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Research progress on the slip ratio control methods for wheeled/tracked harvesters
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Yiyang Du1, 2, Wenxiang Xu2, Haolu Liu1, Xinyuan Yue2, Maohua Xiao2, *, Cheng Shen1, 3, *
International Journal of Agricultural and Biological Engineering | 2026, 19(3) : 20 - 30
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International Journal of Agricultural and Biological Engineering | 2026, 19(3): 20-30
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Research progress on the slip ratio control methods for wheeled/tracked harvesters
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Yiyang Du1, 2, Wenxiang Xu2, Haolu Liu1, Xinyuan Yue2, Maohua Xiao2, *, Cheng Shen1, 3, *
Affiliations
  • 1Nanjing Institute of Agricultural Mechanization, Ministry of Agriculture and Rural Affairs, Nanjing 210014, China
  • 2College of Engineering, Nanjing Agricultural University, Nanjing 211800, China
  • 3Key Laboratory of Modern Agricultural Equipment, Ministry of Agriculture and Rural Affairs, Nanjing 210014, China

    • Yiyang Du, MS, research interest: mechanization engineering, Email:

    Wenxiang Xu, PhD candidate, research interest: agricultural engineering, Email:

    Haolu Liu, Research Assistant, research interest: agricultural engineering, Email:

    Xinyuan Yue, MS, research interest: agricultural engineering, Email:

About Author:

Yiyang Du, MS, research interest: mechanization engineering, Email:

Wenxiang Xu, PhD candidate, research interest: agricultural engineering, Email:

Haolu Liu, Research Assistant, research interest: agricultural engineering, Email:

Xinyuan Yue, MS, research interest: agricultural engineering, Email:

Published: 2026-06-30 doi: 10.25165/j.ijabe.20261903.10583
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As a key piece of agricultural mechanization equipment, harvesters play a crucial role in improving agricultural productivity and operational quality. With the increasing complexity of operating environments, especially under hilly and mountainous terrain and on wet, slippery soils, harvester slip has become an increasingly prominent problem. Excessive slip seriously impairs traction efficiency, energy consumption, operational stability, and working quality, making slip-ratio control a core technology for addressing this challenge. This paper reviews slip control methods for harvesters under complex terrain conditions, including slip-ratio observation and estimation, slip prediction, and control strategies. Different categories of slip control methods and their current applications are discussed in detail. Existing limitations are analyzed, and future research directions are proposed to provide new technical support for improving the efficiency and stability of harvesters in complex operating environments.

slip ratio  /  slip control  /  harvester  /  path tracking
Yiyang Du, Wenxiang Xu, Haolu Liu, Xinyuan Yue, Maohua Xiao, Cheng Shen. Research progress on the slip ratio control methods for wheeled/tracked harvesters[J]. International Journal of Agricultural and Biological Engineering, 2026 , 19 (3) : 20 -30 . DOI: 10.25165/j.ijabe.20261903.10583
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1　Introduction
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As the core equipment in the mechanized harvesting stage of grain production, harvesters have formed an integrated operational chain covering cutting, threshing, cleaning, and storage for major crops such as wheat, rice, maize, and oil crops, thereby significantly improving harvesting efficiency and operational quality[1-7]. The National Agricultural Mechanization Development Plan for the Fourteenth Five-Year Plan explicitly proposes to actively develop efficient specialized machinery for agricultural production in hilly and mountainous areas, promote the R&D of general-purpose power machinery for such regions, and increase equipment supply. With the continuous improvement of mechanization in hilly and mountainous areas and rice-wheat rotation regions, harvester application scenarios have gradually expanded from flat dry fields to complex ground conditions such as wet paddy fields, soft muddy soils, straw-covered surfaces, and fragmented small plots, while also undertaking the critical tasks of timely harvesting, loss reduction, and quality preservation[8-11].
From the perspective of industrial development, the foreign harvester industry started earlier and has long maintained a high level of market concentration. A mature product spectrum and supporting standards have been established around combine harvesters. Mainstream manufacturers represented by John Deere[12], CNH Industrial[13], Kubota[14], CLAAS[15], ISEKI, and YANMAR have strongly promoted global harvester technology development[16]. Harvesters produced by major European and American companies such as John Deere and CNH are generally designed for large-field operations. Owing to their relatively large structures and heavy chassis, these machines are usually less suitable for the complex operating environments of hilly terrain, which can affect operational efficiency and working stability. In contrast, compact harvesters produced by Japanese companies such as Kubota and YANMAR usually adopt more flexible chassis designs and lighter structural schemes, enabling better trafficability and operational stability under complex conditions. Compared with foreign manufacturers, China’s harvester industry started later, but it has developed rapidly and its technical routes have matured quickly. In recent years, domestic enterprises such as Zoomlion[17], Lovol[18], Wode[19], and Changfa[20] have rapidly increased their market penetration by leveraging cost-effectiveness, responsive supply chains, and localized calibration capabilities, and are gradually occupying the major share of the domestic market. On this basis, Chinese harvesters have also carried out a series of customized innovations for hilly areas and small-plot scenarios, with sustained progress in chassis trafficability and reliability for low-bearing-capacity soils[21-23].
Slip refers to the relative movement between the tire, track, and other parts of the machine that contact with the ground and the ground, which is usually manifested as the relative displacement of the contact point of the object on the horizontal plane. Slip rate is an index used to reflect the difference between the circular motion speed of the driving wheel and the actual forward speed of the vehicle, which essentially represents the size of tire slip during vehicle running[24,25].
An excessively high slip ratio reduces traction efficiency and increases energy consumption and operating time. In addition, intensified shear failure and sinkage produce deep ruts and soil compaction, which affect subsequent tillage and crop yield. High slip also worsens running stability, resulting in poorer crushing rate, impurity rate, and loss rate, ultimately degrading operational quality and economic performance. Frequent high-slip conditions accelerate wear of tracks/tires and transmission components, increasing maintenance cost and downtime risk. On slopes and wet-slippery plots, excessive slip is further associated with safety hazards such as bogging and rollover. Therefore, as requirements for trafficability and stability continue to increase, maintaining efficient, low-loss, and low-energy-consumption operation under compound conditions involving wet and heterogeneous soils has become a key challenge in harvester development.
2　Wheel/track-soil interaction mechanism of harvesters
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The wheel/track-soil interaction of a harvester is essentially a coupled process of normal load bearing, tangential traction generation, and energy dissipation. The vehicle load is transferred to the soil through tires or tracks, forming a contact pressure distribution and causing sinkage. Sinkage determines the actual contact area and contact geometry, which in turn affect the available normal stress and shear field. During driving, the contact interface typically evolves from an adhesion zone to a slip zone. Shear stress increases with shear displacement and saturates at the limiting shear strength, thereby establishing traction while also generating rolling resistance and plastic deformation losses. Slip ratio is thus a necessary condition for traction generation, but excessive slip leads to increased energy consumption, aggravated sinkage and rutting, reduced running stability, and further deterioration in operational quality. In wet fields, pore-water pressure and water-film lubrication reduce effective shear strength and amplify the risks of sinkage and slip. On slopes, load transfer changes the normal load distribution and lateral stability. Compared with tires, tracks reduce sinkage and improve trafficability on low-adhesion ground by virtue of their longer contact length and lower unit pressure, but they must also balance steering-related skid slip and soil disturbance control.
Harvesters are off-road vehicles that mainly operate on various types of soil. Their propulsion depends on the tire-track-ground interface. Except for the crop resistance acting on the header, the major external forces during field operation come from the tires or tracks. Therefore, studying the wheel/track-soil interaction mechanism is of fundamental significance because it determines the motion characteristics of the whole vehicle[26]. Research on wheel/track-soil interaction is essentially the core of terramechanics, and the common approaches can generally be classified into five categories: purely empirical methods, semi-empirical methods, theoretical methods, model testing methods, and numerical simulation methods[27-29].
