Research on Control Strategy of Pure Electric Bulldozers Based on Vehicle Speed

Abstract

This study proposes a hierarchical drive control system to ensure speed stability in dual-motor tracked vehicles operating under complex terrain and heavy-load conditions. The system adopts a two-layer structure. At the upper level, the sliding mode controller is designed for both longitudinal speed regulation and yaw rate control, thereby stabilizing straight line motion and the steering maneuvers. At the lower level, a synchronization mechanism aligns the velocities of the two motors, enhancing the vehicle’s robustness against speed fluctuations. Simulation results demonstrate that, across both heavy load and light load bulldozing scenarios, the deviation between the controller output and the reference command remains within 5$\%$. These findings confirm the accuracy of the control implementation and validate the effectiveness of the proposed framework.

1. Introduction

Bulldozers, a type of traction-based construction machinery, often operate under highly complex conditions, characterized by large and nonlinear load fluctuations. These operating conditions lead to low fuel efficiency, high exhaust emissions, and significant environmental pollution. With the growing emphasis on environmental protection and sustainable development worldwide, stricter regulations are being implemented, motivating the development of energy-efficient, low-carbon, and environmentally friendly construction machinery. In this paper, the pure electric bulldozer, powered entirely by batteries and eliminating the internal combustion engine, offers true zero-emission operation and reduced environmental impact [1,2]. Recent advances in electric technology have substantially informed energy management and drive control strategies [3,4,5,6]. Numerous studies have proposed systematic solutions addressing energy optimization, coordinated motor control, and overall vehicle stability through approaches such as hierarchical control, model predictive control, and deep reinforcement learning [7,8,9]. These works have not only improved the dynamic performance and energy efficiency of electric vehicles but also provided valuable theoretical and technical guidance for electric-drive construction machinery, including pure electric bulldozers.

In 2021, Dr. Zeng Gen’s team from the Beijing University of Technology [10] analyzed the dynamics-related characteristics of a tracked vehicle driven by the bilateral motors coupling in the process of slope steering control, determined the magnitude and change in the traction force of the track on both sides in real time, and realized the smooth steering control of the tracked vehicle at any slope angle and any speed through the multivariate predictive control of the motion state. In 2019, Shuai Yin of Chang’an University [11], based on MATLAB/Simulink 2019 to establish the dynamic model of a crawler bulldozer vehicle, concluded that the dynamic performance of the tandem hybrid bulldozer is better than that of the hydraulic bulldozer in the three aspects of traction performance: hill climbing and steering. In 2024, Prof. Wei’s team from Hubei University of Technology [12] took the crawler robot bilaterally driven motor as the research object and made the kinematic model of crawler robot to analyze how the interference caused by resistance load on motor speed will lead to the output of the bilateral motors and is not synchronized, through the design of straight line experiments. The findings indicate that the amplitude of lateral offset variation decreased from 0.084 m to 0.038 m, thereby enhancing the synchronization performance of the dual motors. Ma et al. [13] introduced a torque compensation control method predicated on the speed differential between two motors. Simulation and experimental findings indicated that real-time adjustments of fuzzy PI parameters made to compensate for the torque output of both motors maintained equal speeds of the drive wheels, thereby facilitating stable straight-line vehicle operation. Li Chunming et al. [14] addressed the synchronization issue of straight-line driving in dual-motor linked tracked vehicles by incorporating a dual-side mechanical coupling method alongside synchronous regulation of motor deviation coupling. Li P et al. [15] noted that motor speed control demonstrates suboptimal transient performance compared to torque control, requiring the application of torque compensation during vehicle operation to enhance dynamic reaction time. Zhai Li et al. [16] employed PID control to enable the drive motor to monitor the motor speed commands issued by the driver via the pedals and steering wheel. Zhang et al. [17] employed a fuzzy adaptive technique to improve the adaptability of the PID controller to diverse vehicle speeds. Yeu et al. [18] evaluated the slip rate of both sides of the tracks based on the driving force and enhanced the trajectory tracking performance by adjusting for the speed of the drive wheels. S A. et al. proposed the Koopman Multi-Level Control (KMPC) framework. Simulations demonstrate that this framework offers significant computational advantages, exhibiting particularly pronounced effects when executing eco-driving plans for long-distance routes [19].

In conventional track vehicle control strategy design, high-precision velocity estimation and resistance to external disturbances are essential. Current control methodologies commonly integrate fuzzy logic, sliding mode control, and model predictive control to enhance system robustness against external disturbances [20,21,22]. Field observations of bulldozer operations reveal that these vehicles predominantly operate in soil-transporting scenarios under high-load conditions. This operational profile contrasts significantly with conventional electric vehicle control systems, which are typically optimized for light-load or no-load operations, resulting in a fundamental mismatch with bulldozer working requirements. To address this disparity, our research concentrates on developing robust control frameworks specifically for heavy-duty bulldozer applications. Existing literature indicates limitations in current control paradigms—including model predictive, fuzzy, and sliding mode approaches, particularly regarding their response latency and tracking precision when subjected to sudden external disturbances. Sun et al. claimed that the partitioned structure of hierarchical control offered major benefits over traditional techniques. While lower-level components manage accuracy, higher-level modules focus on strategic decision making [23]. The hierarchical control strategy improves system robustness through a dual-layer disturbance rejection mechanism. The upper-layer controller has generated compensated reference signals using observed system states and disturbance estimates, while the lower-layer controller ensured precise tracking of the commands via high-bandwidth control, attenuating the propagation of external resistance disturbances throughout the control system.

