In this thesis, I investigate the longitudinal motion control of distributed drive electric vehicles under challenging road conditions. The rapid growth in vehicle ownership has intensified road safety concerns, and adverse pavement conditions with low adhesion are among the major causes of accidents. Among various active safety technologies, traction or drive anti-skid control plays a decisive role in preventing excessive wheel slip during acceleration on slippery roads. My research is supported by the National Natural Science Foundation of China under grants 52225212, 52272418, and U22A20100. I focus on four-wheel-drive electric vehicles and combine vehicle dynamics with computer vision to improve longitudinal stability and driving performance. The main topics include longitudinal vehicle speed estimation, road adhesion coefficient identification, and drive anti-skid control. In what follows, I first derive a comprehensive simulation platform based on vehicle dynamics and a tire model, then I present a vision-based road adhesion estimation method for abnormal lighting, and finally I design a model-free adaptive sliding mode controller that regulates motor torque while tracking the optimal slip ratio. The effectiveness of this strategy is verified by co-simulations and hardware-in-the-loop experiments.
1. Introduction and Background
Modern transportation systems are increasingly electrified, and China has witnessed a remarkable growth in the fleet of electric vehicles. With the number of motor vehicles exceeding 450 million in 2024, traffic accidents still cause substantial casualties and economic losses. Many accidents are closely related to poor tire-road adhesion, especially when the road surface is wet, icy, or covered by snow. Active safety systems, such as anti-lock braking systems and traction control systems, are designed to prevent the vehicle from reaching unstable states. For electric vehicles, the electric motor has an extremely fast torque response, which creates both opportunities and challenges for traction control. If the road friction level is not accurately known, the motor torque may easily exceed the available adhesion, causing drive-wheel spin and losing lateral stability.
Distributed drive electric vehicles, also known as four-wheel-independent-drive electric vehicles, can independently control the torque of each in-wheel motor. This architecture offers high redundancy and flexibility for vehicle dynamics control. However, the longitudinal behavior is strongly nonlinear and highly dependent on the tire-road friction condition. Therefore, accurate road adhesion estimation is one of the most critical tasks in drive anti-skid control. Without a reliable estimate of the maximum friction coefficient, the optimal slip ratio cannot be determined, and the control system cannot utilize the full tire-road potential.
In my work, I classify the road adhesion estimation methods into three categories: dynamics-based, vision-based, and fusion methods. Dynamics-based methods use vehicle acceleration, wheel speeds, and tire force models to estimate the maximum tire-road friction coefficient. Many studies have used extended Kalman filters, unscented Kalman filters, particle filters, sliding mode observers, and adaptive observers. These methods are often limited by the need for sufficient wheel slip excitation, especially in low-excitation driving conditions. Vision-based methods use onboard cameras to classify the road type, such as asphalt, concrete, snow, or ice, and then map the road type to a predefined adhesion coefficient. This approach is forward-looking and does not rely on wheel slip, but it is sensitive to illumination changes, rain, fog, and night-time conditions. Fusion methods attempt to combine vision and dynamics information to obtain fast and accurate estimates; nevertheless, robustly dealing with abnormal illumination remains an open problem.
The longitudinal vehicle speed is another essential variable. In drive anti-skid control, the slip ratio is computed from the wheel speed and the vehicle speed. Accurate vehicle speed estimation is particularly important during heavy acceleration on low-adhesion roads because all four wheels may be spinning. Many conventional methods rely on wheel speeds and cannot distinguish between a true vehicle speed and wheel rotational speed. Inertial sensors can help, but their signals are subject to drift and noise. Kalman filter based observers and other model-based methods improve accuracy, yet they require good vehicle models and may suffer from unmodeled nonlinearities. To address these issues, I propose an unscented particle filter algorithm that combines the strengths of unscented Kalman filtering and particle filtering for longitudinal speed estimation.
