Electric cars have become a central focus of modern transportation research, especially with the rapid growth of distributed drive architectures. In this thesis, I focus on the longitudinal control system of four-wheel-distributed drive electric cars, aiming to improve driving stability and traction performance under complex road conditions. The research integrates vehicle dynamics, computer vision, and advanced nonlinear control theory. I developed a complete simulation platform, proposed a robust road adhesion coefficient estimation method for abnormal illumination scenarios, designed an unscented particle filter for longitudinal vehicle speed estimation, and constructed a model-free adaptive sliding mode controller for drive anti-skid control. Finally, I verified the proposed strategy through hardware-in-the-loop experiments. The overall results indicate that the proposed methods effectively reduce wheel slip, enhance acceleration performance on low-adhesion roads, and improve vehicle safety, which is of significant importance for the application of active safety systems in electric cars.
With the rapid increase in the number of vehicles, traffic accidents have become a major social concern. In 2024, the number of motor vehicles in China reached 453 million, and a large proportion of accidents are caused by poor road surface conditions. In particular, wet, icy, or snowy roads can dramatically reduce the friction between tires and the road surface, leading to loss of control. Active safety technologies, such as anti-skid control, can significantly reduce this risk by optimizing the vehicle’s dynamic response. For distributed drive electric cars, each wheel can be controlled independently, which provides more flexibility but also greater complexity. A precise estimation of the road adhesion coefficient is critical, because it determines the upper bound of tire–road forces. In this study, I rely on the national natural science foundation projects to investigate the key technologies for distributed drive electric cars. The contributions are organized as follows.
1. Vehicle Dynamics Modeling for Distributed Drive Electric Cars
For the purpose of control strategy development and verification, I built a high-fidelity simulation model in MATLAB/Simulink. The model consists of a vehicle body dynamics model, a wheel rotational dynamics model, a tire model, and a wheel-hub motor model. This platform is then integrated with CarSim as the plant model for co-simulation. Since the longitudinal dynamics are the main concern of this thesis, a five-degree-of-freedom model is sufficient: one degree for the longitudinal motion and four degrees for the wheel rotations. The longitudinal motion is described as
$$m\dot{v}_x = F_{xfl} + F_{xfr} + F_{xrl} + F_{xrr},$$
where \(m\) is the vehicle mass, \(v_x\) is the longitudinal velocity, and \(F_{xfl},F_{xfr},F_{xrl},F_{xrr}\) are the longitudinal tire forces at the front-left, front-right, rear-left, and rear-right wheels, respectively. The wheel rotational dynamics are given by
$$I_w \dot{\omega}_i = T_i – F_{xi} R, \quad i \in \{fl,fr,rl,rr\},$$
where \(I_w\) is the wheel moment of inertia, \(\omega_i\) is the wheel angular velocity, \(T_i\) is the driving torque, and \(R\) is the wheel rolling radius. The key parameters are listed in Table 1.
| Parameter | Value | Unit |
|---|---|---|
| Vehicle mass \(m\) | 1270 | kg |
| Distance from CG to front axle | 1.015 | m |
| Distance from CG to rear axle | 1.895 | m |
| Wheel moment of inertia \(I_w\) | 0.87 | kg·m² |
| Wheel rolling radius \(R\) | 0.325 | m |
| Height of CG \(h_g\) | 0.54 | m |
| Gravitational acceleration | 9.8 | m/s² |
For the tire model, I selected the well-known “Magic Formula” semi-empirical model. This model captures the nonlinear relationship between longitudinal tire force and slip ratio with good accuracy and acceptable computation cost. The longitudinal tire force is expressed as
$$F_x(\kappa) = D \sin\left(C \arctan\left(B\kappa – E\left(B\kappa – \arctan(B\kappa)\right)\right)\right),$$
where \(\kappa\) is the wheel slip ratio, \(B\) is the stiffness factor, \(C\) is the shape factor, \(D\) is the peak factor that depends on the vertical load and the road adhesion coefficient, and \(E\) is the curvature factor. This model is used both in the simulation plant and in the derivation of the optimal slip ratio. The vertical loads of the tires are calculated by considering the static weight distribution and the longitudinal load transfer:
$$F_{zfl} = F_{zfr} = \frac{m g l_r – m a_x h_g}{2(l_f+l_r)},$$
$$F_{zrl} = F_{zrr} = \frac{m g l_f + m a_x h_g}{2(l_f+l_r)}.$$
For the electric drive system, a permanent magnet synchronous motor model is established. The open-loop transfer function of the motor drive system is selected as
$$G(s) = \frac{1}{0.4s + 1} \cdot \frac{1}{7.5s + 0.25}.$$
The motor parameters used in the simulation are listed in Table 2.