2.1　Purely empirical methods
A purely empirical method identifies soil properties and vehicle performance through observation and measurement. It usually involves experiments under different soil conditions to determine the relationship between soil characteristics and vehicle performance. By collecting a large amount of field test data, including soil parameters, wheel/track specifications, ground pressure, operating load, and power parameters, and then conducting statistical analysis, empirical formulas describing the relationships among these variables can be obtained.
The most common pure empirical method is the vehicle cone index model, which originated from the US Army Corps of Engineers Waterway Test Station (WES) at the end of World War II. It fitted the mechanical properties of soil into the “cone index” (CI), and then put forward the “remolded cone index” (RCI) to represent the soil strength where vehicles continued to drive[30]. In agricultural settings, a lower cone index suggests better soil penetration, which is critical for minimizing soil compaction and improving fuel efficiency during harvesting.
However, purely empirical methods are limited when dealing with complex soil types, such as muddy rice paddies or uneven tilled land. These methods may not accurately predict the harvester’s performance on different soil types under various weather conditions, limiting their use for high-precision equipment design.
2.2　Semi-empirical methods
Semi-empirical methods combine empirical formulas with theoretical models, usually on the basis of terramechanics and with correction by experimental data. These methods establish mathematical relationships by introducing soil physical parameters and wheel/track geometric characteristics to describe the contact mechanics between the vehicle and the soil.
A representative example is the pressure-sinkage model established by Bekker[31]:
$ p=\left(\dfrac{{k}_{c}}{b}+{k}_{\phi }\right){z}^{n} $
where, $ p $ is the normal grounding pressure, Pa; $ z $ is the settlement, m; $ {k}_{c} $ is the cohesive modulus, Pa∙mn+1; $ {k}_{\phi } $ is the friction modulus, Pa∙mn; $ n $ is the soil deformation index, which is a dimensionless constant, usually 0.5~1.5; $ b $ is the equivalent grounding width, m.
By integrating Bekker’s normal relation with shear behavior, contact geometry, energy decomposition, and track characteristics into a system-level terramechanics framework, Wong and co-workers formed what is now the most widely used Wong-Reece family of models in engineering practice[32]. Then the model is extended to predict the performance of flexible tires, and becomes the basis of the Nepean Wheeled Vehicle Performance Model (NWVPM)[33], which is widely used in engineering practice to predict the performance of various vehicles, including harvesters.
Generally speaking, this method has strong adaptability and is more accurate than the pure empirical method, but its theoretical basis is not strict enough to fundamentally express the internal mechanism of the interaction between the wheel/shoe of the harvester and the soil.
2.3　Theoretical methods
Theoretical methods are based on fundamental theories of physics and engineering mechanics, and they analyze the interaction mechanism between wheels/tracks and soil through mathematical models or analytical approaches. Typical methods include elastic contact theory, plastic flow analysis, and limit equilibrium analysis.
In 1773, the French physicist Charles Augustin de Coulomb proposed the earth pressure theory, and in 1900, the German engineer Christian Otto Mohr proposed the Mohr-Coulomb strength theory, which can comprehensively reflect the strength characteristics of rock and soil[34]. In 1944, the British scholar Miklethwait E.W.E. was the first to propose using Coulomb’s soil mechanics formula to calculate tire thrust and to analyze soil bearing capacity for vehicles using Terzaghi’s theory[35]. In 1956, Bekker proposed the pressure-sinkage model and the shear stress-strain model. In 1965, Janosi[36] further improved the model and proposed a more widely applicable shear model. With the efforts of many scholars such as Wong, Bekker, and Reece, the book Terramechanics and Off-Road Vehicle Engineering was later published, providing a comprehensive introduction to vehicle terramechanics[37].
Additionally, modern updates to these theoretical models consider shear stress and strain as they affect the stability and efficiency of harvesting machines. These models are used to design tires and tracks that maximize traction while minimizing soil disturbance, an important factor in sustainable farming practices.
2.4　Model testing methods
Model testing methods simulate the actual interaction between wheels/tracks and soil through physical experiments on test platforms in order to obtain parameters and performance data.
The most common approach is the soil bin test. Its origin can be traced back to the National Soil Dynamics Laboratory (NSDL) in the United States, whose predecessor, the Agricultural Engineering Research Branch, built a semi-outdoor soil bin in 1935 (Figure 1). Bekker[38] later introduced soil bins into vehicle terramechanics in the 1950s, after which they were widely used in agricultural vehicles, off-road vehicles, and later planetary exploration vehicles. Since the twenty-first century, while maintaining the Bekker-Wong-Reece framework, soil bin testing has been extended to planetary rovers and lunar/Martian soil simulants, and high-speed/dynamic interaction databases have continued to be updated[39]. In recent years, in the agricultural field, Jilin University developed an electric four-wheel-drive agricultural machinery soil-bin test vehicle equipped with high-precision sensors for precise monitoring and control to support machinery design practice[40], while South China Agricultural University developed a large-scale field soil-bin system based on actual paddy-field conditions in southern China, providing a research platform for the design and performance testing of agricultural machinery[41].
By using soil bins, designers can test harvesters for various conditions, such as low traction, wheel slip, and load distribution, which are crucial for ensuring machines work efficiently across different crop types and soil conditions.
2.5　Numerical simulation methods
Numerical simulation methods use advanced techniques such as the finite element method (FEM), discrete element method (DEM), and coupled computational fluid dynamics-discrete element method (CFD-DEM) to simulate the wheel/track-soil interaction process and obtain the distribution and evolution of various physical quantities, including mechanical, dynamic, and thermodynamic variables.
FEM was first introduced into vehicle terramechanics by Perumpral in 1971 to analyze nonlinear soil behavior and discuss in detail the techniques used in nonlinear analysis[42]. In 1995, Schmid[43] summarized ten years of research at the Institute of Automotive Engineering of the Federal Armed Forces University Hamburg, including the development of highly complex models for interactive simulation and the transformation of the wheel-soil interaction problem into a two-dimensional plane problem. In recent years, according to different ground materials, FEM-based terramechanics studies have involved many constitutive models, including the Mohr-Coulomb yield model, Drucker-Prager yield model, and Cam-Clay critical-state plasticity model[44].
DEM was first proposed by Cundall in 1971 and was initially applied to rock mechanics[45]. In 1999, Oida et al.[46] introduced DEM into vehicle terramechanics to study the complexity of the soil-traction device interaction process. In recent years, DEM has been combined with multiple other methods to address terramechanics problems, including DEM-artificial neural network hybrid terramechanics models[47] and coupled FEM/DEM simulations of wheel-soil interaction[48].
These methods are combined with experimental data to improve the design of harvester crawler and wheel system, ensuring that they maintain the best traction and minimize soil damage.
3　Harvester slip observation
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Slip ratio is a core indicator that characterizes the relative motion state between harvester wheels/tracks and the ground. In essence, it reflects how reliably the deviation between driving motion and true ground motion can be obtained in complex and unstructured farmland environments. Compared with on-road vehicles, harvesters operate for long periods in wet fields, soft and heterogeneous soils, slopes, and fragmented plots. Under such conditions, the effective rolling radius of tires or tracks changes continuously with sinkage, slip, and load transfer, while external ground-speed acquisition is often unstable under low-speed operation. As a result, slip ratio becomes a strongly time-varying state that is difficult to measure directly and is highly coupled with operating conditions[49,50]. At the same time, slip ratio not only determines traction efficiency and energy consumption, but also affects the coordination of the header, conveying, threshing, and cleaning subsystems by influencing running stability and pose fluctuations. It is therefore an important feedback variable for traction control systems (TCS/ASR), stability control (ESC), and path-tracking control.
3.1　Direct measurement methods
Direct measurement is the most intuitive and earliest engineering approach for harvester slip-ratio observation. Its basic idea is to separately obtain the theoretical traveling speed of the driving wheels/tracks and the actual ground speed of the whole machine, and then directly calculate the slip ratio from their difference or ratio. In this method, slip ratio is usually defined as the relative deviation between the driving peripheral (or track) speed and the ground speed, and its estimation accuracy depends heavily on the reliability of the speed measurements.