With respect to drive anti-skid control, conventional methods include PID, model predictive control, fuzzy logic, architecture threshold control, and sliding mode control. PID control is simple but lacks robustness for nonlinear changes in friction. Model predictive control achieves good performance but is computationally heavy for real-time embedded controllers. Logic threshold controllers are simple but often lead to torque oscillation. Sliding mode control is insensitive to external disturbances and parameter uncertainties, yet it suffers from chattering. To overcome these disadvantages, I develop a model-free adaptive sliding mode controller, which updates a pseudo-gradient online and combines the data-driven property of model-free adaptive control with the robust nature of sliding mode control. This controller does not require an accurate vehicle or tire model and can suppress slip quickly on complex road surfaces.
2. Vehicle Dynamics Modelling for Electric Vehicles
I built a complete vehicle dynamics simulation environment in MATLAB/Simulink as the basis for algorithm verification. The model consists of a one-degree-of-freedom longitudinal vehicle model, four wheel rotational dynamics models, a magic-formula tire model, and an in-wheel motor model.
The longitudinal vehicle motion is described by the following equation:
$$
m \dot{v}_x = F_{xfl} + F_{xfr} + F_{xrl} + F_{xrr},
$$
where \(m\) is the total mass of the vehicle, \(v_x\) is the longitudinal speed, and \(F_{xfl}, F_{xfr}, F_{xrl},\) and \(F_{xrr}\) are the tire longitudinal forces at the front-left, front-right, rear-left, and rear-right wheels, respectively.
For each wheel, the rotational dynamics can be expressed as:
$$
I_w \dot{\omega}_i = T_i – F_{xi} R, \quad i \in \{fl, fr, rl, rr\},
$$
where \(I_w\) is the wheel rotational inertia, \(\omega_i\) is the angular velocity, \(T_i\) is the torque applied by the corresponding in-wheel motor, \(F_{xi}\) is the longitudinal tire force, and \(R\) is the effective rolling radius. The main vehicle parameters used in this study are listed in Table Parameters.
| Parameter | Value | Unit |
|---|---|---|
| Vehicle mass \(m\) | 1270 | kg |
| Distance from CG to front axle \(l_f\) | 1.015 | m |
| Distance from CG to rear axle \(l_r\) | 1.895 | m |
| Wheel rotational inertia \(I_w\) | 0.87 | kg \(\cdot\) m² |
| Wheel radius \(R\) | 0.325 | m |
| CG height \(h_g\) | 0.54 | m |
| Gravitational acceleration \(g\) | 9.8 | m/s² |
The tire model that I selected is the empirical “magic formula” model, which is known for its simplicity and accuracy. The longitudinal tire force is expressed as:
$$
F_{xj} = D_j \sin \!\left(C_j \arctan\!\left(B_j \kappa_j – E_j \left(B_j \kappa_j – \arctan(B_j \kappa_j)\right)\right)\right),
$$
where \(B_j\) is the stiffness factor, \(C_j\) is the shape factor, \(D_j\) is the peak factor, \(E_j\) is the curvature factor, and \(\kappa_j\) is the slip ratio of the \(j\)-th wheel. The vertical load on each tire is obtained from the static and longitudinal load transfer equations:
$$
F_{zfl}=F_{zfr}=\frac{l_r mg}{l_f+l_r}-\frac{h_g m\dot{v}_x}{l_f+l_r},
$$
$$
F_{zrl}=F_{zrr}=\frac{l_f mg}{l_f+l_r}+\frac{h_g m\dot{v}_x}{l_f+l_r}.
$$
The slip ratio for a driven wheel is defined as:
$$
\kappa_j = \frac{R\omega_j – v_x}{\max(R\omega_j, v_x)},
$$
which is positive during acceleration when the wheel circumferential speed exceeds the vehicle speed.
The electric motor used in this study is a permanent-magnet synchronous motor with a peak torque of 820 N·m and a rated power of 40 kW. I model the motor drive system with a simplified second-order transfer function to capture the delay and damping characteristics:
$$
G(s) = \frac{1}{0.4s^2 + 7.5s + 0.25}.
$$
This motor model receives the desired torque command generated by the traction controller and outputs the actual torque that drives the wheels in CarSim.