This paper proposes a hierarchical control architecture for pure electric bulldozers, building upon established research in the field. The system employs a sliding mode controller at the upper level to determine optimal velocity targets, while a high-response torque controller at the lower layer ensures precise execution of motion commands.

2. Dynamics Analysis and Modeling of the Pure Electric Bulldozer

As depicted in Figure 1, the pure electric bulldozer system design includes the following major modules: vehicle controller, CAN bus, motor and its controller, and power battery pack [24,25]. Among these, the vehicle controller, as the primary control unit of the vehicle, collects driving signals through the CAN bus and evaluates and creates the motor torque control instructions. The command is communicated to motor controllers on both sides in real time through the CAN bus. The motors on both sides drive the matching driving wheels of the vehicle body through the reducer accordingly to drive the vehicle. At the same time, the real-time operational characteristics of the bulldozer are also transmitted back to the vehicle controller to establish a closed-loop control.

Taking the center of the vehicle body, shown as point C, as the origin, we built the body-fixed coordinate system Cxy. Simultaneously, we defined the global and geodetic coordinate system OXY with point O as its origin. Initially, the two coordinate systems were deemed coincident, indicating that the axes Cx and OX, as well as Cy and OY, were fully aligned. This initial situation eased the mathematical transformation and reference conversion between the two systems during the early stages of study. As the bulldozer drives forward, the body-fixed coordinate system translates and rotates relative to the global coordinate system, accurately capturing the vehicle’s trajectory, orientation, and dynamic state across time, hence simplifying exact motion modeling and control analysis.

For the purposes of this study, we assume certain simplifying assumptions to focus on the key dynamics of interest. Firstly, we neglected the pitching motion and lateral tilt motion of the vehicle body. Under these assumptions, the bulldozer’s movement can be considered as a planar rigid body motion, with all mass centered at a single center of mass. This allowed the application of two-dimensional kinematics and dynamics, considerably lowering the complexity of the mathematical modeling process. Furthermore, we focused primarily on the longitudinal motion of the tracked vehicle, omitting lateral displacement of the tracks. It was believed that the center of mass velocity was always directed along the longitudinal axis of the vehicle body. This assumption was appropriate in conditions such as straight-line driving or ascending, where lateral effects are minor. This reduced modeling framework serves as the basis for future dynamic analysis, control design, and simulation.

In Figure 2, $L$ is the length of the grounded end of the track, $B$ is the center distance of the track, $R$ is the steering radius, $V$, $\omega$ are the speed of the bulldozer and the steering angular velocity of the bulldozer, $v1,v2$ are the speeds of the inner and outer tracks, $F1,F2$ are the driving forces of the left and right main wheels, and $Fr1,Fr2$ are the resistance forces during the pure electric tracked bulldozer traveling operation.

Based on the coordinate system established in Figure 2, a kinematic analysis of the bulldozer is conducted to provide a foundation for subsequent dynamic studies [26].

$$\left\{\begin{array}{l}{F}_c={\displaystyle \frac{2b}{(n+1)k^{\frac{1}{n}}}}{({\displaystyle \frac{G}{2bL}})}^{{\displaystyle \frac{n+1}{n}}}\\ F_{\mathrm{b}}=\gamma Z^{2}b{K}_{\gamma }+2bZc{K}_{\mathrm{pc}}\\ K_{\gamma }=\left({\displaystyle \frac{2N_{\gamma }}{\tan \phi }}+1\right){\cos }^2\phi \\ K_{\mathrm{pc}}=(N_{\mathrm{c}}-\tan \phi ){\cos }^2\phi \end{array}\right.$$

(1)

Among them, $F_C$—compaction resistance $\left(\mathrm{K}\mathrm{N}\right)$, $G$—the operating weight of the bulldozer $\left(\mathrm{K}\mathrm{N}\right)$, $b$—track width $\left(\mathrm{m}\right)$, $L$—track grounding length $\left(\mathrm{m}\right)$, $k$—modulus of deformation $(\mathrm{K}\mathrm{N}/{\mathrm{m}}^{\mathrm{n}+2})$, $n$—the deformation index of soil, $F_b$—soil pushing resistance $\left(\mathrm{N}\right)$, and $F_T$—working resistance $\left(\mathrm{N}\right)$.