| Parameter | Value | Unit |
|---|---|---|
| Rated power | 40 | kW |
| Peak power | 220 | kW |
| Rated torque | 180 | N·m |
| Peak torque | 820 | N·m |
This complete vehicle dynamics model provides a reliable simulation environment for the subsequent estimation algorithms and the drive anti-skid controller.
2. Road Adhesion Coefficient Estimation under Abnormal Illumination
The road adhesion coefficient is a crucial parameter for drive anti-skid control. I designed a road adhesion estimation method based on data augmentation and a Transformer network, which is robust to abnormal illumination scenes such as nighttime low light, rain, fog, and sudden exposure changes. The overall framework is shown in Figure 1. First, a dataset of road images is constructed from self-captured images, public datasets, and synthesized foggy images. Then, a DeepLabV3+ semantic segmentation network is applied to extract the road area. After that, an EnlightenGAN-based image enhancement model improves the quality of images captured under harsh illumination. A Transformer-in-Transformer (TNT) classification model is then trained to recognize the road surface type. Finally, a confidence-weighted temporal fusion module is used to obtain a stable and spatiotemporally consistent road adhesion coefficient estimate.
Several types of deep learning modules are used in the framework, and it is necessary to introduce the basic structure of convolutional neural networks first. A convolutional layer uses kernels to perform feature extraction with local connectivity and parameter sharing. For a two-dimensional convolution, the operation is
$$Y(i,j) = \sum_{m=0}^{k_1-1}\sum_{n=0}^{k_2-1} X(i+m,j+n) W(m,n) + b.$$
Batch normalization is placed after the convolution to standardize each mini-batch so that the input of each layer has a zero mean and unit variance. The normalization procedure is
$$\hat{x}_i = \frac{x_i – \mu_B}{\sqrt{\sigma_B^2+\epsilon}}, \quad y_i = \gamma \hat{x}_i + \beta,$$
where \(\mu_B\) and \(\sigma_B^2\) are the mini-batch mean and variance, and \(\gamma,\beta\) are learnable scale and shift parameters. Activation functions introduce nonlinearity. The widely used ReLU function is
$$f(x) = \max(0,x),$$
while Leaky ReLU is a variant that avoids dying neurons:
$$f(x) = \begin{cases} x & \text{if } x\ge 0,\\ \alpha x & \text{otherwise.} \end{cases}$$
Pooling layers downsample the feature maps. Maximum pooling retains the strongest local feature, while average pooling smooths the region and retains global information. A fully connected layer then maps the high-dimensional features to classification scores, which are normalized by the softmax function:
$$p_i = \frac{e^{z_i}}{\sum_{j=1}^{C} e^{z_j}},$$
where \(C\) is the number of classes and \(z_i\) is the score for class \(i\).
The road surface categories considered in this study are dry asphalt, wet asphalt, foggy asphalt, and nighttime asphalt. The constructed dataset contains 13,478 images in total. The distribution of samples is listed in Table 3.
| Road type | Rainy | Foggy | Night | Sunny | Total |
|---|---|---|---|---|---|
| Number of samples | 3729 | 2669 | 3298 | 3782 | 13478 |
| Own-captured ratio (%) | 80 | 0 | 80 | 90 | 60 |
| Public dataset ratio (%) | 20 | 0 | 20 | 10 | 20 |
| Synthetic fog ratio (%) | 0 | 100 | 0 | 0 | 20 |
All images are of structured roads, specifically urban or highway asphalt roads with clear lane markings, as these are the most common scenarios for electric cars equipped with advanced driver assistance systems. The foggy images are synthesized by the atmospheric scattering model:
$$I(x) = J(x) t(x) + A(1-t(x)), \quad t(x)=e^{-\beta d(x)},$$
where \(I(x)\) is the foggy image, \(J(x)\) is the clear image, \(A\) is the atmospheric light, \(\beta\) is the scattering coefficient, and \(d(x)\) is the scene depth. This approach creates a diverse set of fog levels from existing sunny and rainy images.