On the drive side, wheeled harvesters usually use wheel-speed sensors, encoders, or motor-speed signals combined with the nominal tire radius or equivalent rolling radius to calculate the theoretical traveling speed. Tracked harvesters often estimate track linear speed from the angular velocity of the drive sprocket and the pitch-circle radius. However, off-road vehicles frequently operate on soft soils, where the effective rolling radius of tires or tracks changes because of sinkage, slippage, and soil plastic deformation, leading to systematic errors.
Common ground-speed measurement methods include wheel odometers[51], global navigation satellite systems (GNSS)[52], Doppler ground-speed radar[53], and vision-based sensors[54]. However, these methods still suffer from inaccurate ground-speed information in actual harvesting environments. For example, GNSS signals are easily attenuated or interrupted in non-open terrains; vision-based methods are sensitive to illumination changes, mud splashing, and straw coverage; and ground-speed radar may be affected by changes in sensor height and surface roughness under muddy conditions. Therefore, discontinuity and noise amplification in the ground-speed signal remain key factors limiting the long-term stable application of direct measurement methods in complex farmland environments.
3.2　Mathematical model-based estimation
Slip is the result of the complex interaction between wheels and soil. Wheel slip can be estimated by establishing accurate kinematic and dynamic equations containing slip variables, while body slip can be estimated using a three-dimensional vehicle kinematic model[55]. Both wheeled and tracked harvesters have seen the development of novel and more efficient model-based slip observation methods in recent years.
For wheeled vehicles, Zhou et al.[56] established a mathematical model for unmanned ground vehicles (UGVs) based on geometric characteristics and kinematics to quantitatively analyze slip and improve motion-control performance (Figure 2). The model defines key parameters based on geometric symmetry and kinematics and derives formulas related to slip. In terms of geometric relations, the steering angles $ \beta $, $ {\alpha }_{o1} $, and $ {\alpha }_{i1} $ are determined by the center-of-mass offset D and steering radius R0:
$ \begin{aligned} &\beta =\arctan \dfrac{D}{{R}'_{0}}\\&{\alpha }_{o1}=\arctan \dfrac{L-2D}{2{R}_{0}+B'} \\&{\alpha }_{i1}=\arctan \dfrac{L-2D}{2{R}_{0}-B}\end{aligned} $
where, $ \beta $, $ {\alpha }_{o1} $, and $ {\alpha }_{i1} $ are the corresponding steering angles in the figure, (°); $ L $ is the length of the vehicle, m; $ D $ is the centroid offset, m; $ {R}_{0} $ is the steering radius, m.
These angles provide the theoretical basis for slip analysis because slip changes the angle between the actual wheel trajectory and the theoretical path.
The speed difference ΔVx between the inner and outer wheels is directly related to the steering radius R0 and the forward velocity u:
$ \mathit{\Delta }{V}_{x}=\left| {V}_{xo}-{V}_{xi}\right| =\dfrac{uB}{2{R}_{0}},\quad {R}_{0}=\dfrac{B}{2\mathit{\Delta }{V}_{x}/u} $
where, $ \text{Δ}{V}_{x} $ is the speed difference between the inner wheel and the outer wheel, m/s; $ {V}_{xo} $ is the longitudinal speed of the outer wheel, m/s; $ {V}_{xi} $ is the longitudinal speed of the inner wheel, m/s; $ u $ is the forward speed of the vehicle, m/s.
Using this equation as the core basis for slip observation, any mismatch between the measured and theoretical values indicates the presence of slip. In the initial experiment, the error obtained by directly using wheel speeds was relatively large, which confirmed the influence of slip.
The theoretical trajectory lengths $ L_{xo}^{t} $ and $ L_{xi}^{t} $ are defined by data, and then the slip ratio $ s{l}_{o1} $ and $ s{l}_{i1} $ of each wheel is calculated:
$ s{l}_{o1}=\dfrac{{L}_{xo1}}{L_{xo}^{t}},\quad s{l}_{i1}=\dfrac{L_{xi}^{t}}{{L}_{xi1}} $
where, $ s{l}_{o1} $ and $ s{l}_{i1} $ are wheel slip rates; $ {L}_{xo1} $ and $ {L}_{xi1} $ are trajectory lengths, m; $ L_{xo}^{t} $ and $ L_{xi}^{t} $ are theoretical trajectory lengths, m.
The theoretical length is given by:
$ L_{xo}^{t}=\left({R}_{0}+B/2\right)\cdot Y|_{s}^{e},\quad L_{xi}^{t}=\left({R}_{0}-B/2\right)\cdot Y|_{s}^{e} $
where, $ Y|_{s}^{e} $ is variation of yaw angle from start to end, °.
The corresponding ratios indicate that outer-wheel slip lengthens the trajectory, whereas inner-wheel slip shortens it.
By fitting the observed data, the relationship between the theoretical velocity difference $ E_{v}^{t} $ and the measured value $ E_{v}^{a} $ can be expressed as:
$ E_{v}^{t}=0.526\times E_{v}^{a}+0.027\;61 $
where, $ E_{v}^{t} $ is the theoretical speed difference, m/s; $ E_{v}^{a} $ is the measurement speed difference, m/s.
After substitution into the steering-radius formula, the corrected model reduced the calculation error to less than 5%, whereas the error obtained by directly using wheel speed could reach 23%.
For tracked vehicles, Tang et al.[57] proposed a nonlinear track-ground coupling model that can be modularly integrated and is applicable to both straight-line motion and steering (Figures 3 and 4). This model is fully embedded in a dynamics framework. The track-terrain model forms the basis of the whole method and assumes an exponential relationship between shear stress and shear displacement:
$ \tau =(c+\sigma \mathit{\tan } \phi )\left(1-{e}^{-j/K}\right) $
where, $ \tau $ is the shear stress of soil, kPa; $ j $ is the shear displacement, mm; $ K $ is the shear deformation modulus, mm; $ c $ is the cohesion of soil, kPa; $ \sigma $ is the normal stress, kPa; $ \phi $ is the internal friction angle of soil, (°).
The relative velocity components at any point on the track are defined in the track coordinate system in terms of longitudinal velocity ut, lateral velocity Vt, and yaw rate ωt:
$ {V}_{x}={u}_{t}-{y}_{t}{\omega }_{t}-r{\omega }_{s},\quad {V}_{y}={v}_{t}+{x}_{t}{\omega }_{t} $
where, $ {V}_{x} $ and $ {V}_{y} $ are relative velocity component of arbitrary point $ ({x}_{t},{y}_{t}) $ on the track-ground interface in the $ {x}_{t} $ and $ {y}_{t} $ direction, m/s; $ {v}_{t} $ is lateral velocity of the track coordinate system, m/s; $ {u}_{t} $ is longitudinal velocity of the track coordinate system, m/s; $ ({x}_{t},{y}_{t}) $ is arbitrary point; $ {\omega }_{t} $ is yaw angular velocity of track coordinate system, rad/s; $ {\omega }_{s} $ is rotating angular speed of sprocket, rad/s; $ r $ is radius of sprocket, m.
The components of shear displacement are obtained by integration:
$ \begin{aligned} &{J}_{x}=({u}_{t}-{y}_{t}{\omega }_{t}-r{\omega }_{s})\dfrac{(L/2-{x}_{t})}{r{\omega }_{s}},\\& {J}_{y}=\dfrac{\left(L/2-{x}_{t}\right){v}_{t}+\dfrac{1}{2}\left[(L/2{)}^{2}-x_{t}^{2}\right]{\omega }_{t}}{r{\omega }_{s}}\end{aligned} $
where, $ {J}_{x} $ and $ {J}_{y} $ are shear displacement along the $ {x}_{t} $ and $ {y}_{t} $ direction at point $ ({x}_{t},{y}_{t}) $, m; $ L $ is track-ground contact length, m.
The combined shear displacement $ J=\sqrt{J_{x}^{2}+J_{y}^{2}} $ determines the shear stress.
Slip is reflected in both longitudinal and lateral components: longitudinal slip is related to one component, and lateral slip to the other.
The vehicle model is a three-degree-of-freedom system in which slip affects force balance through track-motion inputs.
