Error Threshold-Based Autonomous Navigation with Right-Angle Turning for Crawler-Type Combine Harvesters in Paddy Fields

Abstract

Crawler-type combine harvesters feature labor-intensive operation, tough steering and complex environments in paddy fields, necessitating reliable automatic operation to ensure efficient and complete harvesting. An error threshold-based autonomous navigation system for crawler-type combine harvesters was developed by using right-angle turning according to unilateral brake steering. Based on the chassis structure and working principles, a moving control system was designed to achieve automatic control of steering, speed and throttle. A global path planning method was proposed to generate a spiral path by giving reference points and operation directions. A path tracking method based on the error threshold was developed to calculate both lateral and heading errors in real-time, and we executed the adjustment strategy to ensure rapid alignment and high-precision tracking. A right-angle turning method was implemented to prevent missed cutting and crop damage by giving an adjustment distance. Field tests showed that the maximum lateral and heading errors for straight-line path tracking were 10.25 cm and 1.94°, respectively. The maximum lateral and heading errors for right-angle turning were 17.64 cm and −14.46°, respectively. It was concluded that the newly developed autonomous navigation system showed adequate path tracking accuracy and stability, meeting working requirements in crop harvesting.

1. Introduction

With the development of precision agriculture and smart agriculture, the automation and intelligence level of agricultural machinery has been continuously improving. Autonomous navigation serves as a key technology for modern agricultural machinery automation and intelligence, significantly reducing operator workload while enhancing operational quality and efficiency [1,2,3]. In the process of agricultural production, the working environment of harvesting machinery is relatively harsh, and the operation is relatively complex, making the demand for autonomous navigation more urgent. Crawler-type combine harvesters are widely used in paddy field harvesting due to their low ground pressure and strong traction capability [4]. Therefore, the development of an autonomous navigation for crawler-type combine harvester holds significant practical importance and broad application prospects.

In recent years, numerous scholars have conducted research on autonomous navigation for crawler-type agricultural machinery. In terms of moving control, steering control methods are generally designed based on the kinematic model of crawler chassis. Hu et al. [5] established a dual-wheel differential kinematic model for crawler vehicles with unilateral brake steering and developed a smooth steering method based on Pulse-Width Modulation (PWM). Ding et al. [6] used electromagnets to actuate clutch forks, controlling their on/off state via PWM-adjusted optocoupler relays to regulate the steering angle of a crawler-type rapeseed planter. Regarding path planning, scientific and efficient harvester routes can ensure full coverage of harvesting areas while minimizing compaction and non-working path lengths, thereby improving operational efficiency [7,8,9]. Wang et al. [10] proposed a hybrid path planning method combining nested and spiral approaches for polygonal fields, which reduced planning time by over 11% compared to nested algorithms and decreased non-working path length by approximately 18% compared to mixed inner-spiral and reciprocating methods. Lu et al. [11] extracted field boundaries from satellite images using the canny algorithm, approximated these boundaries as polygons, and achieved edge offsetting for fields and obstacles based on straight skeleton principles. Their path planning method enabled combine harvesters to perform coverage path planning in irregular or obstructed fields. For path tracking, control algorithms mainly include pure pursuit control, Proportional-Integral-Derivative (PID) control, and Model Predictive Control (MPC). Takai et al. [12,13] developed a navigation control algorithm for crawler tractors using Real-Time Kinematic Global Positioning System (RTK-GPS) and Inertial Measurement Unit (IMU) as navigation sensors. Steering control and autonomous navigation tests demonstrated lateral errors of 1–3 cm at various speeds, with successful multi-path navigation. Kurita et al. [14] designed an autonomous driving system for rice harvesters using pure pursuit algorithms to achieve spiral-pattern full-field harvesting, maintaining straight-line tracking errors below 10 cm at 0.6 m/s. Wang et al. [15,16,17,18] implemented adaptive pure pursuit controllers on crawler-type sprayers, tractors, and rapeseed planters, enabling automatic look-ahead distance adjustment to improve tracking accuracy and stability. He et al. [19] enhanced PID path tracking by incorporating virtual steering angles, proposing a dual-PID control method with preview tracking that achieved precise path tracking for crawler peanut harvesters via pulse-width controllers. Zhang et al. [20] developed an adaptive path tracking and control system for crawler harvesters, combining multi-parameter optimization feedback with nonlinear PID steering control to enhance dynamic performance and steady-state accuracy. Zhou et al. [21] integrated genetic algorithms with MPC, using genetic algorithms to compute optimal time-domain parameters based on real-time speed, vehicle posture, and road conditions for adaptive MPC. Results showed rapid deviation correction and stable path tracking. Xu et al. [22] proposed an efficiency-oriented MPC algorithm, demonstrating an 8.56% improvement in operational efficiency compared to traditional Nonlinear Model Predictive Control (NMPC).