DeepLabV3+ is a semantic segmentation network that uses atrous convolution and an encoder-decoder structure. The encoder uses a modified MobileNetV3 backbone, while the decoder recovers fine boundary details. The atrous spatial pyramid pooling module captures multi-scale contextual information. After segmentation, a binary mask operation extracts the road pixels. The mask is generated by simple gray thresholding: road pixels are set to 1 and background pixels to 0. The extracted road image is then processed by the enhancement module.
EnlightenGAN is an unsupervised generative adversarial network that can enhance low-light images without paired training data. It consists of a generator and two discriminators: a global discriminator and a local discriminator. The generator is a modified U-Net with self-regularized attention blocks. The global discriminator uses a relativistic discriminator structure, while the local discriminator randomly crops 64×64 patches from the output and the real images to ensure local detail fidelity. The total loss is a combination of global adversarial loss, local adversarial loss, and self-feature preservation loss. The self-feature preservation loss is defined as the distance in VGG feature space between the input low-light image and the enhanced output:
$$L_{SFP} = \frac{1}{W_{i,j} H_{i,j}} \sum_{x=1}^{W_{i,j}}\sum_{y=1}^{H_{i,j}} \left\| \phi_{i,j}(I_L) – \phi_{i,j}(G(I_L)) \right\|^2,$$
where \(\phi_{i,j}\) denotes the feature map extracted from a pretrained VGG16 network.
For the road surface classification task, I selected the Transformer-in-Transformer (TNT) model. TNT models an image as a sequence of visual sentences, where each sentence is further divided into visual words. The image is split into \(n\) patches, and each patch \(X_i\) is divided into \(m\) sub-patches. The sub-patches are linearly projected into word embeddings:
$$Y_{i,j} = \mathrm{FC}(\mathrm{Vec}(x_{i,j})).$$
Then, an inner Transformer block processes the visual word embeddings inside each patch:
$$Y_l^t = Y_{l-1}^t + \mathrm{MSA}(\mathrm{LN}(Y_{l-1}^t)).$$
Next, the word embeddings are projected to the sentence embedding space:
$$Z_l = Z_{l-1} + \mathrm{FC}(\mathrm{Vec}(Y_l)).$$
Finally, an outer Transformer block processes the sentence embeddings. The TNT architecture therefore learns both local and global feature representations, which is beneficial for distinguishing different road surface textures under varying illumination.
To obtain a single road adhesion coefficient from the classified road type, I constructed a mapping table based on extensive published experiment results. Table 4 lists the practical ranges of adhesion coefficients for each road type.
| Road type | Upper bound of adhesion coefficient | Lower bound of adhesion coefficient |
|---|---|---|
| Wet asphalt | 0.6 | 0.3 |
| Foggy asphalt | 0.6 | 0.4 |
| Night asphalt | 0.7 | 0.5 |
| Dry asphalt | 0.8 | 0.7 |
A single-frame classification result is often noisy due to transient occlusions, weather changes, or local reflections. To solve this issue, I developed a weighted temporal fusion strategy. First, all image recognition results are mapped into the vehicle coordinate frame using camera calibration parameters:
$$\begin{pmatrix} x_{img} \\ y_{img} \\ 1 \end{pmatrix} = \begin{pmatrix} 1/d_x & 0 & u_0 \\ 0 & 1/d_y & v_0 \\ 0 & 0 & 1 \end{pmatrix}^{-1} \begin{pmatrix} u \\ v \\ 1 \end{pmatrix},$$
$$\begin{pmatrix} x_v \\ y_v \\ z_v \end{pmatrix} = R \begin{pmatrix} x_{cam} \\ y_{cam} \\ z_{cam} \end{pmatrix} + T.$$
For historical frames, motion compensation is applied using the estimated inter-frame vehicle rotation and translation:
$$\begin{pmatrix} x_v^{(t)} \\ y_v^{(t)} \\ z_v^{(t)} \end{pmatrix} = \Delta R \begin{pmatrix} x_v^{(t-1)} \\ y_v^{(t-1)} \\ z_v^{(t-1)} \end{pmatrix} – \Delta T.$$
Then, for every road point, the recognition results from several historical frames are combined with weights. The final weight for frame \(i\) is the product of a time-decay weight \(w_i=\alpha^{t-i}\) and the classifier confidence \(c_i\). The fused adhesion coefficient is
$$u_{final} = \sum_{i=0}^{n} \left( \frac{w_i c_i}{\sum_{j=0}^{n} w_j c_j} \right) u_i.$$
This mechanism ensures that the final estimate is smooth and does not jump abruptly when a single frame is misclassified. I trained the TNT model with a training set of 10,782 images and a test set of 2,696 images. After 500 epochs, the loss converged, and the average classification accuracy on the test set reached 98.38%. Table 5 shows the ablation study results.