$$\left\{\begin{array}{l}{F}_1={10}^6{B}_1{h}_p{k}_b\\ F_2=G_{\iota }{u}_1\cos a={\displaystyle \frac{V\gamma u_1\cos a}{k_s}}\\ V={\displaystyle \frac{B_1{\left(H-h_p\right)}^2{k}_m}{2\tan a_0}}\\ F_3={10}^6{B}_{1}X{u}_2{k}_y\\ F_4=G_{\iota }{u}_2{\left(\cos \delta \right)}^2\cos a\\ F_T={\displaystyle \frac{(F_1+F_2+F_3+F_4)}{2}}\\ F_{\mathrm{i}}=G\sin \alpha \\ F_{r1}=F_{r2}=F_c+F_b+F_T+F_i\end{array}\right.$$

(2)

$F_1$—tangential cutting resistance $\left(\mathrm{N}\right)$, $\gamma$—the density of soil $(\mathrm{N}/{\mathrm{m}}^3)$, $B_1$—width of the earthmoving shovel $\left(\mathrm{m}\right)$,$H_p$—the cutting depth of the bulldozer $\left(\mathrm{m}\right)$, $k_b$—cutting specific resistance $\left(\mathrm{M}\mathrm{p}\mathrm{a}\right)$, $F_2$—the pushing resistance of accumulated soil in front of the shovel $\left(\mathrm{N}\right)$, $G_t$—the gravity of the soil pile in front of the push plate $\left(\mathrm{N}\right)$, $V$—the volume of the mound on the push board $\left({\mathrm{m}}^3\right)$,$k_s$—the looseness coefficient of soil, $k_m$—the filling coefficient of soil, s $H$—blade height $\left(\mathrm{m}\right)$, $F_3$—frictional resistance between the blade and the soil $\left(\mathrm{N}\right)$, $k_y$—the specific resistance of the cutting into the soil after cutting wear $\left(\mathrm{M}\mathrm{p}\mathrm{a}\right)$,$M$—the grounding length after the cutting edge is worn $\left(\mathrm{m}\right)$, ${\mu }_2$—the coefficient of friction between soil and steel, $F_4$—the horizontal component of the frictional resistance of the soil debris along the scraper $\left(\mathrm{N}\right)$, $F_i$-grade resistance $\left(\mathrm{N}\right)$, and $F_{r1}$, $F_{r2}$—the resistance experienced by the left and right tracks $\left(\mathrm{N}\right)$.

Soil-related parameters are obtained by consulting reference tables.

According to the laws of rigid-body dynamics and the bulldozer dynamics model equations established by Dr. Wang, at any time t in the OXY coordinate system [27]:

$$\left\{\begin{array}{l}\begin{array}{l}{F}_{1,2}=\left\{\begin{array}{c}{\displaystyle \frac{T_{1,2}i\eta }{r}},({\displaystyle \frac{T_{1,2}i\eta }{r}}\le {\displaystyle \frac{1}{2}}\phi G\cos \alpha )\\ {\displaystyle \frac{1}{2}}\phi G\cos \alpha ,({\displaystyle \frac{T_{1,2}i\eta }{r}}>{\displaystyle \frac{1}{2}}\phi G\cos \alpha )\end{array}\right.\\ F_1+F_2-F_{\mathrm{r}1}-F_{\mathrm{r}2}=m\stackrel{\cdot }{\nu }\end{array}\hfill \\ F_1{\displaystyle \frac{B}{2}}-F_2{\displaystyle \frac{B}{2}}-F_{\mathrm{rl}}{\displaystyle \frac{B}{2}}+F_{\mathrm{r}2}{\displaystyle \frac{B}{2}}-T_{\mathrm{r}}=I_{\mathrm{z}}\dot{w}\hfill \\ T_{\mathrm{r}}={\displaystyle \frac{\mu GL}{4}}\hfill \\ \mu ={\displaystyle \frac{{\mu }_{\max }}{0.925+0.15\rho }}\hfill \\ \rho ={\displaystyle \frac{R}{B}}\hfill \end{array}\right.$$

(3)

where $F_1,F_2$—motor traction force on both sides $\left(\mathrm{N}\right)$; $T_1,T_2$—traction torque of drive motors on both sides $(\mathrm{N}.\mathrm{m})$; $\eta$—efficiency between the motor output shaft to the track; $i$—transmission ratio from the motor output shaft to the main wheel; $r$—radius of the drive wheel $\left(\mathrm{m}\right)$; $\phi$—land attachment coefficient;$T_r$—steering resistance moment $(\mathrm{N}.\mathrm{m})$; $I_Z$ is the rotational moment of inertia of the whole vehicle $(\mathrm{k}\mathrm{g}.{\mathrm{m}}^2)$; $\rho$—relative steering radius $\left(\mathrm{m}\right)$; ${\mu }_{max}$ steering resistance coefficient; $\dot{v}$—acceleration of bulldozer $(\mathrm{m}/{\mathrm{s}}^2)$; and $\dot{w}$—angular acceleration of bulldozer $(\mathrm{r}\mathrm{a}\mathrm{d}/{\mathrm{s}}^2)$.