Existing studies primarily focus on general navigation algorithms or idealized crawler chassis models, while limited attention has been given to the combined effects of paddy fields conditions, frequent right-angle turning, and continuous harvesting requirements. To solve the above problems, this research uses a unilateral brake steering crawler-type combine harvester as the platform to develop an autonomous navigation system, investigate research on path planning and navigation control, and conduct full-field navigation performance tests in paddy fields to verify the path tracking accuracy and stability of the system.

2. Materials and Methods

The platform used in this research is the Lovol 4LZ-7G2A crawler-type combine harvester (Weichai Lovol Intelligent Agricultural Technology Co., Ltd. in Weifang, China), which is equipped with a unilateral brake steering crawler chassis, an automatic transmission device and an automatic throttle device. Its key parameters are shown in

Table 1. Key parameters of the Lovol 4LZ-7G2A crawler-type combine harvester.

Parameter	Value
Engine power (ps)	140
Cutting width (m)	2.3
Feeding capacity (kg/s)	7
Machine weight (kg)	3890
Dimensions (m × m × m)	6.2 × 2.75 × 2.9
Track gauge (m)	1.2
Grain tank capacity (m)	1.6

.

The autonomous navigation system for the crawler-type combine harvester primarily consists of a positioning and orientation receiver, a navigation control terminal, a navigation controller, and a moving control system, as shown in Figure 1. The positioning and orientation receiver integrates the UM982 dual-antenna positioning board and the JY61P IMU. The UM982 supports Real-Time Kinematic (RTK) positioning and dual-antenna orientation calculation, with horizontal positioning accuracy of 0.8 cm + 1 ppm, vertical positioning accuracy of 1.5 cm + 1 ppm, and orientation accuracy of 0.2° (1 m baseline). The JY61P compensates for positioning errors induced by machine pitch and roll, with a measurement range of ±180° on the X and Z axes, ±90° on the Y axis, and an accuracy of 0.2° for the X and Y axes and 1° for the Z axis. The navigation control terminal receives position, heading, and attitude data via the RS-232 serial port to perform navigation operations including parameter configuration, path planning, and process monitoring. The navigation controller, with the PIC18F258 microcontroller as its core processor, processes data and executes navigation algorithms while transmitting commands to the moving control system. The moving control system receives instructions from the navigation controller through the Controller Area Network (CAN) bus and controls the solenoid directional valve, automatic transmission device, and automatic throttle device to enable the crawler-type combine harvester to operate in the desired state.

Manual operation experienced drivers maintain the maximum lateral tracking error and heading error within 15 cm and 5° for straight-line path tracking, 20 cm and 10° for right-angle turning, respectively. The error threshold-based navigation system proposed in this research needed to demonstrate superior performance better than manual operation in terms of lateral and heading errors for straight driving and turns.

During the steering of the crawler-type combine harvester, the linear velocity of the steering-side track is 0, while the linear velocity of the opposite-side track remains constant, with the steering center located at the outer edge of the steering-side track. The following assumptions for simplifying the kinematic mode are made: (1) The center of mass coincides with the geometric center; (2) The steering angular velocity and resistance coefficient remain constant; (3) Slippage and skidding between the tracks and the ground are neglected. The kinematic model of the crawler-type combine harvester is established in the coordinate system NOE, as shown in Figure 2.