| Model configuration | Average classification accuracy (%) | Standard deviation of estimation | Inference time (ms) |
|---|---|---|---|
| TNT only | 92.65 | 0.12 | 19.7 |
| TNT + EnlightenGAN | 95.82 | 0.08 | 22.4 |
| TNT + EnlightenGAN + Temporal fusion | 98.38 | 0.05 | 24.3 |
The real-vehicle deployment was performed on an electric car platform equipped with a high-resolution RGB camera and an industrial embedded computer. The camera is installed at the roof center so that the complete road surface in front of the vehicle is captured. The proposed estimation method was tested on a single-surface condition with a road adhesion coefficient of 0.7. The estimated result converged within 0.2 seconds, and the standard deviation was only about 0.05. In a split-mu condition where the first 30 meters were dry asphalt with adhesion 0.7 and the following part was wet asphalt with adhesion 0.5, the algorithm detected the change quickly and re-converged to the new level within about 0.3 seconds. These real-car tests proved that the proposed vision-based estimation method is robust and stable for drive anti-skid control of electric cars.
3. Longitudinal Vehicle Speed Estimation Based on Unscented Particle Filter
Accurate longitudinal vehicle speed is essential for computing the wheel slip ratio. The speed cannot be directly measured from wheel speed sensors when wheels are slipping or locking. Therefore, I designed an unscented particle filter (UPF) that combines the advantages of unscented Kalman filtering and particle filtering. UPF is particularly suitable for highly nonlinear vehicle dynamics with non-Gaussian noise. The state vector is chosen as
$$x = \begin{bmatrix} v_x & \omega_{fl} & \omega_{fr} & \omega_{rl} & \omega_{rr} \end{bmatrix}^T,$$
with the control input
$$u = \begin{bmatrix} T_{fl} & T_{fr} & T_{rl} & T_{rr} \end{bmatrix}^T.$$
The continuous state equations are
$$\dot{v}_x = \frac{1}{m} \left( F_{xfl}+F_{xfr}+F_{xrl}+F_{xrr} \right),$$
$$\dot{\omega}_i = \frac{1}{I_w} \left( T_i – F_{xi} R \right), \quad i=fl,fr,rl,rr.$$
After Euler discretization with time step \(\Delta t\), we obtain
$$x_{k+1} = x_k + f(x_k,u_k) \Delta t + w_k,$$
where \(w_k\) is the process noise. The measurement vector is chosen as the wheel angular velocities and the longitudinal acceleration from an inertial sensor:
$$y_k = h(x_k) + v_k.$$
The UPF algorithm proceeds as follows. For each particle \(i\), an unscented transform is used to generate sigma points around the current state estimate:
$$\mathcal{X}_{k-1}^{(i)} = \left[ \hat{x}_{k-1}^{(i)}, \ \hat{x}_{k-1}^{(i)} \pm \sqrt{(n+\lambda)P_{k-1}^{(i)}} \right].$$
These points are propagated through the nonlinear dynamics, and the predicted mean and covariance are computed:
$$\hat{x}_{k|k-1}^{(i)} = \sum_{j=0}^{2n} W_j^m \mathcal{X}_{k|k-1,j}^{(i)},$$
$$P_{k|k-1}^{(i)} = \sum_{j=0}^{2n} W_j^c \left( \mathcal{X}_{k|k-1,j}^{(i)} – \hat{x}_{k|k-1}^{(i)} \right) \left( \mathcal{X}_{k|k-1,j}^{(i)} – \hat{x}_{k|k-1}^{(i)} \right)^T + Q.$$
Similarly, the measurement prediction and the cross-covariance are obtained through the unscented transform. The Kalman gain is then computed as
$$K_k^{(i)} = P_{xy}^{(i)} (P_{yy}^{(i)})^{-1}.$$
Each particle state and covariance is updated accordingly:
$$\hat{x}_k^{(i)} = \hat{x}_{k|k-1}^{(i)} + K_k^{(i)} (y_k – \hat{y}_{k|k-1}^{(i)}),$$
$$P_k^{(i)} = P_{k|k-1}^{(i)} – K_k^{(i)} P_{yy}^{(i)} (K_k^{(i)})^T.$$
The particle weight is updated based on the likelihood of the actual measurement:
$$w_k^{(i)} \propto w_{k-1}^{(i)} \mathcal{N}\left(y_k; \hat{y}_{k|k-1}^{(i)}, P_{yy}^{(i)}\right).$$
After normalization, we compute the effective sample size \(N_{eff}=1/\sum(w_k^{(i)})^2\). If \(N_{eff}\) is lower than the threshold, resampling is performed. The final longitudinal velocity estimate is
