1. Introduction
With worsening global pollution, reducing fossil fuel emissions and finding alternative energy sources have become key goals in the automotive industry. Electric vehicles, favored for their low emissions and high efficiency, are gaining increased attention [
1,
2]. In recent years, electric vehicle performance and efficiency have improved, with drive-by-wire chassis and distributed drive widely adopted. Four-wheel independent drive technology, valued for its handling, power, and road adaptability, is gaining more attention [
3,
4]. Electric vehicles with four in-wheel motors do not require traditional transmission structures, as each wheel is directly driven by its motor. These motors are typically permanent magnet synchronous motors, known for their high power factor and high starting torque, giving four-wheel independent drive electric vehicles superior power performance [
5,
6]. Under an effective control strategy, both longitudinal and lateral control of distributed drive vehicles can be significantly enhanced. For example, selecting an optimal control architecture can effectively improve the vehicle’s lateral stability [
7]. Additionally, control strategies can achieve more efficient energy-saving control, highlighting the flexibility of such systems [
8]. Furthermore, there is still extensive research potential in the field of longitudinal control, particularly in drive control. By further optimizing drive control strategies, distributed drive vehicles are expected to make significant advancements in power performance, energy efficiency, and driving safety. This research is crucial for improving the overall performance of vehicles. Due to their strong power, four-wheel independent drive electric vehicles can slip on low-traction surfaces, risking tire damage and potential safety hazards [
9]. Therefore, traction control for electric vehicles with four in-wheel motors holds significant research value and importance.
Anti-slip regulation (ASR) plays a key role in vehicle performance and stability. In traditional vehicles, ASR technology is relatively mature, primarily achieved by limiting engine torque and coordinating with the braking system. However, this method has certain limitations [
10]. Four-wheel independent drive electric vehicles rely on in-wheel motors, which offer faster response and more precise control, allowing for better monitoring of each wheel’s slip condition. Compared to hydraulic and traditional mechanical systems, this setup enables more flexible and accurate traction control [
11,
12].
Figure 1 shows the structure of an electric vehicle with four in-wheel motors.
Due to varying research focuses, traction control strategies for fuel vehicles and electric vehicles have been widely developed. These methods are primarily classified into direct torque control and slip ratio control [
13].
Direct torque control aims to limit wheel slip on low-traction surfaces by detecting wheel states such as angular acceleration, inertia, or friction slip derivatives, without relying on slip ratio. Hori and colleagues developed a traction control system (TCS) based on model-following control (MFC) and optimal slip ratio control, assuming that wheel inertia drops sharply during slip to achieve anti-slip control [
14]. Yin, Hori, and Zhang proposed an ASR method based on direct torque output limitation, establishing a link between road traction and target slip ratio using wheel speed and feedback torque [
15,
16]. However, the MFC requires precise road friction information and is highly sensitive to changes in model parameters. Colli et al. used an adhesion estimator and an adhesion gradient controller, which can track the desired target over a large operating range under unknown road surfaces [
17]. Joško, Danijel, and Gilberto improved the robustness of traction control against road surface changes through static curve gradient tire control and robust switching control, based on a bidirectional sawtooth excitation signal [
18]. Zhang designed a TCS based on S-line control and a slope optimization algorithm using minimum steady-state fluctuation extremum seeking to ensure that the slip ratio approaches the optimal value [
19].
Although torque-based control limits wheel slip, real-time estimation of maximum output torque on varying road surfaces is challenging. Chen et al. proposed a slip ratio-based control to improve acceleration, better suited for four-wheel independent drive electric vehicles [
20]. The slip ratio-based control uses the optimal slip ratio as a key state to achieve precise torque management, combining dynamic models with control methods like PID, MPC, and sliding mode control. Yang, Li, and Fu set the target slip ratio at 0.15 to reduce urban driving slip and proposed an ASR method using PID and logic thresholds. While PID control lacks robustness on varying road surfaces, fuzzy algorithms can improve this [
21]. Li et al. applied sliding mode control combined with fuzzy algorithms for torque distribution among power sources, enhancing the handling stability of four-wheel-drive hybrid vehicles [
22]. The MPC algorithm replaces global one-time optimization with a rolling optimization strategy, allowing for timely compensation of uncertainties and better dynamic performance. Sekour and Hartani proposed a direct torque control (DTC) algorithm based on nonlinear model predictive control (NMP) [
23]. Sliding mode control (SMC) offers fast response and robustness to disturbances but suffers from oscillation. Zhou et al. reduced this by using a special switching function to slow the system near the sliding surface [
24]. Ricardo et al. proposed a continuous SMC algorithm using continuous approximation, showing good slip regulation and robustness against disturbances [
25]. Yu et al. designed a robust adaptive ASR controller that estimates the road peak adhesion coefficient using the Burckhard tire model and non-affine parameter estimation, improving acceleration by considering road surfaces [
26]. Guo et al. designed a method to determine the optimal slip ratio based on road surface classification, adjusting torque output to keep the slip ratio near its optimal value [
6].
