The deployment of tracked robots (TR) in field applications has become increasingly prevalent due to their exceptional ability to navigate challenging terrains, such as uneven, soft, or vegetation-covered surfaces. Unlike wheeled robots, TR offer superior traction, stability, and load distribution, making them ideal for tasks in agriculture, exploration, and disaster response (Li et al., 2019; Liu and Liu, 2009). However, their performance in real-world environments is often hindered by the complex dynamic interactions between the tracks and the soil. These interactions introduce disturbances, such as uncertain shear forces and pressure subsidence, which are influenced by factors like soil composition, vegetation density, and external loads (Xie et al., 2024). Such disturbances pose significant challenges to achieving precise driving control, limiting the operational efficiency and reliability of TR in practical applications (Zhang et al., 2022).

Researchers have developed various control systems to achieve good TR performance, employing techniques such as fuzzy control (Hacene et al., 2022; Resende et al., 2013) and nonlinear control (Yan et al., 2022). It is well-established that the aforementioned control approaches, which rely on the robot kinematics model, are primarily applicable to structured environments. However, due to the soft soil and the presence of weeds on the soil surface, the field work environment for TR is quite complex, which is a typical unstructured environment (Xu et al., 2023). The attractive properties of sliding mode control (SMC), namely its ease of execution and robustness to perturbations, make it a favored choice for applications in robotics and mechatronics (Gad et al., 2024; Liu et al., 2020). The application of SMC in robotics is well-documented for addressing challenges like parameter uncertainties and disturbances. For instance, Xi et al. (2022) developed a robust adaptive SMC to achieve accurate and smooth control of robot manipulators under such conditions. Similarly, Liu et al. (2022) designed a novel trajectory tracking controller for a spherical robot by combining controller with a hierarchical SMC scheme, enabling precise velocity tracking across complex terrains. Beyond mobile robots, SMC has also been applied to snake robots for velocity tracking, as demonstrated by Mukherjee et al. (2017). In applications where fast response is critical, such as in TR, the Integral Terminal Sliding Mode Control (ITSMC) variant has been the focus of extensive research (Qin et al., 2024; Su and Zheng, 2020; Sun et al., 2021; Van et al., 2019), due to its enhanced performance. Compared to the traditional SMC with infinite convergence time, ITSMC can stabilize at the equilibrium point within a finite time, ensuring global robustness in the state space from the initial moment, and by using integral sliding mode to design disturbance estimators, continuous control can be achieved, and chattering can be eliminated, while ensuring strong robustness and high accuracy of sliding mode control (Nguyen and Pitakwachara, 2024; Qian et al., 2020; Shen et al., 2023). In (Rahmani et al., 2016), a control scheme based on the fraction integral terminal sliding mode control and adaptive neural network was proposed, which deals with the system model uncertainties and the disturbances to improve the control performance of the manipulator. In (Chiu, 2012), integral TSMC is developed for robust output tracking of uncertain relative-degree-one systems by introducing sign and fractional integral terminal sliding modes, and the control system is forced to start on the terminal sliding hyperplane, so that the reaching time of the sliding modes is eliminated.

Inspired by the aforementioned studies, we propose an adaptive control strategy to address the challenges associated with TR driving control in complex terrains. By leveraging the Bekker pressure-sinkage and Janosi shear theories, we establish disturbance models that capture the robot-terrain interaction dynamics. These models provide a foundation for understanding the effects of soil deformation and shear forces on TR motion. Building on this understanding, we introduce an adaptive integral terminal sliding mode (AITSM) control method, which combines the benefits of adaptive control and terminal sliding mode control to enhance robustness and precision. Experimental validation demonstrates the effectiveness of the proposed method in real-world scenarios, showcasing its ability to maintain precise driving control in challenging environments. This study not only advances the field of TR control but also provides a versatile framework for driving control in a wide range of intelligent field machinery, including agricultural robots (Bai et al., 2023; Wang et al., 2022; Zhang et al., 2022), exploration vehicles, and disaster response systems. By addressing the critical challenges of terrain interaction and disturbance rejection, this work contributes to the broader goal of enhancing the autonomy and reliability of field robots in outdoor applications.

The major contributions can be summarized as follows:

The remainder of this article is constructed below. Section 2 describes the TR system modeling. Section 3 presents the AITSM driving control method with the rigorous stability proof. Section 4 gives real-time experiments on the TR platform and corresponding discussions. Section 5 concludes this paper.

Figure 1a shows a tracked robot (model no. TR400), which is mainly composed of a control system and a drive system, respectively. Note that, in the field environment, since the soil is soft and sticky, the TR has complex track-ground contact surfaces, which greatly increases the difficulty of driving control. Therefore, the subsidence displacement and sheer force of the TR should be considered, before designing a control method for driving system. The positive pressure between track and ground satisfies the pressure-subsidence model proposed by Bekker (Li et al., 2019), which is shown in Figure 1b . Besides, as shown in Figure 1c , the relationship between the shear stress of track and the soil deformation satisfies the formula of shear stress and deformation proposed by Janosi (Kayacan et al., 2018). The pressure subsidence and shear can be expressed as Equations 1, 2.

where p is compressive stress,   k c is modulus of cohesion of soil deformation,   k ∅ is internal friction modulus of soil deformation,   z 0 is soil subsidence, n k is soil deformation index, p L and p R are pressure on left and right track unit areas, respectively, τ l e f t and τ r i g h t are shear force per unit area of left and right track, respectively, c is soil cohesion, ∅ is internal friction angle of soil, j is soil shear displacement, k is horizontal shear modulus of soil.