3. Control Strategy Design for the Pure Electric Bulldozer

This paper employed a sliding mode structure to create an upper-level vehicle speed controller. Due to the wide range of driving resistance changes, it is required to employ a large switch gain and a tiny boundary layer, but this can easily produce control quantity jitter, lowering vehicle smoothness. Therefore, a tiered control technique is utilized with the upper layer maintaining the driving speed stability of the bulldozer and the lower layer handling the bilateral motor speed synchronization, enhancing the bulldozer’s driving interference resistance while minimizing driving deviation.

The steering wheel angle and pedal information were resolved into the target vehicle speed and target traverse angular velocity of the electric drive tracked vehicle [26]. The layered kinematics controller is responsible for implementing precise vehicle speed and traverse angular velocity control while dynamically calculating and outputting the lower-level control instructions based on the real-time feedback of the vehicle’s operating status provided by the simulation model [27]. At the bottom layer, the torque optimization controller determines and provides unilateral torque control commands by considering the required traction force and swing torque from the upper layer, ensuring effective torque distribution and power balance. Furthermore, a sliding mode controller based on vehicle speed is included to enhance robustness, stability, and adaptability of the overall control strategy under variable and complex operating situations.

3.1. Sliding Mode Controller Based on Vehicle Speed

From Equation (1), pure electric bulldozer dynamics model can be obtained. Bulldozer vehicle going in a straight line is the speed control state of the state equation:

$${\displaystyle \frac{1}{m}}{u}_{\nu }-{\displaystyle \frac{F_{\lambda }}{m}}=\dot{\nu }$$

(4)

where $F_{\lambda }=F_{r1}+F_{r2}$, ${\mu }_v\left(t\right)$ is the speed controller output.

Define the speed tracking error as

$$e_1(t)=v_{\mathrm{ref}}(t)-v_{\mathrm{c}}(t)$$

(5)

where $e_1\left(t\right)$ is the speed tracking error; $v_{ref}\left(t\right)$ is the bulldozer’s target speed; and $v_c\left(t\right)$ is the bulldozer’s actual speed.

Define the speed tracking error as

$$s_1(t)=c_1{\displaystyle {\int }_0^t{e}_1}(t)\mathrm{d}t+e_1(t)$$

(6)

where $c_1$ is the integration constant.

The speed integral sliding mode controller is designed by adopting equal speed convergence rate:

$${\dot{s}}_1=-\epsilon \mathrm{sgn}\left(s_1\right)\epsilon >0$$

(7)

where $\epsilon$ is the rate of convergence of the system motion point to the switching surface $s=0$.

In order to weaken the jitter, the saturation function $sat\left(s_1\right)$ is used instead of the sign function $sgn\left(s_1\right)$ in the whole integrated sliding mode controller, and the expression of the saturation function is

$$sat\left(s_1\right)=\left\{\begin{array}{l}{s}_1/{\epsilon }_1\\ \mathrm{sgn}(s_1)\end{array}\right.\begin{array}{c}\\ \end{array}\begin{array}{c}\left|s_1\right|\le {\epsilon }_1\\ \left|s_1\right|>{\epsilon }_1\end{array}$$

(8)

The speed integral sliding mode controller can be designed as

$$u_{\nu }=m\left({\dot{v}}_{\mathrm{ref}}(t)+F_{\lambda }/m+c_1{e}_{\nu }+D_1\mathrm{sat}\left(s_1/{\epsilon }_1\right)\right)$$

(9)

where $D_1$ is the switching gain; ${\epsilon }_1$ is the boundary layer thickness.

$$V_1={\displaystyle \frac{1}{2}}{s}_1{(t)}^2$$

(10)

When $\left|s_1\right|\le {\epsilon }_1$, the mode variable is outside the boundary layer, $sat\left(s_1\right)=sgn\left(s_1\right)$, then the derivative ${\dot{v}}_1$ of $v_1$ is

$$\begin{array}{cc}{\dot{V}}_1& =s_1{\dot{s}}_1\hfill \\ & =s_1\left(c_1{e}_1+{\dot{v}}_{\mathrm{ref}}-{\displaystyle \frac{u_v-F_{\lambda }}{m}}\right)\hfill \\ & =s_1\left(-D_1\mathrm{sgn}\left(s_1\right)+{\displaystyle \frac{F_{\lambda }}{m}}\right)\hfill \\ & =-D_1\left|s_1\right|+s_1{\displaystyle \frac{F_{\lambda }}{m}}\hfill \end{array}$$

(11)

For ${\dot{v}}_1$ < 0, we need $D_1>{\displaystyle \frac{F_{\lambda }}{m}}$:

$${\dot{V}}_1=-D_1\left|s_1\right|+s_1{\displaystyle \frac{F_{\lambda }}{m}}<0$$

(12)

The closed-loop system is stabilized when $t\to \infty ,s_1\to 0$.

