes straight-line segments for efficient coverage and smooth transitions for row-changing maneuvers, utilizing Bezier curves to ensure stability and reduce mechanical stress. In path tracking, we analyze the movement characteristics of agricultural machinery through a simplified two-wheel model, establishing relationships between steering angles and trajectory following. To handle real-world uncertainties, we implement a fuzzy control strategy that adjusts steering based on path deviation and heading errors, simplifying complex computations into efficient table lookups. Our experiments, conducted on a custom-built model vehicle, validate the system’s performance, showing minimal lateral deviations and robust navigation capabilities. Throughout this work, we emphasize the role of robot technology in transforming agricultural practices, highlighting its potential to drive automation and intelligence in the sector.
Path planning is a critical component of autonomous agricultural operations, as it determines the efficiency and coverage of field tasks. We focus on straight-line path planning for rectangular fields, where the machinery follows the longer edges of the plot, turning at the headlands without performing operations to maintain quality. Given the field corners A, B, C, and D with coordinates $(x_a, y_a)$, $(x_b, y_b)$, $(x_c, y_c)$, and $(x_d, y_d)$, respectively, we derive the boundary equations. For instance, the line AB can be represented as:
$$ y = y_a + \frac{y_b – y_a}{x_b – x_a} (x – x_a) $$
Similarly, other boundaries are defined, and the operational paths are generated by offsetting these lines based on the working width $h$. For a path parallel to AB, the equation becomes:
$$ y = y_a + \frac{y_b – y_a}{x_b – x_a} (x – x_a) + \frac{h}{\cos(\arctan((y_b – y_a) / (x_b – x_a)))} $$
This approach ensures that all paths are evenly spaced and cover the entire field without overlaps or gaps. To handle row-changing transitions, we employ a fish-tail pattern, which reduces land waste compared to semi-circular turns. However, abrupt curvature changes can affect stability, so we incorporate Bezier curves for smooth interpolation. An n-th order Bezier curve is defined recursively as:
$$ P_n^0 = (1 – t) P_{n-1}^0 + t P_{n-1}^1 \quad \text{for } t \in [0,1] $$
For control points $P_0$ to $P_n$, the general formula is:
$$ B(t) = \sum_{i=0}^{n} \binom{n}{i} P_i (1 – t)^{n-i} t^i \quad \text{for } t \in [0,1] $$
The curvature at the start point is given by:
$$ k = \frac{(n-1) | (P_1 – P_0) \times (P_2 – P_1) |}{n |P_1 – P_0|^3} $$
Using a fourth-order Bezier curve, we achieve smooth transitions that minimize jerks and enhance operational continuity. This path planning strategy, rooted in computational geometry, exemplifies how robot technology can optimize agricultural workflows by ensuring precise and efficient route generation.
To evaluate the effectiveness of different path planning parameters, we consider field dimensions and working widths. The table below summarizes key variables in path planning:
| Parameter | Symbol | Description |
|---|---|---|
| Field Length | $L_f$ | Length of the field along the longer edge |
| Working Width | $h$ | Distance between adjacent paths |
| Number of Paths | $N_p$ | Total paths generated for coverage |
| Bezier Order | $n$ | Order of the Bezier curve for smoothing |
Path tracking is essential for ensuring that the agricultural machinery follows the planned routes accurately. We begin by modeling the machinery as a two-wheel system, which simplifies the analysis of lateral and yaw motions while retaining key dynamic characteristics. Let $(x_s, y_s)$ and $(x_d, y_d)$ denote the coordinates of the front and rear wheels, respectively, with speeds $v_s$ and $v_d$. The rear wheel side force $F_r$, front wheel side force $F_b$, front wheel steering angle $\delta_s$, yaw angle $a_h$, yaw rate $\omega_h$, sideslip angle $a_c$, front wheel sideslip angle $a_b$, rear wheel sideslip angle $a_r$, and steering angle $\delta$ are defined. The longitudinal velocity is $v_z$, lateral velocity $v_h$, and distances from the center of mass to the front and rear wheels are $a$ and $b$, respectively. The turning radius is $R$, mass is $m$, and rotational inertia is $I_z$. The dynamic equations are:
$$ F_b \cos \delta + F_r = m (\dot{v}_h + v_z \omega_h) $$
$$ a F_b \cos \delta – b F_r = I_z \dot{\omega}_h $$
For small angles, the sideslip angles approximate to:
$$ a_b \approx \delta – \frac{v_h + a \omega_h}{v_z} $$
$$ a_r \approx -\frac{v_h – b \omega_h}{v_z} $$
Defining the state vector as $\mathbf{x} = [x, y, a_h, v_h, \omega_h]^T$, the dynamic model becomes:
$$ \begin{bmatrix} \dot{v}_h \\ \dot{\omega}_h \\ \dot{y} \\ \dot{a}_h \end{bmatrix} = \begin{bmatrix} -\frac{C_b + C_r}{m v_z} & -\frac{a C_b + b C_r}{m v_z^2} – v_h & 0 & 0 \\ -\frac{a C_b + b C_r}{v_z I_z} & -\frac{a^2 C_b – b^2 C_r}{v_z I_z} & 0 & 0 \\ 1 & 0 & 0 & v_z \\ 0 & 1 & 0 & 0 \end{bmatrix} \begin{bmatrix} v_h \\ \omega_h \\ y \\ a_h \end{bmatrix} + \begin{bmatrix} \frac{C_b}{m} \\ \frac{a C_b}{I_z} \\ 0 \\ 0 \end{bmatrix} \delta $$
The kinematic model, under ideal conditions, is derived from the geometry of the system. The rear wheel velocity $v_d$ is:
$$ v_d = \dot{x}_d \cos a_r + \dot{y}_d \sin a_r $$
With constraints for front-wheel steering:
$$ \dot{x}_d \sin a_r = \dot{y}_d \cos a_r $$
$$ \dot{x}_s \sin(a_r + \delta_s) = \dot{y}_d \cos(a_r + \delta_s) $$
The positions relate as:
$$ x_s = x_d + (a + b) \cos a_r $$
$$ y_s = y_d + (a + b) \sin a_r $$
$$ \delta_s = \arctan\left(\frac{a + b}{R}\right) $$
Thus, the kinematic model is:
$$ \begin{bmatrix} \dot{x}_d \\ \dot{y}_d \\ \dot{a}_r \end{bmatrix} = \begin{bmatrix} \cos a_r \\ \sin a_r \\ \frac{\tan \delta_s}{a + b} \end{bmatrix} v_d $$
For path tracking, we employ a pure pursuit algorithm that computes the steering angle based on the deviation from the reference path. In this model, let $L$ be the wheelbase, $\phi$ the rear wheel steering angle, $R$ the turning radius, $L_d$ the look-ahead distance to the target point, $k$ the actual path curvature, and $\theta$ the heading error. The coordinates of the target point $A’$ are:
$$ x_g = R (1 – \cos \phi) $$
$$ y_g = R \sin \phi $$
From the Pythagorean theorem:
$$ L_d^2 = x_g^2 + y_g^2 $$
$$ R = \frac{L_d^2}{2 x_g} $$
The steering angle $\delta$ is derived as:
$$ \delta = \arctan\left( \frac{2L (d \cos \theta – \sqrt{L_d^2 – d^2} \sin \theta)}{L_d^2} \right) $$
where $d$ is the lateral deviation. The look-ahead distance $L_d$ significantly influences tracking performance; a smaller $L_d$ results in aggressive turning with potential oscillations, while a larger $L_d$ yields smoother but slower responses. Through simulations in MATLAB, we optimized $L_d$ to balance responsiveness and stability. This algorithmic approach underscores how robot technology enables precise control in dynamic environments.
To handle uncertainties and nonlinearities in real-field conditions, we implement a fuzzy control system. This method translates input variables like path deviation and heading error into steering adjustments using fuzzy logic, reducing computational load and enhancing robustness. The fuzzy control process involves fuzzification, rule evaluation, inference, and defuzzification. We define input and output variables with fuzzy sets: path deviation has members {LF, LM, LN, ZO, RN, RM, RF} for left-far, left-medium, left-near, zero, right-near, right-medium, and right-far deviations, ranging from -30 cm to 30 cm. Heading error has sets {LB, LM, LS, ZO, RS, RM, RB} for left-big to right-big errors, from -30° to 30°. The output steering angle uses {LH, LM, LS, ZO, RS, RM, RH} for left-high to right-high, from -30° to 30°. The fuzzy rules are summarized in the following table:
| Heading Error | Path Deviation | ||||||
|---|---|---|---|---|---|---|---|
| LF | LM | LN | ZO | RN | RM | RF | |
| LB | RH | RH | RH | RH | RM | ZO | ZO |
| LM | RH | RH | RM | RM | RS | ZO | ZO |
| LS | RH | RS | RS | RS | ZO | LS | LS |
| ZO | RM | RS | ZO | ZO | ZO | LS | LM |
| RS | RS | RS | ZO | LS | LS | LS | LH |
| RM | ZO | ZO | LS | LM | LM | LH | LH |
| RB | ZO | ZO | LM | LH | LH | LH | LH |
Using MATLAB, we generate a fuzzy control surface that maps inputs to outputs, facilitating real-time decision-making. This fuzzy system exemplifies the adaptability of robot technology in managing complex agricultural scenarios without requiring extensive computational resources.
For experimental validation, we constructed a model vehicle platform to test the autonomous navigation system. The vehicle features a three-layer structure with an STM32 development board mounted on top, dual L298N motor drivers, an ATK-1218-BD module for positioning, and integrated power, steering, and drive modules at the base. A navigation antenna is fixed atop the vehicle, and a receiver is attached at the rear. The system modules include the ARM control core for data processing, power supply, positioning data acquisition (fusing BDS and GPS signals), storage for environmental data, path tracking and steering correction, and communication for manual-automatic mode switching. This setup highlights the practical application of robot technology in developing scalable agricultural solutions.
We conducted straight-line path tracking tests by manually recording a reference path and then activating autonomous navigation. The system initialized in 4.4 seconds, and over a 100-second tracking period covering 61.8 meters at an average speed of 0.618 m/s, we measured lateral deviations at 100 points. The results show a maximum lateral deviation of 5.4 cm and an average absolute deviation of 1.281 cm, demonstrating high tracking accuracy. The table below summarizes key performance metrics:
| Metric | Value |
|---|---|
| Initialization Time | 4.4 s |
| Average Speed | 0.618 m/s |
| Maximum Lateral Deviation | 5.4 cm |
| Average Absolute Deviation | 1.281 cm |
| Tracking Duration | 100 s |
| Path Length | 61.8 m |
In conclusion, our research on autonomous driving control for agricultural wheeled robots demonstrates the efficacy of integrating path planning and tracking algorithms with fuzzy logic control. The use of Bezier curves for smooth transitions and a two-wheel model for dynamic analysis provides a solid foundation for precise navigation. The fuzzy control system, with its rule-based approach, efficiently handles real-world variability, reducing computational demands while maintaining accuracy. Experimental results confirm that our system achieves minimal deviations and reliable performance, underscoring the transformative potential of robot technology in agriculture. Future work will focus on scaling the system for larger machinery and incorporating additional sensors for enhanced environmental awareness. By advancing robot technology, we aim to contribute to more automated, efficient, and sustainable agricultural practices worldwide.