3. Road Adhesion Coefficient Estimation Based on Vision and Data Augmentation
Road adhesion information is a prerequisite for maximizing effective traction control. I propose a novel vision-based estimation algorithm that is specifically designed for abnormal illumination scenarios. The algorithm has four main stages: semantic road segmentation, low-light image enhancement, Transformer-based road type classification, and weighted temporal information fusion.
First, I created a large road image dataset covering four typical asphalt pavement conditions: sunny, rainy, foggy, and night-time. To improve diversity and represent real-world driving environments, I collected images from an onboard camera, supplemented them with images from public datasets, and synthesized foggy images using the atmospheric scattering model:
$$
I(x) = J(x) t(x) + A (1 – t(x)),
$$
where \(I(x)\) is the foggy image, \(J(x)\) is the clear image, \(t(x)\) is the transmittance, and \(A\) is the atmospheric light. Table Dataset summarizes the number of samples in the dataset.
| Road Type | Rainy | Foggy | Night | Sunny | Total |
|---|---|---|---|---|---|
| Number of samples | 3729 | 2669 | 3298 | 3782 | 13478 |
| Proportion captured by us | 80% | 0% | 80% | 90% | 60% |
| Public dataset proportion | 20% | 0% | 20% | 10% | 20% |
| Synthetic proportion | 0% | 100% | 0% | 0% | 20% |
3.1 Semantic Road Segmentation with DeepLabV3+
To remove irrelevant background information, I employed the DeepLabV3+ semantic segmentation network with a lightweight MobileNetV3 backbone. The encoder-decoder architecture uses atrous spatial pyramid pooling to extract contextual information at multiple scales while preserving sharp object boundaries. In the decoder path, high-resolution features from the encoder are concatenated with the upsampled output before final pixel-wise classification. After inference, I generate a binary road mask and apply it to the original image by element-wise multiplication. Thus, only the road area is retained for the subsequent classification stages.
3.2 Image Enhancement Using EnlightenGAN
A key contribution of my work is to insert an unsupervised generative adversarial network, EnlightenGAN, into the pipeline before classification. Since paired low-light and normal-light images are difficult to obtain in practice, I trained EnlightenGAN without paired supervision. The generator adopts a U-Net-like structure with attention modules. The discriminator consists of a global branch and a local branch; the local branch randomly crops small patches from the image to improve texture realism. The relative discriminator loss is written as:
$$
L_D^{\text{Global}} = \mathbb{E}_{x_r \sim \text{real}, x_f \sim \text{fake}}\left[(D_{Ra}(x_r, x_f) – 1)^2\right] + \mathbb{E}_{x_f \sim \text{fake}, x_r \sim \text{real}}\left[D_{Ra}(x_f, x_r)^2\right],
$$
$$
L_G^{\text{Global}} = \mathbb{E}_{x_f \sim \text{fake}, x_r \sim \text{real}}\left[(D_{Ra}(x_f, x_r) – 1)^2\right] + \mathbb{E}_{x_r \sim \text{real}, x_f \sim \text{fake}}\left[D_{Ra}(x_r, x_f)^2\right].
$$
In addition, I used a self-feature preserving loss to constrain the perceptual content of the generated image. Given the low-light input \(I_L\), the enhanced output \(G(I_L)\), and the feature map \(\phi_{i,j}\) from a pretrained VGG-16 network, the loss is defined by:
$$
L_{\text{SFP}} = \sum_{i,j} \frac{1}{W_{i,j} H_{i,j}} \sum_{x=1}^{W_{i,j}} \sum_{y=1}^{H_{i,j}} \left\|\phi_{i,j}(I_L)^{x,y} – \phi_{i,j}(G(I_L))^{x,y}\right\|_2^2.
$$
After training, the enhancement module restores hidden texture and color information under dark or dense fog conditions, thereby improving the classification accuracy of the subsequent network.