The kinematic equation for the crawler-type combine harvester is calculated:

$$\left(\begin{array}{c}{v}_c\\ \omega \end{array}\right)=\left(\begin{array}{c}{\displaystyle \frac{v_l+v_r}{2}}\\ {\displaystyle \frac{v_r-v_l}{a}}\end{array}\right)$$

(1)

When the crawler-type combine harvester turns left, the left track is fully braked, while the right track maintains propulsion. The kinematic equation under this condition is derived as follows:

$$\left(\begin{array}{c}{v}_c\\ \omega \end{array}\right)=\left(\begin{array}{c}{\displaystyle \frac{v_r}{2}}\\ {\displaystyle \frac{v_r}{a}}\end{array}\right)$$

(2)

The steering angle θ of the crawler-type combine harvester is proportional to the energization time t of the solenoid coil in the solenoid directional valve, with the proportionality coefficient being the steering angular velocity ω. To achieve flexible steering in complex field operating environments, the steering control module should be capable of controlling the crawler-type combine harvester to turn at various amplitudes. This study employs N-channel Metal Oxide Semiconductor (NMOS) electronic switch modules to control the energization time of the solenoid coil. The module supports PWM signal triggering with a frequency range from 0 to 20 kHz.

The steering control module primarily consists of a steering controller, two electronic switch modules, and a solenoid directional valve. The steering controller uses a PIC18F258 microcontroller (Microchip Technology Inc., Chandler, AZ, USA) as the core processor, with the PCA82C250 (NXP Semiconductors N.V., Eindhoven, The Netherlands) providing the CAN bus physical interface. Based on the steering commands issued on the CAN bus, it outputs PWM pulse signals with corresponding frequencies and duty cycles to control the electronic switch module, thereby adjusting the energization time of the solenoid coil and achieving flexible control of the steering action. If the steering controller outputs a PWM signal with frequency f and duty cycle D, the steering angle θ of the crawler-type combine harvester can be derived from the kinematic model as follows:

$$\theta =\omega t={\displaystyle \frac{2D{v}_c}{af}}={\displaystyle \frac{D{v}_r}{af}}$$

(3)

Since crawler slip and skid were inevitable in the paddy field, assumptions were given to create an ideal kinematic model for navigation control according to geometric dimensions of the Lovol 4LZ-7G2A combine harvester.

The diagram of the steering control module is shown in Figure 3. When output C0 is high and C1 is low, electronic switch module A activates for a left turn; the reverse activates electronic switch module B for a right turn; both low results in straight travel.

2.1. Path Planning

The spiral path is widely used in the working process of crawler-type combine harvesters due to its characteristics of continuous operation without headland turns and high field coverage efficiency [23,24,25,26]. After completing operations in the previous work area, the crawler-type combine harvester will enter the current work area via headland roads or by crossing field ridges, and different entry methods will result in different starting positions and directions for the operation. To address this issue, this study proposed a spiral path planning method to achieve complete field harvesting.

It can be seen from Figure 4 that the position coordinates of reference points A, B, and C are obtained to determine the rectangular working area Z₁Z₂Z₃Z₄. Taking Figure 4a as an example, point A is 0.5W away from both boundary lines Z₁Z₂ and Z₂Z₃, point B is 0.5W away from both boundary lines Z₂Z₃ and Z₃Z₄, and point C is 0.5W away from boundary line Z₁Z₄, where W is the working width of the crawler-type combine harvester. For clarity of description, the total number of paths is defined as N, with the nth path being P_n−1P_n and its length as L_n. The coordinates of the starting point P_n−1 and the endpoint P_n are (E_n−1, N_n−1) and (E_n, N_n), respectively. The path P₀P₁ is the baseline AB with length L₁; path P₁P₂ is perpendicular to path P₀P₁, with its length L₂ equal to the distance from point C to the baseline AB. In the planned spiral paths, adjacent paths are connected end-to-end and perpendicular to each other, with each completed loop contracting inward by the working width. Since the width of the working area is not exactly an integer multiple of the working width, when the crawler-type combine harvester completes the harvesting along path P_N−3P_N−2, the width of the unharvested area will be less than the working width. In this case, the length L_N−1 of path P_N−2P_N−1 is planned as half of the length L_N−3 of path P_N−4P_N−3, while the length L_N of path P_N−1P_N is planned to be equal to the length L_N−2 of path P_N−3P_N−2.

From these path characteristics, it can be seen that the relative positions of reference points A, B, and C determine the type of the planned spiral paths. Therefore, it is necessary to evaluate the length relationship between L₁ and L₂, as well as the positional relationship between point C and the baseline AB.