In summary, the optimal slip ratio-based ASR controller includes optimal slip ratio identification and torque control. For electric vehicles with four in-wheel motors, the distributed drive offers greater optimization potential. This paper designs a road surface optimal slip ratio observer, estimating vertical and longitudinal forces using a seven-degree-of-freedom (7DOF) vehicle model and the Dugoff tire model. Fuzzy control and PSO-based BP neural networks are used to fit the optimal slip ratio curve. For torque control, an improved adaptive sliding mode control is adopted, improving the adaptive law and adjusting the sliding surface using the super-twisting sliding mode algorithm. This adjusts the hub motor torque, enhancing driving performance.
The structure of this paper is as follows:
Section 2 establishes the 7DOF vehicle dynamics model and related models;
Section 3 introduces the design of the overall control system, including the vehicle speed estimation method based on the UKF observer, an optimal slip ratio identification algorithm combined with the dynamic model, and an improved adaptive sliding mode control for optimal slip ratio tracking, achieving anti-slip regulation control;
Section 4 conducts simulation tests, validating the effectiveness of the proposed methods through comparison; finally,
Section 5 concludes the paper.
4. Simulation and Data Analysis
This paper conducts co-simulation based on Matlab/Simulink R2021a and Carsim 2020, with the simulation structure diagram shown in
Figure 13.
To verify the drive anti-slip control strategy based on road surface recognition, this paper selects a low-adhesion surface (
= 0.2), a straight road surface with three different adhesion coefficients (
= 0.8,
= 0.3,
= 0.6), and a split road surface (
= 0.8,
= 0.3) for simulation. This analysis aims to verify the feasibility of the road surface observer and the accuracy of the improved adaptive anti-slip controller in tracking the optimal slip ratio. First, the vehicle model parameters established in Carsim are shown in
Table 3.
4.1. Driving on a Low-Adhesion Road
The test road is set as a flat, straight road with an adhesion coefficient of 0.2, shown in
Figure 14. The initial vehicle speed is set to 0 km/h, and the desired driver speed is set to 80 km/h.
The vehicle is accelerated on the set low-adhesion road surface, and the simulation results are shown in
Figure 15.
The simulation results show that as the vehicle begins to accelerate, both the wheel speeds and the vehicle speed increase. The road surface observer identifies the adhesion coefficients for the contact surfaces of each wheel. On the road with an adhesion coefficient of 0.2, the identification results stabilize after approximately 2.3 s: 0.201 for the front wheels, with an error of 0.001, and 0.203 for the rear wheels, with an error of 0.003. This indicates that the road surface observer can effectively identify the adhesion coefficient under the low-adhesion road, thereby fitting the optimal target slip ratio.
At the moment the vehicle begins to accelerate, both the torque and slip ratio increase rapidly with vehicle speed. The initial slip ratio approaches 1 due to the vehicle and wheel speeds both being zero, causing a near-limit phenomenon when wheel speed is used as the denominator. After approximately 2.4 s, the slip ratios of all wheels gradually stabilize, with the front wheels’ slip ratio remaining around 0.0665, with an error of 0.0003, and the rear wheels stabilizing at 0.067, with an error of 0.0002. Under ASR control, the tracking performance of the optimal slip ratio meets the required standards. The simulation results are summarized in
Table 4.
To verify the effectiveness of the drive anti-slip control strategy in improving vehicle acceleration performance, a comparison of acceleration performance with and without the drive anti-slip function was conducted under the same simulation conditions. The simulation results are shown in
Figure 16.
From the results, it can be seen that under the drive anti-slip controller used in this paper, the vehicle speed after 10 s of acceleration in the same conditions is 62.99 km/h, while without the drive anti-slip function, the speed at this point is 58.55 km/h. A comparison shows that on low-adhesion surfaces, the acceleration with drive anti-slip control is 1.7497, whereas without the drive anti-slip function, the acceleration is 1.63, representing an improvement of 0.119. Additionally, as shown in the figure, the UKF speed estimation can accurately estimate the longitudinal vehicle speed.
To verify the robustness of the drive anti-slip controller proposed in this paper, a comparison of simulation results with a conventional sliding mode controller is conducted (using the left front wheel as an example). Results are shown in
Figure 17.
As shown in
Figure 17a, the output torque under different control strategies increases instantly when acceleration starts at 0 s. The control torque gradually approaches a steady-state value within the 0–2 s interval, but the SMC control exhibits noticeable oscillations. This is because, when approaching the sliding mode surface, the control system experiences frequent switching near the surface, leading to high-frequency chattering. However, the improved ASMC proposed in this paper effectively mitigates the oscillation issue by using an adaptive law and adjusting the switching function.