3.3 Transformer-in-Transformer Road Type Classification
The classification module is based on the Transformer-in-Transformer (TNT) model. A standard vision transformer treats an entire image patch as one token, but TNT explores both visual sentences and visual words. Each image patch is further split into smaller word patches. The word-level Transformer models local fine-grained features, while the sentence-level Transformer models relationships among patches. The update process for word embeddings is expressed as:
$$
Y_l^i = Y_{l-1}^i + \mathrm{MSA}\left(\mathrm{LN}(Y_{l-1}^i)\right),
$$
$$
Y_l^i = Y_l^i + \mathrm{MLP}\left(\mathrm{LN}(Y_l^i)\right),
$$
where \(\mathrm{MSA}\) denotes multi-head self-attention, \(\mathrm{LN}\) denotes layer normalization, and \(Y_l^i\) denotes the word embeddings at block \(l\) for the \(i\)-th patch. The sentence embedding is updated by combining transformed word information through a linear projection:
$$
Z_l^i = Z_{l-1}^i + \mathrm{FC}\left(\mathrm{Vec}(Y_l^i)\right),
$$
$$
Z_l = Z_{l-1} + \mathrm{MSA}\left(\mathrm{LN}(Z_{l-1})\right),
$$
$$
Z_l = Z_l + \mathrm{MLP}\left(\mathrm{LN}(Z_l)\right).
$$
I inserted learnable position encodings into both word and sentence embeddings to preserve spatial information.
Using the enhanced dataset, I trained the TNT model for 500 epochs with a batch size of 32 and a learning rate of 0.0001. The final test confusion matrix showed average classification accuracy of 98.38%, and the minimum accuracy among the four road types was 96.39%. Table AdhesionMapping shows the mapping from the classified road type to the admissible range of the adhesion coefficient.
| Road Surface Type | Upper Adhesion Limit | Lower Adhesion Limit |
|---|---|---|
| Rainy asphalt | 0.6 | 0.3 |
| Foggy asphalt | 0.6 | 0.4 |
| Night asphalt | 0.7 | 0.5 |
| Sunny asphalt | 0.8 | 0.7 |
3.4 Weighted Temporal Information Fusion
The classification result of one image can be influenced by transient noise, partial occlusion, or misclassification. To generate a stable output, I designed a weighted temporal fusion strategy. The images from different time frames are first transformed into the vehicle coordinate system according to the camera calibration and ego-motion compensation. Let the pixel coordinate be \((u,v)\), the camera intrinsic matrix contain the focal lengths and optical center, and the extrinsic matrix contain rotation and translation. The perspective projection relation is:
$$
\begin{bmatrix} x_{\mathrm{cam}} \\ y_{\mathrm{cam}} \\ z_{\mathrm{cam}} \\ 1 \end{bmatrix}
=
\begin{bmatrix} \mathbf{R} & \mathbf{T}\\ \mathbf{0} & 1 \end{bmatrix}^{-1}
\begin{bmatrix} x_{\mathrm{img}} \\ y_{\mathrm{img}} \\ 1 \end{bmatrix},
$$
where \(\mathbf{R}\) and \(\mathbf{T}\) denote the rotation and translation from the image coordinate system to the vehicle coordinate system. For historical frames, I compensate for vehicle motion using:
$$
\begin{bmatrix} x_{v}^{(t)} \\ y_{v}^{(t)} \\ z_{v}^{(t)} \end{bmatrix}
=
\mathbf{R}_{\Delta}
\begin{bmatrix} x_{v}^{(t-1)} \\ y_{v}^{(t-1)} \\ z_{v}^{(t-1)} \end{bmatrix}
–
\mathbf{T}_{\Delta},
$$
where \(\mathbf{R}_\Delta\) and \(\mathbf{T}_\Delta\) represent the relative vehicle motion between consecutive frames. For each road point observed in a set of recent frames, I combine the adhesion coefficients \(\mu_i\) obtainable from each frame. The final fused coefficient is computed by:
$$
\mu_{\mathrm{final}} = \sum_{i=0}^{N} w_i^{\mathrm{final}} \mu_i,
$$
$$
w_i^{\mathrm{final}} = \frac{w_i^t c_i}{\sum_{j=0}^{N} w_j^t c_j},
$$
$$
w_i^t = (1-\alpha)^{t-i}, \quad i = 0,1,\ldots,N,
$$
where \(w_i^t\) is a time-decay weight, \(c_i\) is the confidence of the network for frame \(i\), and \(\alpha\) is the decay rate. This method effectively reduces the fluctuation of the adhesion estimate and provides a smooth output for the traction controller.