L₁ and L₂ are calculated by Equation (4) and Equation (5), respectively:

$$L_1=\sqrt{{(E_0-E_1)}^2+{(N_0-N_1)}^2}$$

(4)

$$L_2={\displaystyle \frac{\left|(E_1-E_0)(N_C-N_0)-(E_C-E_0)(N_1-N_0)\right|}{\sqrt{{(E_1-E_0)}^2+{(N_1-N_0)}^2}}}$$

(5)

where (E₀, N₀) is the coordinate of point P₀ (A), (E₁, N₁) is the coordinate of point P₁ (B), and (E_C, N_C) is the coordinate of point C.

When L₁ < L₂, the total number N of paths and the length L_n of the nth path are determined by Equation (6) and Equation (7), respectively:

$$N=2⌈{\displaystyle \frac{L_1}{W}}⌉+2$$

(6)

$$L_n=\left\{\begin{array}{ll}{L}_1& n=1\\ L_2-{\displaystyle \frac{n-2}{2}}W& n=2,4,\dots ,N-2\\ L_1-{\displaystyle \frac{n-3}{2}}W& n=3,5,\dots ,N-3\\ {\displaystyle \frac{1}{2}}(L_1-{\displaystyle \frac{N-6}{2}}W)& n=N-1\\ L_2-{\displaystyle \frac{N-4}{2}}W& n=N\end{array}\right.$$

(7)

when L₁ ≥ L₂, the total number N of paths and the length L_n of the nth path are given by Equation (8) and Equation (9), respectively:

$$N=2⌈{\displaystyle \frac{L_2}{W}}⌉+1$$

(8)

$$L_n=\left\{\begin{array}{ll}{L}_1& n=1\\ L_2-{\displaystyle \frac{n-2}{2}}W& n=2,4,\dots ,N-3\\ L_1-{\displaystyle \frac{n-3}{2}}W& n=3,5,\dots ,N-2\\ {\displaystyle \frac{1}{2}}(L_2-{\displaystyle \frac{N-5}{2}}W)& n=N-1\\ L_1-{\displaystyle \frac{N-5}{2}}W& n=N\end{array}\right.$$

(9)

The positional relationship between point C and baseline AB can be represented by the parameter C_AB, which is calculated as follows:

$$C_{AB}=(N_1-N_0)E_C+(E_0-E_1)N_C+E_1{N}_0-E_0{N}_1$$

(10)

When C_AB < 0, the working direction is to the left, and the planned path follows a counterclockwise spiral path; when C_AB > 0, the working direction is to the right, and the planned path follows a clockwise spiral path.

To calculate the endpoint coordinates of each path, it is necessary to determine the direction angle Ψ_AB of vector $\overrightarrow{\mathrm{AB}}$. The direction angle uses the true north direction of the UTM coordinate system as the 0° reference, increases clockwise, and has a range of 0–360°. Ψ_AB is calculated as follows:

$${\Psi }_{AB}=\left\{\begin{array}{ll}{\cos }^{-1}{\displaystyle \frac{N_1-N_0}{L_1}}\hfill & E_0\le E_1\hfill \\ 360-{\cos }^{-1}{\displaystyle \frac{N_1-N_0}{L_1}}\hfill & E_0>E_1\hfill \end{array}\right.$$

(11)

The coordinate of the endpoint P_n for path P_n−1P_n is calculated as follows:

$$\left\{\begin{array}{c}{E}_n=E_0+{\displaystyle \sum _{i=1}^n{L}_i\sin ({\Psi }_{AB}\pm \frac{i-1}{2}\pi )}\\ N_n=N_0+{\displaystyle \sum _{i=1}^n{L}_i\cos ({\Psi }_{AB}\pm \frac{i-1}{2}\pi )}\end{array}\right.$$

(12)

where the “±” sign is determined by the working direction: it is positive when C_AB > 0 and negative when C_AB < 0.