When n$·\left|s_1\right|\ge {\epsilon }_1$, the mode variable is inside the boundary layer, $sat\left(s_1\right)=s_1/{\epsilon }_1$. Let the final constant value perturbation be:

$$\underset{t\to \infty }{\lim }{d}_1(t)=l$$

(13)

Let $\tau =-D_1/{\epsilon }_1$, then:

$${\dot{s}}_1(t)={\tau }_1{s}_1+d_1(t)$$

(14)

The first order inertial link of the above equation is subjected to a Raschel variation as

$$s_1\left(s\right)={\displaystyle \frac{1}{s+{\tau }_1}}{d}_1\left(s\right)$$

(15)

According to the median theorem, the steady state value of $s_1\left(t\right)$ is

$$\underset{t\to \infty }{\lim }{s}_1(t)=\underset{s\to 0}{\lim }{\displaystyle \frac{1}{s+{\tau }_1}}\underset{s\to \infty }{\lim }{d}_1(s)={\displaystyle \frac{l}{\tau }}$$

(16)

From the Barbalat’s theorem [28], when $t\to \infty ,\dot{s_1\left(t\right)}\to 0$, it can be shown that, when $t\to \infty ,{\dot{e}}_1(t)+c_1{e}_1(t)=0$. Take the Lyapunov function as

$$V_2={\displaystyle \frac{1}{2}}{e}_t{(t)}^2$$

(17)

$${\dot{V}}_2=e_1(t){\dot{e}}_1(t)=-c_1{\left[e_1(t)\right]}^2$$

(18)

Since the constant of integration $c_1>0$, then $\dot{V_2\le 0}$ is constant and, according to LaSalle’s invariance principle,$e_1\left(t\right)=0$ is the global asymptotic equilibrium point of the system, $e_1\left(t\right)\to 0$ when $t\to \infty$.

3.2. Sliding Mode Controller Based on Pendulum Angular

According to Equation (1), purely electric bulldozer dynamics model, while the bulldozer conducts steering the equations of the transverse pendulum angular velocity control system are

$$u_{\omega }={\dot{\omega }}_c•I_Z+T_r$$

(19)

Define the transverse pendulum angular velocity tracking error as

$$s_2=e_{\omega }+c_2{\displaystyle {\int }_0^t{e}_{\omega }}\mathrm{d}t$$

(20)

Design the transverse pendulum angular velocity integral sliding mode controller as

$$u_{\omega }=I_Z({\omega }_c^{*}+c_2{e}_{\omega }+D_2\mathrm{sat}(s_2))+T_r$$

(21)

Similarly, using Lyapunov function for verification. The designed transverse pendulum angular velocity control system meets the requirements.

3.3. Lower-Level Motion Controller

In the linear motion of tracked vehicles, variations in ground deformation resistance and internal resistance within the drive mechanism can significantly influence both the vehicle’s velocity and its trajectory over time. These resistive forces, which frequently fluctuate with changes in terrain characteristics such as soil stiffness, surface roughness, and gradient, introduce considerable uncertainty into the vehicle’s dynamic behavior. Moreover, the absence of mechanical coupling between the two drive wheels in independently driven electric vehicles poses a fundamental challenge for motion control. This decoupled architecture necessitates highly coordinated and synchronized control of the dual motors to maintain stability, ensure accurate straight-line travel, and minimize undesirable lateral deviations, particularly under complex and uneven ground conditions. Failure to achieve such coordination may lead to deviations from the intended trajectory.

Current synchronous control strategies include parallel control, master–slave control, cross-coupling control, virtual master shaft control, and deviation coupling control [29,30,31]. This study has used the rapid torque response features of electric motors to implement precise torque regulation.

From Equations (1), (2) and (16), the traction force of tracked vehicle and the relationship between the traverse swing moment and motor torque are calculated as

$$\left\{\begin{array}{ll}{u}_{\nu }={\displaystyle \frac{i\eta }{r}}\left(T_1+T_2\right)\hfill & \hfill \\ u_{\omega }={\displaystyle \frac{i\eta B}{2r}}\left(T_1-T_2\right)\hfill & \hfill \end{array}\right.$$

(22)

The motor torque on both sides can be solved from Equation (20):

$$\left\{\begin{array}{l}{T}_1={\displaystyle \frac{u_{v}r}{2i\eta }}+{\displaystyle \frac{u_{\omega }r}{i\eta B}}\\ T_2={\displaystyle \frac{u_{v}r}{2i\eta }}-{\displaystyle \frac{u_{\omega }r}{i\eta B}}\end{array}\right.$$

(23)

The control flow is shown in Figure 3.

4. Development of a Simulation Model for the Pure Electric Bulldozers

The characteristics of the pure electric bulldozer evaluated in this study were primarily obtained through technical data and performance specifications shared by Shantui, ensuring that the parameters accurately reflect the actual configuration and operational capabilities of the machine.

In addition to the company-provided information, relevant data and conclusions from past research literature were meticulously referenced to validate and enhance the dataset, ensuring a thorough and solid basis for modeling and simulation. These combined inputs allowed for the construction of the bulldozer’s dynamics. The parameters of the pure electric bulldozer used have been collected and organized in

Table 1. Drive Motor and Battery Parameters of The Pure Electric Bulldozer.