Although longitudinal slip can be defined as the ratio of the difference between theoretical speed and actual speed, in this model slip is already implicitly contained in the shear displacement. Under steady-state conditions, the dynamic equations can be simplified, and the influence of slip is reflected in the force balance:
$ \left({F}_{yR}+{F}_{yL}\right){l}_{x}-{F}_{xL}\dfrac{B}{2}+{F}_{xR}\dfrac{B}{2}+{M}_{rL}+{M}_{rR}=0 $
where, $ {F}_{xL},\;{F}_{xR},\;{F}_{yR},\;{F}_{yL} $ are forces on the four tires, N; $ {M}_{rL} $ and $ {M}_{rR} $ are left and right torque, N∙m; $ {l}_{x} $ is longitudinal offset of center of gravity to the geometrical center of the vehicle, m; $ B $ is tread of vehicle, m.
The normal-pressure distribution, often modeled as a trapezoidal distribution, further modulates the slip response. For example, the pressure concentration factor k affects slip distribution:
$ s({x}_{t})=\left\{\begin{aligned} &kL{x}_{t}+1-\dfrac{k{L}^{2}}{4} & \left({x}_{t}\ge 0\right)\\&-kL{x}_{t}+1-\dfrac{k{L}^{2}}{4} & \left({x}_{t}< 0\right)\end{aligned}\right. $
where, $ s({x}_{t}) $ is the normal distribution density function on the track; $ k $ is concentration factor of normal pressure distribution, m–2.
On the basis of mathematical-model-based slip observation and estimation, various compensation and correction methods have also been proposed to further improve accuracy. Zhang et al.[58] from Jilin University designed a nonlinear disturbance observer by combining multiple functions to estimate and compensate for the composite disturbances of the tracking model. Vlakhova et al.[59] constructed a variable-structure model by combining multiple models and used asymptotic and phase-plane methods to study the dynamic characteristics during skidding. Zhuang et al.[60] proposed the EUCB model based on the brush model and vector distribution theory considering anisotropic tire stiffness, making it more suitable for large-slip conditions.
Mathematical-model-based slip observation methods infer vehicle slip by establishing relationships between slip ratio, driving force, normal load, and ground parameters based on wheel/track-soil interaction and vehicle dynamics. These methods are well-suited for harvesters, offering clear physical meaning, parameter interpretability, and easy integration with controllers. However, their accuracy depends on model assumptions and parameter identification. Under complex conditions, such as varying soil resistance, they are prone to errors due to unmodeled dynamics and environmental uncertainties, limiting adaptability in real-world harvesting operations.
3.3　Multi-sensor fusion and filtering estimation
In complex farmland environments, a single sensor is generally unable to obtain harvester slip ratio in a long-term, stable, and accurate manner. To overcome wheel-speed error accumulation, discontinuous ground-speed measurements, and uncertainty caused by nonstationary soil behavior, both academia and industry widely adopt multi-sensor fusion and filtering methods. By constructing a system state-space model and treating slip ratio as a hidden state, online estimation can be performed under the constraints of multi-source observations. This has become the mainstream technical route that balances engineering feasibility and robustness in current harvester slip-observation research[61,62].
The core idea of multi-sensor fusion and filtering is to combine vehicle kinematic and dynamic constraints with multi-source sensor observations within a unified state-space framework, and to obtain an optimal estimate of slip ratio through recursive filtering. A typical state vector can be expressed as follows:
$ x=[v,\psi ,\dot{\psi },s,z,\ldots {]}^{\rm T} $
where, $ v $ is ground speed, m/s; $ \psi $ is heading angle, rad; $ \dot{\psi } $ is yaw rate, rad/s; $ s $ is slip ratio; $ z $ is equivalent contact variation.
The state equation is usually constructed from a simplified dynamic model or kinematic relationship to describe the evolution of states over time, whereas the observation equation is formed from outputs of wheel-speed sensors, IMUs, GNSS, UWB, ground-speed radar, or visual odometry. Slip ratio itself is not measured directly, but is indirectly estimated in the filtering process through the consistency between observations and model equations.
Le et al.[63] proposed an extended Kalman filter capable of identifying track slip on terrain from trajectory data and adapting to soil conditions through reference trajectories and control algorithms combined with soil parameters. Zhao et al.[50] employed an extended Kalman filter (EKF) and an improved sliding mode observer (ISMO) to estimate slip parameters of an agricultural tracked robot during motion, thereby providing prerequisites for subsequent trajectory planning and tracking control (Figure 5). Song et al.[64] proposed a slip-estimation method using optical flow together with nonlinear observers/filters, and comprehensively compared sliding mode observers (SMOs) and EKFs in terms of estimation accuracy and convergence speed. Alshawi et al.[65] designed a framework based on the unscented Kalman filter to estimate vehicle kinematic parameters and further improved observer accuracy and robustness through strong-tracking EKF concepts and adaptive noise adjustment, thereby enhancing active safety performance.
In recent years, researchers have increasingly emphasized confidence output for estimation results. In harvester control systems, slip ratio is not only fed back into traction control or model predictive control modules, but its estimation confidence also directly affects whether the controller should apply torque limiting, speed reduction, or strategy degradation. Overall, multi-sensor fusion and filtering methods integrate multi-source information within one state-space framework and thus realize continuous and robust estimation of slip ratio in complex harvester operating environments. They serve as the key bridge between slip mechanism analysis and slip suppression control.
3.4　Data-driven methods and physics fusion
In complex farmland environments, harvester operation exhibits strong nonlinearity, high uncertainty, and strong time-varying behavior. Factors such as soil moisture content, compaction, particle composition, and straw coverage can rapidly change the effective wheel/track radius, contact area, and shear strength, making it difficult for many traditional methods to maintain long-term accuracy. Against this background, data-driven methods have gradually been introduced into slip-ratio estimation research because of their strong ability to fit complex nonlinear mappings. This trend has further evolved into hybrid frameworks that combine data-driven models with physical mechanisms, i.e., physics-informed or physics-guided approaches, which have become an important research direction in recent years.
Purely data-driven methods usually treat slip ratio as an unknown function-mapping problem. Multi-source sensor signals are used as inputs and slip ratio is used as the output, enabling end-to-end regression through machine-learning models. Common inputs include wheel speed or motor speed, torque, IMU acceleration and angular velocity, attitude angles, load or grain-bin mass estimates, and external ground-speed references. In terms of model structure, many studies use recurrent neural networks such as LSTM and GRU to capture the temporal correlation of slip, while more recent work has introduced Transformer-based models or temporal convolutional networks (TCNs) to strengthen the modeling of long-term dependencies and abrupt operating-condition changes.
Zhang et al.[66] from Jilin University employed an Elman neural network to construct a target slip-ratio prediction model for wheels and used particle swarm optimization to update the model weights in real time, thereby achieving accurate slip observation and estimation. Kang et al.[67] adopted a radial basis function (RBF) neural network as an adaptive yaw-rate controller, with online learning used to adjust network weights in real time so as to indirectly estimate and compensate for disturbances caused by longitudinal slip. With the development of data-driven and physics-fused methods, more new approaches have been proposed. For example, John Chrosniak et al.[68] proposed a physics-constrained neural network (PCNN) for vehicle dynamics modeling in autonomous racing. By estimating key physical coefficients, the method indirectly observes and estimates slip angle, thus improving dynamic prediction accuracy and physical consistency (Figure 6).
4　Harvester slip control
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During harvester operation, slip is almost unavoidable, especially on wet soils or uneven terrain. Excessive slip reduces traction efficiency, increases fuel consumption, makes the vehicle more likely to become stuck in the soil, and may even damage mechanical systems. Conversely, overly low slip may result in excessive power consumption, reduced operational efficiency, and, in some cases, insufficient traction for normal operation. Therefore, harvesters require slip control to balance traction efficiency, energy consumption, and safety.