The linear equation for path P_n−1P_n is shown as follows:

$$\left\{\begin{array}{l}{A}_{n}E+B_{n}N+C_n=0\hfill \\ A_n=N_n-N_{n-1}\hfill \\ B_n=E_{n-1}-E_n\hfill \\ C_n=E_n{N}_{n-1}-E_{n-1}{N}_n\hfill \end{array}\right.$$

(13)

where A_n and B_n are the coefficients of the linear equation for path P_n−1P_n, and C_n is the constant term.

2.2. Straight-Line Path Tracking

The crawler-type combine harvester’s current position and heading exhibit randomness. To achieve rapid path alignment and ensure accurate operation, this study developed a path tracking method based on error thresholds. This method calculates the lateral error d_e and heading error θ_e in real time, determines the threshold range for the errors, and executes corresponding adjustment strategies. The lateral error represents the offset between the current position and the current path, while the heading error represents the angular difference between the current heading and current path direction. By convention, both d_e and θ_e are defined as positive when the harvester is to the right of the current path with clockwise heading offset, and negative otherwise.

When lateral error is relatively small (|d_e| ≤ d_e3), intermittent adjustments are sufficient to meet straight-line path tracking accuracy requirements. Specifically: if |d_e| ≤ d_e1 and |θ_e| ≤ θ_e1, the crawler-type combine harvester achieves path alignment without requiring adjustment; if |d_e| ≤ d_e1 but θ_e1 < |θ_e| ≤ θ_e2, small heading-based adjustments are applied; when d_e1 < |d_e| ≤ d_e2 with |θ_e| ≤ θ_e2, small lateral-based adjustments are executed; for d_e2 < |d_e| ≤ de₃ while |θ_e| ≤ θ_e2, large lateral-based adjustments are implemented. Special cases occur when |d_e| ≤ d_e3 and |θ_e| > θ_e2: if deθ_e > 0, large lateral-based adjustments are performed, whereas if deθ_e < 0, traveling straight can quickly corrects the lateral error until d_eθ_e > 0. d_e1, d_e2, d_e3 represent the first, second and third lateral error thresholds, while θ_e1 and θ_e2 denote the first and second heading error thresholds, respectively, which were determined empirically through field tests to balance between tracking accuracy and operational smoothness. d_e1, d_e2, d_e3, θ_e1, and θ_e2 are all positive values, and d_e1 < d_e2 < d_e3, θ_e1 < θ_e2. The complete intermittent adjustment strategy is detailed in

Table 2. Intermittent adjustment strategy.

	de	[−de3, −de2)	[−de2, −de1)	[−de1, 0)	(0, de1]	(de1, de2]	(de2, de3]
θe
(−∞, −θe2)		LR	LR	LR	N	N	N
[−θe2, −θe1)		LR	SR	SR	SR	SL	LL
[−θe1, 0)		LR	SR	N	N	SL	LL
(0, θe1]		LR	SR	N	N	SL	LL
(θe1, θe2]		LR	SR	SL	SL	SL	LL
(θe2, +∞)		N	N	N	LL	LL	LL

where SL means small left adjustment; LL means large left adjustment; SR means small right adjustment; LR means large right adjustment; N means traveling straight.

.

When the lateral error is relatively large (|d_e| > d_e3), adopting the intermittent adjustment strategy would result in an excessively long alignment distance, adversely affecting work efficiency. Therefore, a “Turn-Straight-Turn” adjustment strategy is implemented for rapid path alignment.

As shown in Figure 5, the crawler-type combine harvester at the position P has a direction angle of Ψ_V, with lateral error d_e and heading error θ_e relative to the current path P_n−1P_n. The target point T on the current path is determined based on the look-ahead distance l_d. In stage 1, the crawler-type combine harvester performs a pivot turn, while the navigation control terminal calculates Ψ_V and the direction angle Ψ_PT of $\overrightarrow{\mathit{PT}}$ in real time until the stage 1 termination condition is met. In stage 2, the harvester travels straight along PT to rapidly reduce the lateral error until the stage 2 termination condition is satisfied. In stage 3, the harvester performs a pivot turn to correct the heading error until the stage 3 termination condition is fulfilled. After completing the “Turn-Straight-Turn” adjustment, the system returns to the error judgment process.