Name	Value	Unit
Rated Speed	1200	r/min
Peak Torque	1440	N.m
Peak Power	150	KW
Battery Cell Rated Voltage	3.2	V
Battery Cell Nominal Capacity	229	Ah
Number of Series Cells	157	Cell
Number of Parallel Cells	2	Cell

.

This design focuses exclusively on the relationship between motor speed and operational stability of the bulldozer. The battery is modeled as a voltage-stable source with smooth current variation, and its detailed parameters are provided in Table 1.

The simulations were conducted through Amesim-2021–Simulink-2020 co-simulation. The Amesim motor model, calibrated with experimental data, was employed to capture the motor’s complex dynamics, while the control strategy was implemented in Simulink to exploit its strong computational capabilities and improve accuracy.

Based on the comprehensive data presented in Table 1 and

Table 2. Typical Working Conditions of The Pure Electric Bulldozer.

Working Condition Interval	Operation Time (s)	Execution Action
Acceleration interval	0~22 s	Acceleration to 11 km/h
	22~33 s	Decelerate from 11 km/h to 2.5 km/h
30° ramp uphill interval	33~78 s	2.5 km/h climbing at constant speed
15° slope up operation interval	78~82 s	2.5 km/h uniform speed no-load hill climbing
	82~125 s	Accelerate from 0 km/h to 1.5 km/h
	125~128 s	1.5 km/h constant speed traveling
Small radius turning interval	128~166 s	1.5 km/h constant speed driving
	166~168 s	Acceleration from 1.5 km/h to 3 km/h
0.2 m shovel depth operation interval	168~175 s	3 km/h uniform speed traveling
	191~264 s	Decelerate from 3 km/h to 2 km/h, 0.2 m depth shoveling
	264~266 s	2.5 km/h uniform speed soil transportation
	266~291 s	Deceleration from 2.5 km/h to 0 km/h
Reversing interval	281~291 s	Deceleration from 0 km/h to 2 km/h
	291~305 s	Decelerate from 0 km/h to 11 km/h
Large Radius Turning Interval	307~314 s	Uniform speed at 3 km/h
In situ steering interval	370~372 s	Decelerate from 3 km/h to 0 km/h
	372~400 s	In situ center steering

together with the simulation model developed in Figure 4 and Figure 5, a full set of simulated results was generated to systematically evaluate the accuracy, reliability of the proposed dynamics model and control strategy, with Table 1 and Table 2 providing detailed information on the bulldozer’s typical working conditions including load parameters, speed profiles, and operational patterns observed during field tests, while the simulation model captures the fundamental dynamic behaviors and interactions of the vehicle under various scenarios, and the integration of these datasets within the simulation framework allows for a rigorous assessment of the model’s predictive capability and bulldozer’s control strategy’s performance across diverse operating conditions, and ensuring that the dynamics model accurately represents real-world behavior while also identifying potential limitations or areas for further refinement in the control algorithm.

Drawing on the comprehensive operational data compiled by Dr. Wang of the Beijing Institute of Technology, along with datasets from other authoritative studies [32,33,34,35,36], 400 s representative working condition profile of the pure electric bulldozer was constructed to characterize its typical operational patterns. These datasets provide a reliable and scientifically grounded basis for generating operating scenarios that accurately reproduce the actual load and motion conditions observed during field operations.

Building upon this basis, the typical working conditions outlined in Table 2 were developed and used to test and validate the correctness, reliability, and adaptability of the suggested dynamics model.

The values of each parameter in the upper-level vehicle speed controller system are $\epsilon 1$ = 0.5, $c1$ = 2.8, $D1$ = 0.5; the parameters of the motor synchronous controller are $\epsilon 2$ = 10,$c2$ = 5,$D2$ = 3.

Figure 6 depicts the relationship between the specified speed and the measured speed of the pure electric bulldozers. During the acceleration phase, the speed climbs from a stop to 11 km/h. When the ramp operation is performed, the 30 gradients in the unloaded condition cause a speed decay of around 0.1 km/h, and this deviation is regulated by the PI system to restore the steady state equilibrium at 77 s. When entering the ramp shoveling operating zone, the shoveling drag coefficient and the ramp resistance prompted a sustained speed variation of 0.1 km/h. The steering resistance moment in the B/2 steering phase resulted in a 0.2 km/h speed fluctuation.

Comparing Figure 6a,b, it can be observed that the Sliding Mode Control (SMC) is more robust. However, as the vehicle speed lowers, Proportional–Integral (PI) control finds it difficult to re-track the goal value. SMC offers better interference resistance. At 35 s, the pure electric bulldozers begin functioning, and the bulldozers’ speed lowers. Compared with PI control, SMC tracks the desired vehicle speed in a shorter time. When executing slope turning at 130 s, the motor output speed fluctuation ranges of the two control systems are similar, but SMC approaches the goal speed faster than PI. In summary, it may be stated that the SMC algorithm can better track the goal vehicle speed and achieve the driving purpose.