To optimize operational performance and stability, harvester slip control can generally be divided into two strategies: predictive control before slip occurs and feedback adjustment after slip has occurred. Slip-prediction strategies identify potential slip risk in advance through real-time perception of ground conditions, operating load, and other factors, and then avoid slip by adjusting parameters such as vehicle speed and traction force. Feedback-control strategies compensate after slip occurs by adjusting body attitude, speed, or path-tracking control, thereby achieving effective slip regulation[55,69].
4.1　Slip prediction and avoidance
The main purpose of slip prediction is to identify potential slip risk before slip actually occurs through real-time perception and prediction algorithms, thereby improving operational efficiency and avoiding bogging. Slip prediction is a preventive strategy in slip control. By comprehensively analyzing soil state, vehicle dynamics, load, and other factors, it evaluates the likelihood of slip occurrence and enables effective preventive measures to be taken.
In recent years, extensive research on slip prediction has been conducted for wheeled robots, mainly in the fields of automobiles and planetary exploration. Chen et al.[70] proposed a hybrid neural-network-dual unscented Kalman filter framework, in which a decoupled dual-UKF structure was specifically designed to handle wheel slip. Zhang et al.[71] proposed a coordinated control strategy that estimates tire slip ratio in real time through a coupled state-and-parameter estimation algorithm and optimizes the control process through model predictive control (MPC). For lunar and Martian rovers traveling over complex terrain, Ma[72] proposed a complete slip-ratio prediction framework based on binocular vision and machine learning. In agricultural applications, however, accurate slip prediction has been studied much less because of the complexity of farmland environments. Xia et al.[73] proposed a novel land-wheel structure and established a BP neural network prediction model for the slip ratio of a seeder land wheel, while Shafaei et al.[74] used artificial neural networks (ANNs) and adaptive neuro-fuzzy inference systems (ANFIS) to predict rear-wheel slip of tractors. Related research is shown in Table 1.
The core objective of slip prediction remains the same: to detect potential risk in advance and avoid slip before it occurs, thereby improving operational efficiency and reducing the possibility of vehicle entrapment.
4.2　Path-tracking control considering slip
Overall, there are still relatively few studies that accurately predict slip ratio and then regulate it within a proper range through a controller. Such strategies are generally used only in tasks requiring extremely high precision and substantial cost input, such as the vision-based slip-prediction method proposed by Angelova et al.[75] for Mars exploration. In actual harvester operations, however, because agricultural machinery faces diverse conditions such as dry land, muddy soil, and paddy fields, accurate slip prediction is difficult to realize. As a result, more research has focused on feedback adjustment after slip occurs, i.e., path-tracking control that explicitly considers slip.
According to differences in system modeling and control methodology, existing typical path-tracking control schemes can be classified into three categories based on geometric models, kinematic models, and combined kinematic-dynamic models. The diagram of the path-tracking model is shown in Figure 7[76].
4.2.1　Methods based on geometric models
Path-tracking control methods based on geometric models mainly regulate harvester path tracking and slip ratio by using vehicle geometry, kinematic constraints, and trajectory deviation. These methods emphasize the adjustment of control inputs through geometric relationships. Typical examples include the pure-pursuit algorithm and the Stanley algorithm. However, because of the special operating conditions of harvesters and their running states, which differ from those of ordinary road vehicles, pure pursuit is more commonly used in agricultural machinery.
Zhang et al.[77] improved the pure-pursuit model (Figure 8) by determining the steering angle from the current position of the agricultural machine to the target path through geometric relationships. The core idea is to control path-tracking accuracy using the preview distance.
According to the pure-pursuit model, the control equations can be expressed through the following geometric relations:
Relationship between forward-looking distance Ld and turning radius R:
$ \dfrac{{L}_{d}}{\sin \alpha }=2R $
where, $ {L}_{d} $ is forward-looking distance, m; $ R $ is turning radius, m; 2$ \alpha $ is the heading angle turned to reach the target point, (°).
Calculation formula of turning curvature k:
$ k=\dfrac{1}{R}=\dfrac{2x_{g}^{2}}{L_{d}^{2}} $
where, $ k $ is turning curvature, m–1; $ {x}_{g} $ is abscissa of target point.
Relationship between abscissa of target point $ {x}_{g} $ and lateral error $ d $:
$ {x}_{g}=d\cos \theta -\dfrac{L_{d}^{2}-{d}^{2}}{\mathit{\sin } \theta } $
where, $ d $ is lateral error, m; $ \theta $ is course error, (°).
From the above formula, the relationship between the steering angle of the front wheel $ {\delta }_{s} $ can be obtained:
$ {\delta }_{s}=\arctan \left(\dfrac{2L\left(d\mathit{\cos } \theta -\dfrac{L_{d}^{2}-{d}^{2}}{\mathit{\sin } \theta }\right)}{L_{d}^{2}-{d}^{2}}\right) $
where, $ {\delta }_{s} $ is the steering angle of the front wheel, (°).
In order to adjust the preview distance dynamically, the original manuscript introduces particle swarm optimization (PSO). By calculating the lateral error $ d $ and heading error $ \theta $ in real time, PSO can optimize the preview distance $ {L}_{d} $ and improve tracking accuracy.
Particle position update:
$ {x}_{ij}(s+1)={x}_{ij}(s)+{v}_{ij}(s+1) $
Particle velocity update:
$ {v}_{ij}(s+1)=\omega {v}_{ij}(s)+{c}_{1}{r}_{1}({p}_{ij}(s)-{x}_{ij}(s))+{c}_{2}{r}_{2}({p}_{gj}(s)-{x}_{ij}(s)) $
where, $ {x}_{ij} $ represents the current position of the i-th particle in the j-th dimension, $ {v}_{ij} $ represents the current speed of the particle in the corresponding dimension, $ {p}_{ij} $ represents the individual optimal position that the particle has reached in the historical search process, $ {p}_{gj} $ represents the global optimal position of the whole particle swarm in this dimension, $ s $ represents the current iteration times, $ j $ represents the particle dimension number, $ \omega $ represents the inertia weight coefficient, $ {c}_{1} $ and $ {c}_{2} $ represent the step size, and $ {r}_{1} $ and $ {r}_{2} $ are random numbers between 0 and 1.
Experimental results show that the path-tracking algorithm based on the improved pure-pursuit model can effectively reduce lateral error and improve straight-line tracking accuracy in actual agricultural operations.
In general, geometric-model-based methods are simple and computationally efficient, and are suitable for relatively regular soil and terrain conditions. However, they are sensitive to variations in soil state and cannot accurately predict or compensate for the effects of slip, especially under special working conditions such as paddy-field harvesting.
4.2.2　Methods based on kinematic models
Path-tracking control methods based on kinematic models focus on achieving path tracking by means of the vehicle’s kinematic characteristics (as shown in Figure 9). Kinematic models describe state variables such as position, velocity, and acceleration, without involving more complex dynamic factors such as vehicle mass and interaction forces. These methods adjust control inputs mainly according to the relationship between vehicle motion states and the geometry of the target path.
Gao Xu et al.[78] designed an adaptive fuzzy pure-pursuit controller with improved particle swarm optimization of the preview distance for a differential tracked chassis.
According to the kinematic model, the turning radius R and instantaneous yaw rate of the vehicle ωc can be calculated from the linear-speed vL and vR difference between the left and right tracks:
$ {v}_{c}=\dfrac{{v}_{L}+{v}_{R}}{2},\quad R=\dfrac{B({v}_{L}+{v}_{R})}{2({v}_{L}-{v}_{R})},\quad {\omega }_{c}=\dfrac{{v}_{L}-{v}_{R}}{B} $
where, $ {v}_{L} $ and $ {v}_{R} $ are linear speed of left and right tracks, m/s; $ {v}_{c} $ is walking speed of crawler walking mechanism, m/s; $ {\omega }_{c} $ is instantaneous yaw rate of the vehicle, rad/s; $ R $ is the turning radius, m; $ B $ is track gauge, m.
To consider slip in differential tracked vehicles, the model further modifies the relationships involving track turning radius and lateral deviation, and introduces an adaptively adjusted preview distance to account for slip effects under dynamic environments. This preview distance is dynamically optimized through an improved particle swarm optimization (IPSO) algorithm, thereby enhancing path-tracking accuracy.