3.5 Ablation Study for the Estimation Pipeline
I performed an ablation study to investigate the contribution of the EnlightenGAN enhancement module and the temporal fusion module. The results are displayed in Table Ablation.
| Configuration | Mean Classification Accuracy (%) | Fluctuation Std | 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 |
These results show the necessity of image enhancement and fusion. The EnlightenGAN module improves the classification accuracy by about 3.17% while the temporal fusion module further improves it by about 2.56% and significantly reduces the standard deviation of the estimated output.
4. Longitudinal Vehicle Speed Estimation Using Unscented Particle Filtering
Accurate longitudinal vehicle speed is essential for computing the wheel slip ratio, especially for distributed drive electric vehicles where all four wheels may experience simultaneous spin. I propose an unscented particle filter (UPF) to estimate longitudinal speed online. The UPF integrates the unscented Kalman filter (UKF) as the proposal distribution generator inside a particle filtering framework. This leads to better sampling quality than a simple random-walk proposal and can handle nonlinear system dynamics with non-Gaussian noise.
The state vector I selected is:
$$
\mathbf{x} = \begin{bmatrix} v_x & \omega_{fl} & \omega_{fr} & \omega_{rl} & \omega_{rr} \end{bmatrix}^{\mathrm{T}}.
$$
The continuous state equation is:
$$
\dot{\mathbf{x}} = f(\mathbf{x}, \mathbf{u}) + \mathbf{w},
$$
with the control input vector \(\mathbf{u} = \begin{bmatrix} T_{fl} & T_{fr} & T_{rl} & T_{rr} \end{bmatrix}^{\mathrm{T}}\). The corresponding equations are:
$$
\dot{v}_x = \frac{1}{m} \left( F_{xfl}+F_{xfr}+F_{xrl}+F_{xrr} \right),
$$
$$
\dot{\omega}_i = \frac{1}{I_w} \left( T_i – F_{xi} R \right), \quad i \in \{fl,fr,rl,rr\}.
$$
I discretize the continuous equation using Euler integration with time step \(\Delta t\):
$$
\mathbf{x}_{k+1} = \mathbf{x}_k + f(\mathbf{x}_k, \mathbf{u}_k) \Delta t + \mathbf{w}_k.
$$
The UPF algorithm starts with \(N\) particles. For each particle, the UKF is used to obtain the mean and covariance. Specifically, sigma points are generated by:
$$
\boldsymbol{\chi}_{k-1}^{(i)} = \left[ \hat{\mathbf{x}}_{k-1}^{(i)}, \quad \hat{\mathbf{x}}_{k-1}^{(i)} \pm \sqrt{(n+\lambda) P_{k-1}^{(i)}} \right],
$$
where \(n=5\) is the state dimension and \(\lambda\) is a scaling parameter. After propagating the sigma points through the nonlinear model, the predicted state and covariance are computed as:
$$
\hat{\mathbf{x}}_{k \mid k-1}^{(i)} = \sum_{j=0}^{2n} W_j^{(m)} \boldsymbol{\chi}_{j,k \mid k-1}^{(i)},
$$
$$
P_{k \mid k-1}^{(i)} = \sum_{j=0}^{2n} W_j^{(c)} \left(\boldsymbol{\chi}_{j,k \mid k-1}^{(i)} – \hat{\mathbf{x}}_{k \mid k-1}^{(i)}\right)\left(\boldsymbol{\chi}_{j,k \mid k-1}^{(i)} – \hat{\mathbf{x}}_{k \mid k-1}^{(i)}\right)^{\mathrm{T}} + Q.