$$\hat{v}_x = \sum_{i=1}^{N} w_k^{(i)} v_{x,k}^{(i)}.$$
I verified the UPF algorithm in a CarSim/Simulink co-simulation scenario. The vehicle accelerated from 40 km/h to 90 km/h, then decelerated to 40 km/h, and accelerated again to 110 km/h on a dry road. The estimated longitudinal speed closely followed the actual speed with a maximum estimation error of 1.2 km/h. This confirms that the UPF algorithm provides both high accuracy and real-time capability even during rapid acceleration and deceleration events. The precise speed estimate is crucial for drive anti-skid control because the slip ratio calculation directly depends on both the wheel speed and the longitudinal vehicle speed.
4. Drive Anti-Skid Control Based on Optimal Slip Ratio and Model-Free Adaptive Sliding Mode Control
The objective of drive anti-skid control is to regulate the wheel slip ratio to the optimal value that maximizes tire–road adhesion utilization. The wheel slip ratio during traction is defined as
$$\kappa = \frac{\omega R – v_x}{\omega R},$$
where \(\omega R > v_x\). Differentiating this expression with respect to time gives
$$\dot{\kappa} = \frac{\dot{\omega} R v_x – \omega R \dot{v}_x}{(\omega R)^2}.$$
Using the rotational dynamics and the vehicle longitudinal dynamics, we can write the slip ratio dynamics in the form
$$\dot{\kappa} = f(\omega, v_x, F_x) + g(\omega, v_x) T,$$
where \(f\) is an unknown nonlinear term and \(g\) is the control input gain. Since precise modeling of \(f\) is difficult, I adopt a model-free adaptive control approach. The nonlinear system is linearized locally by the concept of pseudo-partial derivative (PPD):
$$\dot{\kappa}(k) = \Phi(k) \Delta T(k) + d(k),$$
where \(\Phi(k)\) is the pseudo-partial derivative, \(\Delta T(k)=T(k)-T(k-1)\) is the control increment, and \(d(k)\) represents the unmodeled dynamics and bounded disturbances. The PPD is estimated online by a projection algorithm:
$$\hat{\Phi}(k) = \hat{\Phi}(k-1) + \frac{\eta \Delta T(k-1)}{\mu + |\Delta T(k-1)|^2} \left( \Delta \kappa(k) – \hat{\Phi}(k-1) \Delta T(k-1) \right),$$
with a reset mechanism to keep \(|\hat{\Phi}(k)| \ge \varepsilon\). The control law is designed using a sliding mode surface for the slip ratio tracking error:
$$e(k) = \kappa(k) – \kappa_{opt}(k),$$
$$s(k) = e(k).$$
The desired control increment is computed using the reaching law \(s(k+1)=(1-\lambda)s(k)\). After algebraic manipulation, the control law becomes
$$\Delta T(k) = \frac{\rho}{\lambda + \hat{\Phi}(k)^2} \left( \hat{\Phi}(k) \left( \kappa_{opt}(k+1) – \kappa(k)\right) + (1-\lambda) s(k) – \hat{d}(k)\right).$$
In the above expression, \(0<\lambda<1\) controls the convergence rate, \(\rho>0\) is a step factor, and \(\hat{d}(k)\) is the estimated disturbance updated by an adaptive law. This model-free sliding mode controller does not require an explicit vehicle or tire model, which makes it suitable for complex and varying road conditions. The sliding mode component provides robustness against parameter uncertainties, and the model-free adaptive component avoids the chattering problem by not relying on a discontinuous sign function. The overall control input is
$$T(k) = T(k-1) + \Delta T(k).$$
To determine the target optimal slip ratio, I use the Magic Formula tire model and the estimated road adhesion coefficient. The adhesion coefficient \(\mu(\kappa)\) is plotted as a function of slip ratio, and the optimal slip ratio is defined as the value that maximizes \(\mu(\kappa)\). Since an analytic solution is difficult because of the nested trigonometric functions, I solve it numerically using Brent’s method. The optimization problem is
$$\kappa_{opt} = \arg\min_{\kappa\in[0,0.5]} -\mu(\kappa).$$
Table 6 lists the calculated optimal slip ratios for several typical road types.