He et al.[79] established a kinematic model of a tracked peanut harvester to account for the influence of slip on path tracking, used a Kalman filter to estimate the virtual steering angle, and proposed a dual-PID path-tracking control method based on preview tracking to reduce the adverse effects of slip. Lenain et al.[80] introduced an extended kinematic model that incorporated front- and rear-axle sideslip angles into the traditional Ackermann steering model, thereby more realistically reflecting vehicle motion behavior under slip conditions. Li et al.[81] incorporated body roll angle and slip-angle correction into a conventional kinematic model and proposed a robust heading-angle predictive control method that estimates slip parameters in real time through a disturbance observer and compensates for them through predictive control, thereby effectively improving heading-tracking accuracy.
Kinematic-model-based control methods do not require explicit consideration of the full complexity of vehicle-environment dynamics. They are therefore simple and practical, and usually perform well under medium-low-speed and low-curvature conditions. However, their applicability becomes limited under conditions of large lateral acceleration.
4.2.3　Methods based on combined kinematic-dynamic models
Control methods based on combined kinematic and dynamic models aim to improve control accuracy, robustness, and adaptability by integrating the advantages of both modeling approaches. Unlike purely kinematic control methods, these approaches not only consider the vehicle’s motion characteristics, but also explicitly account for the complex interaction between the vehicle and the ground, especially traction, tire-soil friction, and sinkage effects. As a result, they usually perform better in slip control, adaptation to complex terrain, and heavy-load operation[82,83].
Tracked vehicles are common harvester platforms. For tracked vehicles, Wu et al.[84], based on a kinematic model, proposed a hybrid kinematic-dynamic model that uses track angular acceleration as a virtual control input and employs generalized disturbance to describe the uncertainty caused by track slip.
The model describes the effect of slip ratio on traction generation by explicitly introducing slip ratio into the formulation:
$ \left\{\begin{aligned}& {F}_{t,i}\left({\eta }_{i}\right)={F}_{m,i}\left[1-\dfrac{K}{{\eta }_{i}{l}_{i}}\left(1-\exp \left(-\dfrac{{\eta }_{i}{{l}}_{i}}{K}\right)\right)\right]\\&{F}_{m,i}=A\left(c+p\times \tan \varphi \right)=Ac+\dfrac{mg}{2}\tan \varphi \end{aligned}\right. $
where, $ {F}_{t,i} (i=1,r)$ is traction acting on one-sided crawler, N; $ {\eta }_{i} $ is the longitudinal slip rate of the crawler; $ K $ is the shear modulus of the soil, kPa; $ {F}_{m,i} $ is the maximum traction force of a single track, N; $ A $ is the track contact area, m2; $ c $ is the traction coefficient of the ground, kPa; $ p $ is the track pressure to the ground, kPa; $ \varphi $ is the inscribed angle of rolling resistance, (°); $ {l}_{i} $ is the longitudinal contact length of the track, m.
By considering the longitudinal slip ratios of the tracks, the model can more accurately reflect vehicle motion response under complex ground conditions. At the same time, because speed and slip ratio are difficult to measure directly, an extended state observer (ESO) is designed for real-time estimation of vehicle speed and generalized disturbances.
For wheeled harvesters, related ideas can be referenced from self-propelled sprayers, which are also agricultural vehicles. Wang[85], based on the kinematic model of a sprayer, and considering the front and rear steering axles and the four-wheel independent drive structure, established a kinematic model containing tire-slip effects, proposed an improved control strategy based on tire dynamics to address the complex working conditions of agricultural machinery, and further adopted a hierarchical control strategy based on model predictive control (MPC). The upper controller calculates steering angle and vehicle speed according to the desired path and current position using the sprayer kinematic model, while the lower controller compensates for tire slip through fuzzy control and PID control to realize accurate path tracking.
By combining vehicle kinematic behavior with dynamic characteristics, path-tracking control methods based on coupled kinematic-dynamic models can regulate path tracking and slip more accurately, which is especially beneficial for harvesters operating on uneven or challenging terrains like agricultural fields. These models allow for more precise control over the harvester’s movement, optimizing both speed and traction on soft, sloped, or wet soils. However, in practical application, model errors may still lead to unsatisfactory control performance, especially in complex soils or dynamic environments where harvesters operate. Future studies should focus on improving model robustness and exploring adaptive control methods that can adjust control strategies according to real-time feedback, thereby reducing the influence of model uncertainty on control performance.
5　Conclusions
Less
Research on harvester slip control has made considerable progress in recent years. With the continuous advancement of agricultural mechanization, harvester operating environments have become increasingly complex, especially in hilly and mountainous areas and wet paddy fields, where slip has become a key factor affecting operational efficiency and quality. Therefore, reducing slip, improving traction efficiency, and lowering energy consumption have become core issues in improving harvester performance. Current slip-control technologies mainly include slip-ratio prediction and control, as well as feedback control after slip occurs. Through the integration of perception and control technologies, such as mathematical-model-based slip estimation and multi-sensor fusion and filtering, researchers have continuously improved both the theory and engineering implementation of slip observation and control, thereby enabling more accurate control under different operating environments.
Future research should focus on enhancing the robustness of slip prediction models and developing more adaptive, real-time control strategies. Specifically, there is a need for methods that can account for dynamic environmental factors and improve performance in varied operating conditions, such as wet, muddy, or fragmented soils. Combining data-driven approaches with physical models holds great potential for achieving higher accuracy in slip estimation and control. Moreover, interdisciplinary collaboration—particularly between control algorithms and sensing technologies—could lead to more refined solutions for slip control. This, in turn, would further enhance harvester performance and broaden their applicability in diverse agricultural environments.
References
Less
1
Lei C X, Jin C Q, Li P P, Yang X Y, Zhao Z H, Lyu L L. Development status of threshing technology and equipment of grain combine harvester. Journal of Agricultural Science and Technology, 2025; 27(5): 90. (in Chinese)
2
Liu C, Zhang H T, Zhu J W, Wang W, Zhang C L, Chen L Q. Design and test of isolated-motor-driven cleaning system for high moisture wheat thresher. Transactions of the CSAM, 2025; 56(7): 82–93. (in Chinese)
3
Wu Q J, Wang J J, Sun D P. Design and research of wheat seed harvester. Journal of Agricultural Mechanization Research, 2021; 43(9): 024. (in Chinese)
4
Shan H Y, Yan Y N, Zhang J, Liu X J, Han X, Liu J. Research progress on mechanization of soybean-corn belt composite planting. Journal of Chinese Agricultural Mechanization, 2024; 45(6): 42–52. (in Chinese)
5
Chen J, Lian Y, Li Y M. Real-time grain impurity sensing for rice combine harvesters using image processing and decision-tree algorithm. Computers and Electronics in Agriculture, 2020; 175: 105591.
6
Ding F, Luo X W, Zhang Z G, Hu L, Wu X L, Bao K Y, et al. Dual-unloading mode autonomous operation strategy and cotransporter system for rice harvester and transporter. Engineering, 2025; 48: 220–233.
7
Wang F M, Ni X D, Zhang Q, Guo S J, Zhou J, Chen D. Estimation of combine harvester throughput using multisensor data fusion. Computers and Electronics in Agriculture, 2025; 237: 110713.
8
National development plan of agricultural mechanization in the tenth five-year plan. Agriculture Machinery Technology Extension, 2022; 1: 4–14. (in Chinese)
9
Sun J B, Liu Z J, Yang F Z, Sun Q, Liu Q, Luo P X. Research review of agricultural equipment and slope operation key technologies in hilly and mountains region. Transactions of the CSAM, 2023; 54(5): 1–18. (in Chinese)
10
Wang B Y, Zhu J X, Chai X L, Liu B, Zhang G W, Yao W. Research status and development trend of key technology of agricultural machinery chassis in hilly and mountainous areas. Computers and Electronics in Agriculture, 2024; 226: 109447.
11
Wang X W, Yuan S Q, Jia W D. Current situation and development of agricultural mechanization in hilly and mountainous areas. Journal of Drainage and Irrigation Machinery Engineering, 2022; 40(5): 535–540.