As shown in
Figure 17b, after the 2−s mark, there is some chattering in the slip ratio tracking, and the convergence time of the tracking slip ratio is relatively long. The tracking slip ratio for the conventional SMC is 0.0746, with an error of 0.0072, which indicates lower tracking accuracy compared to the improved ASMC. The comparison results are shown in
Table 5.
4.2. Driving on a Joint Road
The test road is set as a flat, joint road with step changes in adhesion coefficients (0.8–0.3–0.6), shown in
Figure 18. The initial vehicle speed is set to 0 km/h, and the driver’s desired speed is set to 80 km/h.
The vehicle is accelerated on the set joint road, and the simulation results are shown in
Figure 19.
After the vehicle starts on the joint road surface, the wheel speeds gradually increase, and the road surface observer begins monitoring at 0.05 s. On the road surface with an adhesion coefficient of 0.8, the identified adhesion coefficient for the front axle wheels is 0.805, with an error of 0.005, and for the rear axle wheels, it is 0.803, with an error of 0.003. Compared to the ideal slip ratio of 0.1294, the actual slip ratio for the front axle is 0.1296, with an error of 0.0002, and for the rear axle, it is 0.1295, with an error of 0.0001. This indicates that the actual tracking performance meets expectations.
At 2 s, the front wheels first enter the low-adhesion road surface with an adhesion coefficient of 0.3, and the increase in wheel speed slows down to track the optimal slip ratio. Once the vehicle is fully on the low-adhesion surface, the identified adhesion coefficient for the front axle wheels is 0.304, with an error of 0.004, and for the rear axle wheels, it is 0.307, with an error of 0.007. Compared to the ideal slip ratio of 0.07878, the slip ratio for the front wheels is 0.0792, with an error of 0.00042, and for the rear wheels, it is 0.0797, with an error of 0.00092.
At 3.6 s, the front wheels enter the road surface with an adhesion coefficient of 0.6, and the increase in wheel speed accelerates to track the optimal slip ratio. Once the vehicle is fully on this surface, the identified adhesion coefficient for the front axle wheels is 0.6001, with an error of 0.0001, and for the rear axle wheels, it is 0.6004, with an error of 0.0004. Compared to the ideal slip ratio of 0.1109, the actual slip ratio for the front axle wheels is 0.11135, with an error of 0.00045, and for the rear axle wheels, it is 0.11174, with an error of 0.00084. This indicates that the control performance on this section of the road meets the expected results. The simulation results are summarized in
Table 6.
To assess the impact of the drive anti-slip control strategy on acceleration performance, a comparison was made with and without the anti-slip function under the same conditions. The results are shown in
Figure 20.
The results show that with the drive anti-slip function enabled, the vehicle reached the target speed in 4.3 s, with a speed of 80.001 km/h, compared to 67.743 km/h without the function. The acceleration on the joint road surface was 5.05 m/s2 with the anti-slip function, and 4.28 m/s2 without it, an improvement of 0.77 m/s2. This demonstrates that the drive anti-slip control significantly enhances vehicle acceleration performance.
To verify the robustness of the drive anti-slip controller proposed in this paper, a comparison of simulation results with a conventional sliding mode controller was conducted (using the left front wheel as an example). The results are shown in
Figure 21.
As shown in
Figure 21a, the output torque increases instantly at 0 s when acceleration begins. Between 0.2 and 0.5 s, the ASMC converges more quickly and reaches a steady state, while the SMC exhibits noticeable oscillations. Although the oscillation amplitude is small and its impact on the slip ratio is limited, the oscillation is still present. Based on road surface changes, the output torque quickly adjusts to control the slip ratio. However, under SMC control, there is a larger steady-state error and significant torque oscillation, which the ASMC effectively resolves.
As shown in
Figure 21b, on a road surface with an adhesion coefficient of 0.8, the slip ratio under SMC control is 0.1356, with an error of 0.0062; on a 0.3 coefficient surface, the slip ratio is 0.0845, with an error of 0.0057; and on a 0.6 surface, the slip ratio is 0.1186, with an error of 0.0077. Compared to the improved ASMC, the control performance of SMC still shows a gap. The comparison results are shown in
Table 7.
4.3. Driving on a Split Road
The test road is set as a straight split road (left side adhesion coefficient of 0.8, right side adhesion coefficient of 0.2), with an initial vehicle speed of 0 km/h and a desired driver speed of 80 km/h, as shown in
Figure 22.