$$
Then each sigma point is transformed to its observation, yielding the output mean and innovation covariance:
$$
\hat{\mathbf{y}}_{k \mid k-1}^{(i)} = \sum_{j=0}^{2n} W_j^{(m)} \boldsymbol{\gamma}_{j,k \mid k-1}^{(i)},
$$
$$
P_{yy,k}^{(i)} = \sum_{j=0}^{2n} W_j^{(c)} \left(\boldsymbol{\gamma}_{j,k \mid k-1}^{(i)} – \hat{\mathbf{y}}_{k \mid k-1}^{(i)}\right)\left(\boldsymbol{\gamma}_{j,k \mid k-1}^{(i)} – \hat{\mathbf{y}}_{k \mid k-1}^{(i)}\right)^{\mathrm{T}} + R,
$$
$$
P_{xy,k}^{(i)} = \sum_{j=0}^{2n} W_j^{(c)} \left(\boldsymbol{\chi}_{j,k \mid k-1}^{(i)} – \hat{\mathbf{x}}_{k \mid k-1}^{(i)}\right)\left(\boldsymbol{\gamma}_{j,k \mid k-1}^{(i)} – \hat{\mathbf{y}}_{k \mid k-1}^{(i)}\right)^{\mathrm{T}}.
$$
The Kalman gain is:
$$
K_k^{(i)} = P_{xy,k}^{(i)} \left(P_{yy,k}^{(i)}\right)^{-1},
$$
and particle state and covariance are updated as:
$$
\hat{\mathbf{x}}_{k}^{(i)} = \hat{\mathbf{x}}_{k \mid k-1}^{(i)} + K_k^{(i)} \left( \mathbf{y}_k – \hat{\mathbf{y}}_{k \mid k-1}^{(i)} \right),
$$
$$
P_k^{(i)} = P_{k \mid k-1}^{(i)} – K_k^{(i)} P_{yy,k}^{(i)} \left(K_k^{(i)}\right)^{\mathrm{T}}.
$$
Finally, particle weights are updated according to the likelihood:
$$
w_k^{(i)} \propto w_{k-1}^{(i)} p\left(\mathbf{y}_k \mid \hat{\mathbf{x}}_k^{(i)}\right),
$$
and normalized. To avoid degeneracy, I resample when the effective sample size is below a threshold. The estimated longitudinal vehicle speed is obtained by the weighted average of all particles:
$$
\hat{v}_x = \sum_{i=1}^{N} w_k^{(i)} v_{x,k}^{(i)}.
$$
I verified the proposed estimator in CarSim/Simulink under a driving cycle that includes acceleration from 40 km/h to 90 km/h, deceleration back to 40 km/h, and further acceleration to 110 km/h on a high-friction road. The estimated vehicle speed follows the true speed with a maximum error of only 1.2 km/h. Therefore, the UPF-based method is sufficiently accurate and real-time capable for traction control applications.
5. Drive Anti-Skid Control Strategy Based on Optimal Slip Ratio and Model-Free Adaptive Sliding Mode Control
Drive anti-skid control regulates the longitudinal slip ratio of each driving wheel close to a desired optimal value. The desired slip ratio is selected to maximize tire-road adhesion while preserving lateral stability. In this section, I present the optimal slip ratio calculation method and derive the model-free adaptive sliding mode controller.
5.1 Optimal Slip Ratio Determination
The magic-formula tire model describes the relationship between the adhesion coefficient and the slip ratio. In the normalized form, the longitudinal friction coefficient \(\mu(\kappa)\) is:
$$
\mu(\kappa) = D \sin\left(C \arctan\left(B\kappa – E\left(B\kappa – \arctan(B\kappa)\right)\right)\right),
$$
where \(D\) is related to the peak friction coefficient. The optimal slip ratio is defined as the slip ratio maximizing \(\mu(\kappa)\). Since an analytic solution of \(d\mu/d\kappa = 0\) is cumbersome due to the nested trigonometric functions, I use Brent’s method inside the admissible interval \(\kappa \in [0, 0.5]\) to find the global maximum. The optimization is formulated as:
$$
\kappa_{\mathrm{opt}} = \arg \min_{\kappa \in [0, 0.5]} \left[ -\mu(\kappa) \right].
$$
The computation time is in the millisecond range, which is suitable for real-time control. Table TypicalSlip lists the optimal slip ratios for several typical road surfaces.
| Road Surface | Optimal Slip Ratio | Peak Adhesion Coefficient |
|---|---|---|
| Dry asphalt | 0.168 | 1.173 |
| Dry cement | 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 |
By linear regression over the table entries, I obtain a simple relation:
$$
\kappa_{\mathrm{opt}} = p_1 \mu_{\mathrm{max}} + p_2,
$$
with \(p_1 = 0.1252\) and \(p_2 = 0.0245\). This fitted curve allows the traction controller to determine the optimal slip ratio immediately after the road adhesion coefficient is estimated by the vision pipeline.