12
John Deere. High-end control, high efficiency and multifunction-John Deere C2400 combine harvester. Farm Machinery, 2024; 5: 24. (in Chinese)
13
Guan Q. Case New Holland high-end equipment becomes the focus of the exhibition. Agricultural Machinery Market, 2021(11): 42–43. (in Chinese)
14
Kubota. Kubota “Guo Ⅳ” EX-M series full-feed crawler harvester. Farm Machinery, 2023; 1: 28–29. (in Chinese)
15
Keleshou. Harvesting expert: Keleshou D370 combine harvester. Farm Machinery, 2023; 3: 39–40. (in Chinese)
16
Zhao C J, Ma C, Li J, Wang X M. Research status and prospects of mechanization technology for rice in hilly and mountainous areas. Transactions of the CSAE, 2025; 41(1): 1–11. (in Chinese)
17
Han H B. Zoomlion’s intelligent agricultural machinery helps early rice harvest “accelerate running”. Agricultural Machinery Market, 2025; 8: 61. (in Chinese)
18
The 2023 Leiwo Valley corn harvester with both stalks and ears was unveiled, and the upgrade was “more than a little”. Farm Machinery, 2023; 4: 43–44. (in Chinese)
19
Li S C. 9 peanut harvesters, which are full of vitality. Farm Machinery, 2020; 9: 28–29. (in Chinese)
20
Chang Fa 4YZ-5A (CF905A) self-propelled corn harvester. Farm Machinery, 2020; (10): 37. (in Chinese)
21
Mu Z Q, Zhang B, Tian K P, Huang J C, Kong F T, Wu T. Current status and technical challenges of corn mechanized harvesting in the southwestern hilly and mountainous regions. Journal of Chinese Agricultural Mechanization, 2025; 46(11): 331–335. (in Chinese)
22
Wang F A, Feng Y Y, Wang D, Zhang Z G, Yin G D, Shen C, et al. Turning mechanism and performance testing of crawler chassis for panax notoginseng harvester. Transactions of the CSAM, 2025; 56(8): 692–703. (in Chinese)
23
Yang K, Li J, Chen Y, Li H, Ao Y, Lei X L. Design and testing of a liftable chassis for rice harvester. Journal of Intelligent Agricultural Mechanization, 2025; 6(1): 59–70. (in Chinese)
24
Huang Z Y. Terrain vehicle mechanics. Beijing: Machinery Industry Press. 1985; 20p. (in Chinese)
25
Hu J B, Li X Y, Wei C. Driving principle of armored vehicle. Beijing: Beijing Institute of Technology Press. 2020; 15p. (in Chinese)
26
Zhu J J, Wang Z P, Zhang L, Dorrell D G. Braking/steering coordination control for in-wheel motor drive electric vehicles based on nonlinear model predictive control. Mechanism and Machine Theory, 2019; 142: 103586.
27
Chen B. Research on traction characteristics of the rigid wheel with grousers on sandy soil. Jilin University, 2007. (in Chinese)
28
Sun G, Gao F, Li W, Sun P. Research contents and methods of vehicle ground mechanics in deep space exploration; Proceedings of the second academic conference of the deep space exploration technology Committee of China Aerospace Society, Beijing, China, 2005. (in Chinese)
29
Tian X F. Research on interaction between tire and ground with the numerical simulation method. National University of Defense Technology, 2012. (in Chinese)
30
Su X T. On the applicability of cone index. Transactions of the CSAM, 1985; 1: 12–23. (in Chinese)
31
Bekker M G. Introduction to terrain-vehicle systems. Ann Arbor: University of Michigan Press, 1969.
32
Wong J Y, Reece A R. Prediction of rigid wheel performance based on the analysis of soil-wheel stresses part I. Performance of driven rigid wheels. Journal of Terramechanics, 1967; 4(1): 81–98.
33
Wong J Y. Theory of ground vehicles. John Wiley, 2008. DOI: 10.1002/9781119719984
34
Lu Z J. Present situation and prospect of shear strength research of cohesive soil. China Civil Engineering Journal, 1999; 4: 3–9. (in Chinese)
35
Du Y H. A SWI theory and numerical research on tractive performance of military vehicle under multi-operation conditions. National University of Defense Technology, 2017. DOI: 10.27052/d.cnki.gzjgu.2017.000721 (in Chinese)
36
Janosi Z J. Analysis and presentation of soil-vehicle mechanics data. Journal of Terramechanics, 1965; 2(3): 69–79.
37
Wong J Y. Chapter 1 - Introduction. Terramechanics and off-road vehicle engineering (Second edition). Oxford; Butterworth-Heinemann, 2010; 1–19.
38
Tian X F, Jiang L H, Nie X H. Research progress on soil bin test in vehicle terramechanics. Auto Sci-Tech, 2013; 2: 1–5. (in Chinese)
39
Rodríguez-Martínez D, Van Winnendael M, Yoshida K. High-speed mobility on planetary surfaces: A technical review. Journal of Field Robotics, 2019; 36(8): 1436–1455.
40
Yang X. The design of the electric all-wheel-drive farm machinery soil bin testing car. Changchun: Jilin University, 2014. (in Chinese)
41
Xu P. Development of agricultural machinery field soil trough system. South China Agricultural University, 2020. DOI: 10.27152/d.cnki.ghanu.2020.000354 (in Chinese)
42
Perumpral J V, Liljedahl J B, Perloff W H. A numerical method for predicting the stress distribution and soil deformation under a tractor wheel. Journal of Terramechanics, 1971; 8(1): 9–22.
43
Schmid I C. Interaction of vehicle and terrain results from 10 years research at IKK. Journal of Terramechanics, 1995; 32(1): 3–26.
44
Bai Y D, Sun L Y, Zhang M L, Liu X Y, Li Z L. Progress of research on terramechanics for tracked mobile robots. Journal of Machine Design, 2020; 37(10): 1–13. (in Chinese)
45
Cundall P A. A computer model for simulating progressive large-scale movements in blocky rock systems. Procintsympon Rock Fracture, 1971; 1(ii-b): 11–18.
46
Oida A, Schwanghart H, Ohakubo S. Effect of tire lug cross section on tire performance simulated by distinct element method. 1999.
47
Kim J T, Hwang H, Lee H S, Park Y J. Development of DEM–ANN-based hybrid terramechanics model considering dynamic sinkage. Journal of Terramechanics, 2024; 116: 100989.
48
Zhao C L, Zang M Y. Application of the FEM/DEM and alternately moving road method to the simulation of tire-sand interactions. Journal of Terramechanics, 2017; 72: 27–38.
49
Liu H, Li T, Nie Y, Xie N. Study of torque distribution strategy based on slip ratio prediction. Automobile Technology, 2020; 9: 39–44. (in Chinese)
50
Zhao X, Lu E, Tang Z, Luo C M, Xu L Z, Wang H. Trajectory prediction method for agricultural tracked robots based on slip parameter estimation. Computers and Electronics in Agriculture, 2024; 222: 109057.
51
Sun Y J. Design of wheeled robot adaptive odometer based on terrain classification. Shijiazhuang Railway University, 2023. DOI: 10.27334/d.cnki.gstdy.2023.000845 (in Chinese)
52
Zhong Y, Xue M Q, Yuan H L. Design of the GNSS/INS integrated navigation system for intelligent agricultural machinery. Transactions of the CSAE, 2021; 37(9): 40–46. (in Chinese)
53
Jiang B, Yin H F. Research and implementation of tractor speed measurement method based on Beidou navigation system. Farm Machinery, 2019; 10: 83–85. (in Chinese)
54
Zheng D J. Application of automatic speed control system based on K210 visual identification module. Equipment Technology, 2025; 4: 38–41. (in Chinese)
55
Du X Q, Hong F W, Ma K H, Li Y C, Zhao L J. State-of-the-art and prospect on sliding identification and control of agricultural machinery. Transactions of the CSAM, 2024; 55(8): 1–20. (in Chinese)
56
Zhou K, Lei S S, Du X Z. Modelling and dynamic analysis of slippage level for large-scale skid-steered unmanned ground vehicle. Scientific Reports, 2022; 12(1): 16014.