The termination condition for stage 1 is given by Equation (14) as follows:

$$\left\{\begin{array}{cc}{\Psi }_V\ge {\Psi }_{PT}& d_e<0\\ {\Psi }_V\le {\Psi }_{PT}& d_e>0\end{array}\right.$$

(14)

The termination condition for stage 2 is specified by Equation (15) as follows:

$$\left\{\begin{array}{cc}{d}_e\ge {\displaystyle \frac{a}{2}}(\cos \left|{\theta }_e\right|-1)+b\sin \left|{\theta }_e\right|& {\theta }_e>0\\ d_e\ge {\displaystyle \frac{a}{2}}(1-\cos \left|{\theta }_e\right|)-b\sin \left|{\theta }_e\right|& {\theta }_e<0\end{array}\right.$$

(15)

where b represents the distance between the positioning and orientation receiver and the geometric center of the crawler-type combine harvester.

The termination condition for stage 3 is defined by Equation (16) as follows:

$$\left|{\theta }_e\right|\le {\theta }_{e1}$$

(16)

2.3. Right-Angle Turning

The crawler-type combine harvester must execute a right-angle turn at the endpoint of the current path to transition between rows. The right-angle turning process can be simply described as a five-step sequence: forward, turn, backward, turn, and forward. The trajectory of the crawler-type combine harvester during this process is shown in Figure 6.

When the harvester reaches the endpoint P_m of the current path P_m−1P_m (where m ∈ N* and m < N), it maintains straight forward motion while the navigation control terminal calculates the distance D₁′ between the current position and point P_m. If D₁′ ≥ D₁, the harvester performs the first 45° pivot turn in the working direction and stops, where D₁ is the first theoretical distance set. The harvester then reverses along FG while the navigation control terminal calculates the distance D₂′ between the current position and path P_m−1P_m. If D₂′ ≥ D₂, the harvester stops, where D₂ is the second theoretical distance set. The harvester switches back to forward motion while performing the second 45° pivot turn in the working direction. The current path is updated to P_mP_m+1, and the system returns to the straight-line path tracking process. The crawler-type combine harvester reaches the starting point P_m of the path P_mP_m+1, and the right-angle turning process is completed. The flowchart of the right-angle turning is presented in Figure 7.

Considering the slip and skid effects between the tracks and soil during actual turning maneuvers, significant variations may occur in right-angle turning errors [11,19,23,24]. Excessive errors can lead to prolonged alignment distances, resulting in unharvested areas and crop damage. Therefore, when completing the right-angle turning, an adjustment distance d should be reserved between the header’s front edge and the starting point P_m of the next path. Based on the trajectory characteristics of right-angle turning, D₁ and D₂ are calculated by Equation (17) and Equation (18), respectively.

$$D_1=2b+c+d$$

(17)

$$D_2={\displaystyle \frac{\sqrt{2}}{4}}a+{\displaystyle \frac{2-\sqrt{2}}{2}}b+c+d$$

(18)

3. Results and Discussion

To evaluate the accuracy and stability of the developed autonomous navigation system for the crawler-type combine harvester, field tests were conducted in Hangzhou, Zhejiang Province, in October 2024. The test area featured mature rice crops in a waterlogged field with clayey and wet soil, as shown in Figure 8.

For path planning in the test area, the reference points A (732,399.72, 3,345,049.47), B (732,379.61, 3,345,021.09), and C (732,368.37, 3,345,028.84) under the UTM reference system were acquired, with distances of 34.78 m between point A and B, and 13.73 m between point C and baseline AB. The main parameters set for the test were as follows: working width W of 2 m, test speed of 0.8 m/s, sampling frequency of 10 Hz, the first lateral error threshold d_e1 of 10 cm, the second lateral error threshold d_e2 of 20 cm, the third lateral error threshold d_e3 of 30 cm, the first heading error threshold θ_e1 of 1.5°, and the second heading error threshold θ_e2 of 5°. The PWM signal frequency and duty cycle for small adjustments were 0.7 Hz and 20%, respectively, while those for large adjustments were 1 Hz and 50%, with a 100% duty cycle for pivot turns. The positioning and orientation receiver and directional antenna were mounted above the cabin, at the front and rear, respectively. The autonomous navigation mode was activated at the navigation starting point, enabling the crawler-type combine harvester to autonomously complete the processes of path alignment, straight-line path tracking, and right-angle turnings along the planned spiral path until it automatically stopped at the navigation endpoint. During the test, the navigation control terminal recorded the moving trajectory and calculated lateral and heading errors in real time. The navigation map and actual navigation trajectory are shown in Figure 9.