5.2 Model-Free Adaptive Sliding Mode Controller
The conventional sliding mode controller requires a mathematical model of the wheel dynamics. However, tire forces and road conditions are difficult to model accurately. I therefore adopt a data-driven dynamic linearization framework. For the \(j\)-th wheel, the slip-ratio dynamics are represented by an equivalent incremental model:
$$
\dot{\kappa}_j(k) = \Phi_j(k) \Delta T_j(k) + d_j(k),
$$
where \(\Phi_j(k)\) is a pseudo-gradient or pseudo-partial derivative, \(\Delta T_j(k)\) is the increment of motor torque, and \(d_j(k)\) represents unmodeled dynamics and external disturbances.
The pseudo-gradient is updated online using:
$$
\hat{\Phi}_j(k) = \hat{\Phi}_j(k-1) + \frac{\eta \Delta T_j(k-1)}{\mu + \left|\Delta T_j(k-1)\right|^2} \left(\Delta \kappa_j(k) – \hat{\Phi}_j(k-1)\Delta T_j(k-1)\right),
$$
where \(\eta \in (0,2)\) is the learning rate and \(\mu > 0\) is a regularization factor. To avoid singularity, the estimated pseudo-gradient is reset when its absolute value drops below a lower bound:
$$
\hat{\Phi}_j(k) = \hat{\Phi}_j(k-1) \quad \text{if } |\hat{\Phi}_j(k)| \le \varepsilon,
$$
or it is constrained by a sign-preserving threshold:
$$
\hat{\Phi}_j(k) = \mathrm{sign}(\hat{\Phi}_j(k)) \varepsilon \quad \text{if } |\hat{\Phi}_j(k)| < \varepsilon.
$$
The slip ratio error is:
$$
e_j(k) = \kappa_j(k) – \kappa_{\mathrm{opt}}(k).
$$
I define a sliding surface as:
$$
s_j(k) = c_j e_j(k),
$$
where \(c_j > 0\) is the sliding gain. Then I design the incremental control law as:
$$
\Delta T_j(k) = \hat{\Phi}_j^{-1}(k) \left[ -\lambda s_j(k) + c_j\left(\kappa_{\mathrm{opt}}(k)-\kappa_{\mathrm{opt}}(k-1)\right) – \hat{d}_j(k)\right],
$$
where \(\lambda \in (0,1)\) is the reaching-law parameter. The disturbance estimate \(\hat{d}_j(k)\) is updated by:
$$
\hat{d}_j(k) = \hat{d}_j(k-1) + \frac{\eta_d}{\mu_d + |s_j(k-1)|^2} s_j(k-1)\left(s_j(k) – s_j(k-1)\right),
$$
with \(\eta_d \in (0,2)\) and \(\mu_d > 0\). Finally, the actual torque command is given by:
$$
T_j(k) = T_j(k-1) + \Delta T_j(k).
$$
This controller inherits the desirable robustness of sliding mode control while avoiding explicit system model identification. Because the pseudo-gradient is adjusted online, the controller can rapidly adapt to changes in road friction, motor delays, and vehicle load. The discontinuous sign function in conventional sliding mode is avoided by the incremental form; consequently, chattering is effectively reduced.