57
Tang S X, Yuan S H, Hu J B, Li X Y, Zhou J J, Guo J. Modeling of steady-state performance of skid-steering for high-speed tracked vehicles. Journal of Terramechanics, 2017; 73: 25–35.
58
Zhang J X, Zhou S Y, Zhao J, Shi T. Wheel slip rate tracking control based on nonlinear disturbance observer. J Huazhong Univ Sci Technol Nat Sci Ed, 2020; 48: 44–49. (in Chinese)
59
Vlakhova A V, Novoderova A P. A variable-structure model for studying skidding of a four-wheeled vehicle with slipping wheels. Moscow University Mechanics Bulletin, 2024; 79(3): 75–81.
60
Zhuang Y, Song Z S, Gao X L, Yang X G, Liu W P. A combined-slip physical tire model based on the vector distribution considering tire anisotropic stiffness. Nonlinear Dynamics, 2022; 108(4): 2961–2976.
61
Wada M, Kang Sup Y, Hashimoto H. High accuracy road vehicle state estimation using extended Kalman filter. Proceedings of the ITSC2000 IEEE Intelligent Transportation Systems Proceedings (Cat No00TH8493), 2000; Oct 1–3. DOI: 10.1109/ITSC.2000.881069
62
Tong L. An approach for vehicle state estimation using extended Kalman filter. Springer, Berlin Heidelberg, 2012.
63
Anh Tuan L, Rye D C, Durrant-Whyte H F. Estimation of track-soil interactions for autonomous tracked vehicles. Proceedings of the International Conference on Robotics and Automation, 1997; April 25. DOI: 10.1109/ROBOT.1997.614331
64
Song X, Seneviratne L D, Althoefer K. Slip parameter estimation for tele-operated ground vehicles in slippery terrain. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 2011; 225(6): 814–830.
65
Alshawi A, De Pinto S, Stano P, Van Aalst S, Praet K, Boulay E, et al. An adaptive unscented Kalman filter for the estimation of the vehicle velocity components, slip angles, and slip ratios in extreme driving manoeuvres. Sensors, 2024; 24(2): 436.
66
Zhang J X, Shi Z T, Yang X, Zhao J. Wheel slip tracking control of vehicle based on Elman neural network. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2020; 48(6): 64–69. (in Chinese)
67
Kang Y T, Xue B, Zeng R Y. Self-adaptive path tracking control for mobile robots under slippage conditions based on an RBF neural network. Algorithms, 2021; 14(7): 196.
68
Chrosniak J, Ning J, Behl M. Deep dynamics: Vehicle dynamics modeling with a physics-constrained neural network for autonomous racing. IEEE Robotics and Automation Letters, 2024; 9(6): 5292–5297.
69
Xu W X, Zhu Y J, Xiao M H, Liu M N, Ye L L, Yang Y P, et al. Energy-saving and stability-enhancing control for unmanned distributed drive electric plant protection vehicle based on active torque distribution. Artificial Intelligence in Agriculture, 2025; 11: 004.
70
Chen J W, Pan W, Cao T, Qian Z Y, Zhang L, Chen X B, et al. Auxiliary-enhanced neural networks for electric vehicle dynamics: Advancing tire force and state estimation during wheel slip. Control Engineering Practice, 2025; 165: 106550.
71
Zhang H, Xv K, Li Y H, Zhao W Z, Wang C Y. Coordination control strategy of motion stability and tire slip for electric vehicle driven by in-wheel-motors. Journal of the Franklin Institute, 2024; 361(15): 107126.
72
Ma H. Vision based lunar/Mars rover slip prediction research. University of Chinese Academy of Sciences (Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences), 2019. DOI: 10.27612/d.cnki.gyyys.2019.000002 (in Chinese)
73
Xia L M, Changjiang W, Zhao K B. Prediction of sliding of ground wheel of the planter based on BP neural network. Journal of Agricultural Mechanization Research, 2012; 34(11): 167–170. (in Chinese)
74
Shafaei S M, Loghavi M, Kamgar S. Feasibility of implementation of intelligent simulation configurations based on data mining methodologies for prediction of tractor wheel slip. Information Processing in Agriculture, 2019; 6(2): 183–199.
75
Angelova A, Matthies L, Helmick D, Perona P. Learning and prediction of slip from visual information. Journal of Field Robotics, 2007; 24(3): 205–231.
76
Xiong L, Yang X, Zhuo G, Leng B, Zhang R X. Review on motion control of autonomous vehicles. Journal of Mechanical Engineering, 2020; 56(10): 127–143. (in Chinese)
77
Zhang H Q, Wang G D, Lyu Y F, Qin C L, Liu L, Gong J L. Agricultural machinery automatic navigation control system based on improved pure tracking model. Transactions of the CSAM, 2020; 51(9): 18–25. (in Chinese)
78
Gao X, Zhang J F, Zhao R, Yang X H, Liu J B. Research on path tracking controller of crawler-type cabbage harvester based on IPSO-FUZZY-PP. Journal of Intelligent Agricultural Mechanization, 2026; 7(1): 86–95. (in Chinese)
79
He J, Man Z X, Hu L, Luo X, Wang P, Li M, et al. Path tracking control method and experiments for the crawler-mounted peanut combine harvester. Trans Chin Soc Agric Eng, 2023; 39: 9–17. (in Chinese)
80
Lenain R, Thuilot B, Cariou C, Martinet P. Mobile robot control in presence of sliding: Application to agricultural vehicle path tracking; Proceedings of the 45th IEEE Conference on Decision and Control, 2006; Dec. 13–15. DOI: 10.1109/CDC.2006.377520
81
Li M, Wang Y, Tang Y L, Wang P, Liu L Q, Xia Y. Course control technology of unmanned agricultural machinery considering body shake and slip. China Southern Agricultural Machinery, 2024; 55(8): 1–4, 11. (in Chinese)
82
Yang W S, Su Y X, Chen Y P, Lian C. Integrated spatial kinematics–dynamics model predictive control for collision-free autonomous vehicle tracking. Actuators, 2024; 13(4): 153.
83
Ye B L, Niu S F, Li L X, Wu W M. A comparison study of kinematic and dynamic models for trajectory tracking of autonomous vehicles using model predictive control. International Journal of Control, Automation and Systems, 2023; 21(9): 3006–3021.
84
Wu Y, Wang C, Dong G X, Zeng R Y, Cao K, Cao D P. Slip-aware adaptive trajectory tracking control strategy for autonomous tracked vehicle. Journal of Mechanical Engineering, 2024; 60(24): 211–25. DOI: 10.3901/JME.2024.24.211 (in Chinese)
85
Wang Z J. Path tracking model predictive control for 4WID high gap sprayer considering driving wheel slip. Jiangsu University, 2022. DOI: 10.27170/d.cnki.gjsuu.2022.002047 (in Chinese)
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Cite this Article
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Article Info
doi: 10.25165/j.ijabe.20261903.10583
  • Receive Date：2026-03-20
  • Online Date：2026-08-27
  • Published：2026-06-30
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  • Received：2026-03-20
  • Accepted：2026-04-13
Affiliations
    1Nanjing Institute of Agricultural Mechanization, Ministry of Agriculture and Rural Affairs, Nanjing 210014, China
    2College of Engineering, Nanjing Agricultural University, Nanjing 211800, China
    3Key Laboratory of Modern Agricultural Equipment, Ministry of Agriculture and Rural Affairs, Nanjing 210014, China

Corresponding:

Maohua Xiao, Professor, research interest: intelligent agricultural machinery. Nanjing Agricultural University, No.666 Binjiang Road, Nanjing 210031, China. Tel: +86-13951756153, Email:
Cheng Shen, Associate Professor, research interest: agricultural mechanization. Nanjing Institute of Agricultural Mechanization, MARA, No.100 Liuying, Xuanwu District, Nanjing 210014, China. Tel: +86-25-84346078, Email:
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表12种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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