The data were comprehensively analyzed to validate the precision and robustness of the model as well as the effectiveness of the proposed control technique under various operating scenarios. In particular, the vehicle speed simulation data were examined in detail to perform a comparative evaluation of Sliding Mode Control and Proportional–Integral control in maintaining driving stability under dynamic conditions.

The results consistently demonstrate that SMC regulation provides superior stability and faster response characteristics compared to PI regulation, particularly when subjected to external disturbances or load variations. During the reversing interval, the forward speed deviation is maintained at approximately 0.05 km/h, indicating high precision in speed control. The tracking error during the large-radius steering interval remains within 0.02 km/h, fully meeting steering accuracy requirements and demonstrating the control strategy’s responsiveness under curved-path conditions. This precision supports stable maneuverability under variable loads and uneven terrain. Analysis of typical operating conditions indicates only a 0.23% deviation between measured and model-predicted speeds, validating the model’s predictive capability and establishing a robust foundation for refining control algorithms and advancing operational strategies.

The analysis examines simulation data on motor speed, torque, angular velocity, and turning radius of the pure electric bulldozer under standard conditions. It validates the accuracy and reliability of the simulation model and provides insights into the vehicle’s dynamic behavior and control performance. Analysis of these parameters establishes a foundation for evaluating the control strategy, identifying optimization opportunities, and guiding refinements for practical applications.

The distributions of parameters for the pure electric bulldozer’s bilateral motors, as illustrated in Figure 6b and Figure 7a, reveal their dynamic response characteristics under various operating conditions. The motor output modes are intimately related to the bulldozer’s operational state. In the acceleration zone (0 $\mathrm{s}$–33 $\mathrm{s}$), torque on both sides remains perfectly balanced, ensuring smooth and consistent speed increase. Under the low load conditions, the outputs are stable within the standard range, reflecting consistent and reliable motor performance. During slope operations (33 $\mathrm{s}$–78 $\mathrm{s}$), the influence of slope resistance mandates that both motors synchronize to generate a torque of 477 $\mathrm{N}·\mathrm{M}$, indicating the bulldozer’s capabilities to sustain ascending stability under inclined terrain. In the ramp shoveling operations (78 $\mathrm{s}$–128 $\mathrm{s}$), unexpected surges in resistance led to peak driving torques reaching 600 $\mathrm{N}·\mathrm{M}$., illustrating the durability of the dual-motor system in handling abrupt load fluctuations. These data provide vital insights into the relationship between motor torque distribution, operational conditions, and the overall driving performance of the pure electric bulldozer.

Figure 7c,d depict the torque distribution and steering dynamics of the bulldozer during various steering movements. In the small-radius steering interval (128 $\mathrm{s}$–168 $\mathrm{s}$), the torque of the left drive shaft rises abruptly to 500 $\mathrm{N}·\mathrm{M}$, while the right drive shaft generates a reverse torque of 338 $\mathrm{N}·\mathrm{M}$. This power difference between the two sides produces the yaw moment to achieve the small turning radius. During the simulated steering process, the steering radius initially shows a sharp fluctuation around 130 $\mathrm{s}$, followed by a rapid convergence to a stable trajectory, indicating strong responsiveness and effective dynamic regulation of the control system. In the large radius steering interval (307 $\mathrm{s}$–370 $\mathrm{s}$), the torque outputs adapt asymmetrically, with approximately 288 $\mathrm{N}·\mathrm{M}$ delivered by each shaft, ensuring smooth and controlled wide-angle steering. In the in situ steering interval (370 $\mathrm{s}$–400 $\mathrm{s}$), both sides generate reverse symmetric torques of 550 $\mathrm{N}·\mathrm{M}$, allowing the bulldozer to perform 0 radius turns with high precision. These results demonstrate that the motor control strategy enables accurate and reliable execution of diverse steering maneuvers under varying operational conditions.

5. Real Vehicle Test and Result Analysis

The testing machine and test site are shown in Figure 8. The test site has a sandy soil surface. The turning radius and speed of the tracked vehicle are calculated based on the speed of the drive wheels. The speed of the drive wheels is calculated based on the speed of the motor through the transmission ratio relationship of the dual-sided motor coupling drive. The speed of the motor is obtained by collecting the angular position signal of the motor through the motor controller.

Linear acceleration and uphill driving scenarios were chosen as key conditions to evaluate the performance of the proposed control method, as they directly reflect the tracked vehicle’s dynamic response and load-handling capabilities in realistic operating environments. The linear acceleration test examines the vehicle’s ability to achieve smooth and rapid speed changes, while the uphill driving test assesses performance under increased resistance caused by the slope. The experimental setup is illustrated in Figure 7, where the test site features a sandy soil surface. The vehicle’s turning radius and speed are calculated based on the active wheel speed, which is determined from the motor speed through the dual-sided coupling drive ratio. Motor speed is obtained by recording the angular position signal via the motor controller. To validate the simulation model, critical parameters including motor torque, slope angle, vehicle mass, and rolling resistance were incorporated, ensuring that the simulated speed profile closely aligns with the experimental measurements.