As shown in Figure 1e , on the soft ground, the shear force between the track and the ground is opposite to the sliding velocity direction of the track. In the Figure 1e , v 1 ,   v _ 2 is Sliding speed of trackpad at any point during steering, r 1 , r 2 is Distance from any point to geometric center during steering. According to (2), the shear force acting on the grounding section of the track on both sides can be described as follows (Equations 3, 4).

Where F 1 , F 2 is Shear force on track plate, A is unit area of track contact ground. From (3), (4), the longitudinal forces acting on both sides of the track are as follows (Equation 5).

Where b is load plate width,   δ 1 and δ 2 are angles between sliding velocity at any point of track grounding section and x-axis direction, L is track shoe length. The lateral force acting on both sides of the track is as follows (Equations 6, 7).

Where x 1 ,   x 2 is X-axis abscissa of any point of trackpad.

Remark: To accurately depict the dynamic interaction between the crawler robot and the soft ground and lay the foundation for the subsequent design of high-performance controllers, this paper adopts the classic Bekker pressure-settlement model and the Janosi shear model for mechanical modeling. The advantage of this modeling method lies in its ability to comprehensively describe the core mechanical characteristics of track-soil contact (i.e., compaction resistance and shear thrust) from both vertical and horizontal dimensions. Its parameters have clear physical meanings and serve as a widely verified theoretical basis in the field of ground mechanics. However, this model is rather sensitive to the accuracy of soil parameters and has limitations under heterogeneous soil conditions. For this reason, this paper will design an adaptive control strategy that does not rely on precise model information to estimate and compensate for the lumped uncertainty composed of model uncertainty and external disturbances online, thereby ensuring the robustness of the system in real and complex environments.

?>The schematic diagram of unilateral track control system is shown in Figure 1d . Note that the desired velocity and steering angular velocity required for TR to track the desired path are obtained through the Pure-Pursuit path tracking algorithm (PPPT) (Zhang et al., 2019). Take one side crawler driving wheel as an example, the ω d is desired angular velocity of the driving wheel. The actual angular velocity of the driving wheel, ω t , is actually measured by the angular velocity sensor of the driving wheel. The voltage control signal u is calculated from the controller, such that the accurate control of the angular velocity of the driving wheel can be realized. The track is driven by the drive motor through the reducer to drive the drive wheel. The system dynamics of the unilateral track system of TR and the DC motor are given by (Equations 8–11).

Where J L and J m are the moments of inertia of the unilateral track system and motor, respectively, B L and B m are the viscous damping coefficients of the unilateral track system and motor, respectively, ω m is the motor angular velocity, satisfying ω m = i ω t with i defined as the gear ratio, k t and k e are the constants of motor torque and electromotive force, respectively, τ F is the load torque caused by external disturbance such as F x i and F y i ( i = 1 , 2 ), R d is the total resistance of the armature circuit, u is the control input voltage, τ a is the motor torque, τ m is the torque transmitted from the motor to the reducer, τ is drive wheel torque, and ς is torque transmission loss coefficient. Using (9)-(11) into (8) by eliminating ω m , the dynamics of the unilateral track system can be simplified as (Equation 12).

To facilitate the further controller design, (12) is reformulated as (Equation 13).

Where m = ( J L + i 2 ς J m ) R d / i ς k t , n = ( B L + i 2 ς B m + i 2 ς k t k e / R d ) R d / i ς k t , d l = τ F R d / i ς k t . In this paper, we consider the following parametric variations in (13) as follows (Equations 14, 15).

Where m 0 = 0.043   k g · m 2 , n 0 = 1.025 N · m · s / r a d are the nominal values and Δ m , Δ n are their uncertainties, respectively. Note that, m 0 and n 0 are the nominal parameters of the system, and their values are determined based on the specific physical parameters of the motor and mechanical structure of the TR400 experimental platform. The tracking error of the angular velocity is defined as (Equation 16).

Where ω d ( t ) should be once differentiable as ω d ˙ ( t ) . The error dynamics can then be obtained from (13) and (16) as follows (Equation 17).

Where D l u m ( t ) = [ Δ m ω t ˙ ( t ) + Δ n ω t ( t ) + d l ( t ) ] / m 0 represents the lumped uncertainty in the error dynamics.

In terms of the bound derivation of the lumped uncertainty. if the closed-loop control u is designed to satisfy the following polynomial-type upper bound as (Equation 18).

Where ζ i   ( i = 0 , 1 ) are positive constants, then the lumped uncertainty in (17) will be bounded as (Equation 19).

Where d(t) is defined as (Equation 20).

with D i   ( i = 0 , 1 ) being positive constants.

In this part, an AITSM driving control scheme is developed for the unilateral track system of TR with uncertain dynamics. A precise position tracking performance with finite-time convergence and good robustness can be well ensured, also, the lumped uncertainty bound and the sliding mode parameters are all online updated by the designed adaptive laws, such that the requirements of obtaining the bound information in the controller are successfully eliminated.

In conclusion, this study successfully developed an Adaptive Integral Terminal Sliding Mode (AITSM) control strategy for TR operating in field environments. The experimental validation across L-shaped and U-shaped path scenarios confirmed the controller’s ability to maintain precision during dynamic maneuvers while adaptively compensating for disturbances, with tracking accuracy improved compared to PID and smoother actuation than SMC. However, the study has limitations, including the reliance on predefined disturbance models (Bekker and Janosi theories), and the need for further optimization of adaptive parameters to balance convergence speed and computational efficiency. Future research should explore the integration of machine learning techniques for disturbances identification, and investigate energy-efficient implementations for prolonged field operations.