3.1. Evaluation of Straight-Line Path Tracking Performance

In straight-line path tracking, the errors displayed a sawtooth-like pattern due to field surface undulations and steering adjustments as shown in Figure 10. Positive lateral errors significantly outnumbered the negative values, primarily due to the rightward offset of the crawler-type combine harvester’s center of gravity, induced by the heavy grain tank, which results in more pronounced subsidence of the right-side track. Furthermore, the wet and slippery paddy soil conditions reduce the track’s lateral adhesion capability, leading to a consistent rightward sliding tendency of the harvester. A comparison between lateral and heading errors reveals that adjustments are typically triggered when the heading error reaches the predefined threshold, effectively suppressing further increases in lateral error and improving straight-line path tracking accuracy.

The mean value of absolute tracking errors in straight was statistically analyzed using the average value, maximum value, and RMS (Root Mean Square) error as metrics to evaluate the accuracy and stability of straight-line path tracking. The statistical results of the straight-line path tracking errors are presented in

Table 3. Statistics of straight-line path tracking errors.

Path	Lateral Error (cm)			Heading Error (°)
	Average	Maximum	RMS	Average	Maximum	RMS
P0P1	2.74	7.52	3.35	0.46	1.29	0.58
P1P2	2.71	9.77	3.36	1.07	1.71	1.14
P2P3	3.69	10.25	4.8	0.64	1.94	0.78
P3P4	5.19	7.83	5.38	0.56	1.8	0.71
P4P5	3.12	7.72	3.57	0.67	1.73	0.78
P5P6	3.31	9.11	4.11	0.71	1.15	0.73
P6P7	2.28	7.3	2.61	0.5	1.49	0.64
P7P8	3.91	9.95	5	1.18	1.47	1.19
P8P9	2.79	7.3	3.48	0.7	1.47	0.79
P9P10	1.58	4	1.86	1.07	1.44	1.1
P10P11	1.9	7.65	2.4	0.72	1.44	0.78
P11P12	6.19	8.38	6.26	0.66	0.97	0.67
P12P13	3.3	9.83	3.98	0.56	1.65	0.67
P13P14	6.44	8.39	6.48	0.44	0.95	0.5

.

The maximum average lateral and heading errors were 6.44 cm and 1.18°, respectively. The maximum lateral and heading errors were 10.25 cm and 1.94°, respectively. And the maximum RMS lateral and heading errors were 6.48 cm and 1.19°, respectively. For the path P₀P₁~P₁₀P₁₁, the lateral error and heading error of each path were similar, with no obvious variation pattern. For the path P₁₁P₁₂~P₁₄P₁₅, the straight-line path tracking accuracy of P₁₂P₁₃ and P₁₄P₁₅ was relatively poor. This is due to the shorter path length, as the crawler-type combine harvester reaches the alignment condition when it is close to the path’s endpoint, and the error is not further reduced. These results demonstrated that the crawler-type combine harvester, equipped with the autonomous navigation system, achieves high accuracy and stability in straight-line tracking.

3.2. Evaluation of Right-Angle Turning Performance

The peak error occurs at the beginning of straight-line path tracking. Due to the presence of the adjustment distance, the crawler-type combine harvester has not yet reached the endpoint of the right-angle turning at this time, so the peak error cannot be used as the evaluation metric for right-angle turning performance. When the crawler-type combine harvester completes the right-angle turning, the header begins harvesting rice, and the error at this moment can be used as the right-angle turning error to evaluate the turning accuracy. Additionally, the alignment time and alignment distance are used to evaluate the timeliness of the crawler-type combine harvester’s adjustment after the right-angle turning. Here, the alignment time and alignment distance represent the time and travel distance required from the completion of the right-angle turning until the error meets the alignment condition and remains stable. The right-angle turning performance is shown in Figure 11.

During the test, a total of 14 right-angle turnings were performed, and the recorded errors and alignment status are shown in

Table 4. Statistics of right-angle turning errors.