The accuracy and effectiveness of the proposed control strategy were validated through a detailed comparison between vehicle speeds measured on the test bench and those predicted by the simulation model. This comparison provides a quantitative assessment of the simulation model’s fidelity and offers insights into the performance of the control approach under realistic operating conditions. Specific test parameters, including slope angle, initial speed, and load conditions, are presented in Figure 9b for reference. The selected test scenarios are designed to replicate typical driving behaviors, enabling a comprehensive evaluation of the system’s response to varied inputs and dynamic conditions. The rotational speed trends of the left and right motors, as shown in Figure 9a,b, indicate that the motors respond in a highly coordinated manner, with minimal deviation between measured and simulated data. Observations confirm that the vehicle follows driver inputs precisely, executing required maneuvers with both stability and accuracy. Minor discrepancies observed during transient events remain within acceptable engineering tolerances. Overall, the results demonstrate that the rotational speed-based control mechanism achieves reliable, precise, and robust vehicle operation, confirming its suitability for practical applications in electric tracked vehicles under diverse real-world conditions.

The experimental evaluation of the pure electric bulldozer was conducted under several key operational scenarios, including the straight-line acceleration, the straight-line deceleration, and sustained constant-speed motion. These conditions were chosen to comprehensively assess the performance and responsiveness of the proposed control strategy across different dynamic demands. Throughout the tests, the rotational speeds of both the left and right motors were continuously monitored, and the resulting trends are presented in Figure 9a,b. Comparison with the simulation results demonstrates a high degree of correspondence, with minimal discrepancies observed between the measured and predicted motor behaviors. During straight-line acceleration and deceleration, the control system effectively coordinated the dual motors, ensuring smooth and balanced vehicle motion without significant oscillation or instability. In the constant-speed scenario, the vehicle maintained a stable velocity, accurately following the desired input from the driver while compensating for minor variations in load or terrain resistance.

Overall, the test results confirm that the proposed control technique provides precise and reliable regulation of motor outputs, enabling the vehicle to execute driver commands accurately and maintain stable operation under diverse driving conditions. These findings underscore the effectiveness and robustness of the control strategy in practical applications.

6. Conclusions

This article focuses on the dynamic modeling and control tactics of the pure electric bulldozers, with specific attention on motor-independent drive designs. The following is a summary of the study’s main results and contributions. A detailed dynamic model of the pure electric bulldozer was constructed, including both the mechanical and electrical interactions under various operating situations. Building upon this dynamic study, a thorough simulation model was constructed to depict the dual-motor independent system, enabling a coordinated evaluation of both the vehicle’s mechanical system and the accompanying control algorithms. To ensure precise vehicle operation, a dual-sided independent drive control approach based on rotational speed regulation was implemented. In this system, the driving input signal is split into target torque commands for motors, allowing accurate control of both straight-line travel and complex turning maneuvers. Simulation findings reveal that, during straight-line driving, the speed and torque outputs of both motors stay closely synchronized, ensuring smooth and steady vehicle operation with minimum speed deviation. During turning maneuvers, the control strategy adjusts the torque difference between the inner and outer motors, allowing the vehicle to handle a range of turning radii with accuracy and stability. This includes tight-radius turns as well as zero-radius in-place rotations, both executed reliably under test conditions.

The results show that the method successfully coordinates the outputs of the two motors, maintains overall vehicle stability, and achieves the intended maneuverability across different operational scenarios. These findings demonstrate the practical effectiveness of the control approach and provide a solid basis for further refinement and application of pure electric tracked vehicles in real-world environments.

The efficacy of the proposed control strategy and the precision of the developed dynamic model were extensively verified. To replicate realistic operating scenarios of the pure electric bulldozer, simulations were conducted under a range of typical operating conditions, including variations in speed, load, and steering maneuvers. Key performance metrics, such as vehicle speed, motor rotational speed, torque output, and the steering behavior, were continuously monitored throughout the simulations.

The results confirmed the accuracy and reliability of the dynamic model, as reflected in the strong correspondence between the theoretical design and the simulation data. A specialized test platform, specifically designed for pure electric bulldozers, was employed for both simulations and physical experiments. These controlled tests yielded empirical data that could be directly compared to the simulation results. The experimental data analysis demonstrated that the speed regulation-based control approach successfully managed the dual motors, providing smooth acceleration, stable straight-line operation, and accurate steering performance. Throughout the tests, the vehicle maintained stability and operational accuracy, consistently responding to control inputs. Collectively, these results demonstrate the robustness and reliability of the proposed control strategy, providing a solid foundation for further refinement and practical application under real-world operating conditions. The strong agreement between simulation and experimental results further highlights the robustness and practical applicability of the control approach for fully electric tracked vehicles.

This study focuses exclusively on the design of bulldozer control strategies under the assumption that control signals are predetermined. Future work will aim to develop methods that enable bulldozers to autonomously generate control signals while also investigating the optimal coordination between batteries and motors, analogous to the fuel consumption–engine efficiency relationship in conventional fuel-powered bulldozers.