| Road type | Optimal slip ratio | Peak adhesion coefficient |
|---|---|---|
| Dry asphalt | 0.168 | 1.173 |
| Dry concrete | 0.157 | 1.091 |
| Wet asphalt | 0.129 | 0.800 |
| Wet cobblestone | 0.086 | 0.380 |
| Snow | 0.049 | 0.182 |
| Ice | 0.028 | 0.047 |
To obtain a continuous relationship between the optimal slip ratio and the peak adhesion coefficient, I performed a linear regression on the data:
$$\kappa_{opt} = p_1 \mu_{max} + p_2,$$
where \(p_1=0.1252\) and \(p_2=0.0245\). This curve is then used online to generate the reference slip ratio from the estimated road adhesion coefficient. For instance, when the road adhesion coefficient is estimated as 0.2, the optimal slip ratio is approximately 0.05; when the estimated coefficient is 0.8, the optimal slip ratio is approximately 0.20. The torque command is also physically bounded by the motor peak torque and the tire-road force limit:
$$T_{i,\max} = \mu F_{zi} R.$$
The controller was validated through CarSim/Simulink co-simulation in two scenarios. First, I simulated a uniform low-adhesion road with a peak adhesion coefficient of 0.2. The vehicle started from rest with full throttle. The simulation results are summarized in Table 7.
| Scenario | Control | Final vehicle speed | Time to final speed | Wheel slip behavior |
|---|---|---|---|---|
| Uniform road (μ=0.2) | With anti-skid | 118.4 km/h | 19.03 s | Slip ratio converged to 0.05 |
| Uniform road (μ=0.2) | Without anti-skid | Low speed | Severe wheel spin | Slip ratio above 0.8 |
| Split-mu road (μ=0.2→0.8) | With anti-skid | 118.2 km/h | 9.4 s | No visible slip |
| Split-mu road (μ=0.2→0.8) | Without anti-skid | Significant speed loss | Wheels spinning | Slip ratio high before entering high-μ road |
In the uniform low-μ condition, the controller quickly limited the slip ratio and enabled the vehicle to use the limited available friction efficiently. Without anti-skid control, the wheels spun severely and almost no traction force was generated. Similar observations were made for the split-mu road from 0.2 to 0.8. The proposed strategy successfully adapted to the changing surface condition without any mode switching logic or precise model information. The simulation results indicate that the drive anti-skid controller significantly improves both traction and stability for electric cars driving on low-adhesion roads.
5. Hardware-in-the-Loop Verification
To verify that the proposed control strategy works correctly in a realistic electronic control unit environment, I performed hardware-in-the-loop (HiL) experiments. The HiL platform comprises a test bench with a D2P rapid-prototyping controller, an NI real-time simulator, and a CarSim vehicle model. The D2P controller runs the compiled control strategy, while the NI real-time simulator executes the CarSim vehicle model in real time. CAN communication provides the interface between the two systems. The general HiL setup is depicted in the following flow:
- Build the CarSim vehicle model and export it as a dynamic-link library.
- Generate a VeriStand project and configure the real-time simulator.
- Build the control strategy in Simulink using MotoHawk blocks.
- Compile the control model and download it to the D2P controller.
- Configure CAN messages and start the real-time loop.