Number	Lateral Error (cm)	Heading Error (°)	Alignment Time (s)	Alignment Distance (m)
1	7.13	−0.94	0	0
2	17.64	0.61	3.8	3.04
3	13.53	−3.54	3.6	2.88
4	−6.87	−14.46	4	3.2
5	6.85	−2.09	0.6	0.48
6	9.35	−1.15	0	0
7	8.95	−1.21	0	0
8	7.64	−2.32	2	1.6
9	0.41	3.13	1	0.8
10	2.08	2.44	0.8	0.64
11	7.36	−2.65	3.2	2.56
12	14.18	0.32	3.2	2.56
13	−8.79	2.29	1.4	1.12
14	8.39	9.1	2.8	2.24

. The maximum lateral and heading errors for the right-angle turning were 17.64 cm and −14.46°, respectively, while the minimum values were 0.41 cm and 0.32°, indicating significant variations in turn accuracy between rows. The primary reasons are Under wet soil conditions, the intensified slippage of the inner track and skidding of the outer track during pivot turns shift the steering center away from the track’s outer edge. (2) Turning resistance varies substantially across different field zones and changes dynamically during maneuvers. (3) The hydraulic-powered steering cylinder exhibits response delays relative to control signals, resulting in imprecise angle control. The heading error of the number 4 right-angle turning is significantly higher than that of the other right-angle turnings, as the harvester is in the stage 2 of the “Turn-Straight-Turn” adjustment strategy and has not yet undergone heading correction. Additionally, the positive values of the right-angle turning error in the crawler-type combine harvester were greater than the negative values, which is mainly caused by the first theoretical distance D₁ being set too small or the second theoretical distance D₂ being set too large. However, due to the interaction between the wet and slippery soil and the tracks, as well as the offset of the combine harvester’s center of gravity, it is difficult to determine the ideal values for the first and second theoretical distances. The maximum alignment time and alignment distance were 4 s and 3.2 m, respectively, indicating that the crawler-type combine harvester could rapidly meet the alignment condition and maintain stable operation, even when the right-angle turning accuracy was slightly compromised.

These factors indicated the limitations of the simplified kinematic model, which neglects slip and dynamic load variations. Those represent key targets for future system improvement. Nevertheless, the implemented error-threshold-based control strategy, combined with the empirical adjustment distance (d), demonstrated robustness in managing these disturbances, allowing the harvester to quickly re-align and continue stable operation after turns. Field tests results demonstrated that the developed autonomous navigation system for the crawler-type combine harvester achieves high navigation accuracy and stability, meeting the requirements of practical field operations.

4. Conclusions

In this research, the autonomous navigation system was developed to realize autonomous operation in paddy fields for a crawler-type combine harvester. Adaptive path planning, a dual-mode tracking strategy for brake-steering dynamics, and automation of right-angle turns were described to ensure harvesting performance. The error-threshold-based control logic not only ensured high tracking accuracy but also provided inherent robustness against high-frequency noise from navigation sensors. The straight-line tracking algorithm ensured high path-tracking accuracy despite soil slip and chassis asymmetry, through a combination of a multi-level error threshold adjustment strategy and a rapid alignment procedure. The adjustment distance in right-angle turns was optimized to effectively reduce cutting misses and crop damage. By enabling continuous spiral movement with reliable straight-line tracking and right-angle turning, the developed system is expected to reduce unnecessary passes and excessive maneuvering during harvesting operations. The developed navigation system does not require changes to the parameters of the working unit or field layout. The additional travel distance caused by the turning trajectory is limited and acceptable for improvement of operational stability and harvesting quality. Field test results showed that the maximum lateral and heading errors for the right-angle turning were 10.25 cm and 1.94° for straight-line tracking, 17.64 cm and −14.46° for right-angle turning, respectively, which indicated that stable and accurate performance was achieved by the developed autonomous navigation system across the entire harvesting process, demonstrating superior performance better than manual operation in terms of lateral and heading errors for straight driving and turns.

Nevertheless, this research is limited by the absence of comparisons with classical control algorithms and the use of a simplified kinematic model that omits dynamic slip. Future work will focus on adaptive determination of turning parameters under varying soil properties, reducing hydraulic steering lag, and integrating the navigation module with real-time harvesting logistics such as grain unloading to support fully autonomous field operation.