The vehicle is accelerated on the set split road, and the simulation results are shown in
Figure 23:
When the vehicle starts on the split road surface, due to the different adhesion coefficients of the left and right wheels, each wheel accelerates at different rates. After 0.8 s, the adhesion coefficient of the left front wheel stabilizes at 0.804 with an error of 0.004, the left rear wheel stabilizes at 0.802 with an error of 0.002; the right front wheel stabilizes at 0.205 with an error of 0.005, and the right rear wheel stabilizes at 0.202 with an error of 0.002. The slip ratio of the right front wheel is 0.0672 with an error of 0.0004, and the right rear wheel slip ratio is 0.067 with an error of 0.0002. The simulation results are summarized in
Table 8.
However, during the simulation, it was found that the recognition results of the left wheels suddenly dropped, which can be attributed to the large difference in road conditions between the left and right sides, resulting in a large yaw moment during start-up and causing the vehicle to deviate from the track. The results of the vehicle yaw rate are shown in
Figure 24.
Due to the significant difference in the adhesion coefficients of the split road surface, there is a large torque difference between the two sides, resulting in a high yaw rate, causing the vehicle to deviate from its path. Once the vehicle fully transitions to the low-adhesion surface, the yaw rate drops to zero.
To address this issue, a torque distribution adjustment is implemented. When a large difference in adhesion coefficients between the left and right sides is detected, the lowest distribution principle is applied. Specifically, when the adhesion coefficient on the left side is greater than that on the right side, the left-side torque is adjusted to match the right-side torque. The simulation results are shown in
Figure 25, where the torque distribution adjustment takes effect at 1 s.
Due to differing adhesion coefficients, the left wheels start with a coefficient of 0.8, while the right wheels start with 0.2, generating a yaw rate. Before the adjustment activates at 1 s, the yaw rate increases. After applying the lowest torque output principle due to the adhesion difference, the left front wheel’s torque decreases, and the yaw rate approaches zero. The slip ratio remains low due to the use of low-adhesion torque on the high-adhesion surface. To verify the robustness of the proposed drive anti-slip controller, a comparison with a conventional sliding mode controller is performed (left front wheel as an example). The results are shown in
Figure 26.
As shown in
Figure 26a, under different control strategies, the output torque increases rapidly during acceleration. The improved ASMC quickly converges to a steady-state value, while the SMC exhibits oscillations and converges more slowly. After 1 s, the adjustment strategy takes effect, and both strategies stabilize at lower torque outputs. The simulation results are summarized in
Table 9.
As shown in
Figure 26b, in this scenario, when the slip ratio has not fully converged and the distribution strategy is executed, the slip ratios are maintained at a relatively low level, meaning that the low-adhesion optimal torque control is executed on the high-adhesion surface. It can be observed that under SMC, there is a certain level of oscillation and error. The improved ASMC achieves better control performance.
5. Conclusions
This paper establishes a vehicle dynamics and Dugoff tire model, using an unscented Kalman filter to estimate the longitudinal speed with parameters from Carsim. Fuzzy control based on the Burckhardt tire model is implemented, with peak adhesion and optimal slip ratio curves fitted via a particle swarm-optimized BP neural network. An improved adaptive sliding mode controller optimizes torque distribution on split roads. Simulation results confirm the effectiveness of the approach.
On low-adhesion, jointed, and split roads, the proposed optimal slip ratio identification algorithm accurately identifies the road’s optimal slip ratio, featuring fast response and high adaptability.
The improved adaptive sliding mode ASR controller demonstrates high accuracy, fast convergence, and strong robustness, effectively tracking optimal slip ratios and improving acceleration on various road surfaces. Compared to standard SMC, it reduces chattering, improves stability, and enhances response time and tracking precision.
In split road simulations, solely pursuing optimal slip ratios for each side increases the yaw rate and causes vehicle deviation. The proposed torque distribution strategy effectively mitigates this, ensuring stable straight-line driving with minimal yaw rate.
This study is primarily based on theoretical simulations. In practical applications, multiple factors may affect control performance. For example, sensor noise can impact vehicle speed estimation and slip ratio calculation, complex road conditions can increase the difficulty of road surface recognition, and the computational burden of the controller can affect accuracy. Additionally, the simplifications made in the model can be further explored in future research. For instance, road gradients, especially in steep conditions, can significantly impact the vehicle’s center of gravity transfer and acceleration/deceleration, affecting road surface recognition. Air resistance can have a significant impact on vehicle speed and energy consumption at high speeds, and suspension damping is an important factor in analyzing vehicle stability and comfort. Future work could focus on adjusting control strategies qualitatively and quantitatively based on these factors, which would be of great value. To address these issues, real vehicle tests with signal filtering and experiments under various operating conditions are needed, along with the selection of appropriate hardware (Hall effect wheel speed sensors for accurate feedback), testing on surfaces with different friction coefficients, and testing at higher target speeds. Finally, adjusting controller parameters will help improve vehicle acceleration performance. Conducting and furthering the above-mentioned future work will be highly valuable for deepening and broadening this study.