- Record the experimental data and validate the control performance.
In the HiL test, I selected two representative conditions: a uniform road with an adhesion coefficient of 0.8, and a split-mu road where the adhesion coefficient changes from 0.8 to 0.2. The vehicle starts from rest with a full throttle command. The measured results are listed in Table 8.
| Scenario | Control | Time (s) | Final speed (km/h) | Slip ratio behavior |
|---|---|---|---|---|
| Uniform μ=0.8 | With anti-skid | 4.6 | 112.35 | Converged to 0.2, no spin |
| Uniform μ=0.8 | Without anti-skid | 4.6 | Wheel spin observed | Slip ratio around 0.8 |
| Split μ=0.8→0.2 | With anti-skid | 9.7 | 115.17 | Torque reduced after entering low-μ road |
| Split μ=0.8→0.2 | Without anti-skid | 9.7 | Severe wheel spin on low-μ road | High slip ratio |
In the uniform high-adhesion road condition, the wheels accelerated very fast initially. Without anti-skid control, even on a high-μ road, a sudden high demand of torque from standstill can cause a short period of excessive slip. The proposed controller rapidly reduced the torque command to the optimal value so that the slip ratio converged to 0.2. This allows the vehicle to achieve high longitudinal acceleration without losing control. The HiL results are consistent with the simulations and prove that the control algorithm is feasible for real-time embedded control.
In the split-mu condition, the vehicle first drives on a dry road with \(\mu=0.8\), then enters a low-adhesion road with \(\mu=0.2\). When the vehicle transitions from the high-adhesion to the low-adhesion surface, the controller detects the increasing slip ratio and immediately reduces the motor torque. The wheel slip ratio is maintained near the optimal value of 0.05. In contrast, without the controller, the wheels spin violently since the torque remains at the maximum value. This demonstrates the necessity of road adhesion estimation and fast torque regulation. The HiL results confirm that the proposed strategy is effective and robust under real-time hardware implementation.
6. Conclusion and Outlook
In this thesis, I have developed a complete drive anti-skid control strategy for distributed drive electric cars based on road adhesion coefficient estimation. The main conclusions of this work are summarized as follows.
First, I established a five-degree-of-freedom vehicle dynamics model in MATLAB/Simulink with a Magic Formula tire model and a permanent magnet synchronous motor model. This platform was successfully integrated with CarSim for high-fidelity simulations. It was used for testing both the speed estimation algorithm and the anti-skid controller under various road conditions.
Second, I proposed a road adhesion coefficient estimation method that is robust to abnormal illumination. This method combines semantic road segmentation, unsupervised image enhancement, and a Transformer-based classifier. The proposed classifier achieved an average accuracy of 98.38% for four road surface types. A confidence-weighted temporal fusion algorithm improved the temporal consistency of the estimation results. Real-vehicle tests showed that the standard deviation of the estimated adhesion coefficient was only 0.05, which is important for reliable control of electric cars.
Third, I designed an unscented particle filter for longitudinal vehicle speed estimation. The simulation results showed that the maximum estimation error was only 1.2 km/h, even during rapid acceleration and deceleration. The accurate speed estimate is an essential basis for calculating the wheel slip ratio and for the feedback control loop.
Fourth, I developed a model-free adaptive sliding mode controller (MFASMC) to track the optimal slip ratio. The controller directly adjusts the four motor torques and does not rely on an accurate vehicle model. The simulation results demonstrated that this controller can effectively suppress wheel slip on a uniform low-friction road and also on a split-mu road. The acceleration performance and driving stability are significantly improved compared to the case without control.
Fifth, the hardware-in-the-loop tests validated the practical applicability of the proposed control strategy. The control algorithm was deployed to a D2P rapid-prototyping controller and tested against a CarSim model running on an NI real-time simulator. The HiL results confirmed that the controller is able to adapt the output torque quickly and prevent excessive wheel slip on both uniform high-μ and split low-μ roads.
Future work should extend the method to more extreme road surfaces, such as deep snow, ice, or unpaved roads, and integrate multimodal sensor information including radar and lidar. I also intend to conduct more extensive vehicle testing to evaluate the performance in real public roads with different environmental disturbances. The proposed technique may be further extended to cooperative control of traction and braking so that electric cars can achieve both high efficiency and active safety in all conditions.