5.3 Simulation Results on Uniform Low-Adhesion Road
I first evaluated the controller on a uniform road with an adhesion coefficient of 0.2. The vehicle starts from standstill with full throttle. The optimal slip ratio is \(\kappa_{\mathrm{opt}} = 0.05\). Table UniformResult summarizes the comparison between the vehicle with the traction controller and the uncontrolled vehicle.
| Case | Final speed after 19.03 s (km/h) | Slip ratio at final state | Remark |
|---|---|---|---|
| With drive anti-skid control | 118.4 | 0.05 | No wheel spin after transient |
| Without control | approximately 103 | 0.82 | Serious wheel spin |
When the traction controller is active, the torque is initially increased and then rapidly stabilized. The wheel speeds remain close to the vehicle speed, and the slip ratio converges to the target after a small overshoot around 0.65 s. The controlled torque prevents the wheels from overspinning and maintains an efficient force transfer. In the uncontrolled case, the wheels accelerate almost immediately, producing a very large slip ratio and a low net driving force; hence, the vehicle acceleration is poor.
5.4 Simulation Results on a Split Adhesion Road
I also tested the controller on a split-mu road where the first 30 m has an adhesion coefficient of 0.2 and the remaining road has a coefficient of 0.8. The vehicle accelerates from standstill with full throttle. The simulated results are shown in Table SplitResult.
| Case | Final speed after 9.4 s (km/h) | Wheel slip status |
|---|---|---|
| With drive anti-skid control | 118.2 | No obvious slip |
| Without control | lower final speed | Severe slip on low-mu section |
The controlled vehicle crosses the low-adhesion segment while keeping the slip ratio near 0.05. When transitioning to the high-adhesion segment, the controller reacts quickly by increasing the torque and tracking the new optimal slip ratio. The wheels remain stable and provide a significant improvement in acceleration. Without control, the wheel speed rises drastically in the low-friction region, causing a loss of traction; even after entering high-friction road, the vehicle takes time to recover from the already high wheel speed. Thus, my anti-skid strategy significantly improves acceleration performance and vehicle stability.
6. Hardware-in-the-Loop Validation
To evaluate the practical viability of the proposed drive anti-skid control strategy, I performed hardware-in-the-loop (HiL) experiments. The HiL test bench comprises a D2P rapid prototyping controller, a NI real-time simulator, interface boards, a signal conditioning box, a break-out box, programmable power supplies, and a host computer. The vehicle model is compiled from CarSim and deployed to the NI real-time simulator through VeriStand. The controller algorithm is implemented in Simulink with the MotoHawk block set. After being compiled into a real-time executable, the control code is loaded into the D2P unit. The controller and simulator communicate over CAN bus and analog signals, forming a closed-loop test environment.
The HiL workflow is described as follows. First, I configured the CarSim model inputs as four longitudinal wheel torques and its outputs as wheel speeds, vehicle speed, yaw rate, and other states. Then I generated the dynamic-link library from CarSim and imported it into VeriStand. After mapping the signals between the NI board and the D2P controller, I downloaded the system to the real-time target. Test commands were sent, and the data were recorded on the host workstation.
6.1 Uniform Road Test with High Adhesion
In the HiL test, I considered a uniform high-adhesion road with friction coefficient 0.8. The motion begins from standstill and the throttle is fully open. The optimal slip ratio is 0.2. Table HiLUniform presents the measured performance.
| Case | Time to reach 112.35 km/h | Final reported slip ratio |
|---|---|---|
| With drive anti-skid control | 4.6 s | 0.2 |
| Without control | Longer time | 0.83 after spin |
With the controller, the wheel speeds tracked the vehicle speed accurately and the torque values were adjusted smoothly. Because the load transfers to the rear axle during acceleration, the rear wheels received slightly higher torque demand, but the sliding surface remained stable. Without the traction controller, the wheels spun excessively and the usable tractive force declined.
6.2 Split Adhesion Road Test with High-to-Low Friction
In the second HiL scenario, the vehicle starts on a high-friction road with coefficient 0.8 and after traveling 30 m it enters a low-friction road with coefficient 0.2. Table HiLSplit summarizes the results.
| Case | Final speed after 9.7 s (km/h) | Wheel slip behavior |
|---|---|---|
| With drive anti-skid control | 115.17 | No excessive wheel slip |
| Without control | much lower speed | Sustained wheel spin |
When the vehicle enters the low-adhesion section, the model-free adaptive sliding mode controller quickly detects the change in the pseudo-gradient. The motor torque is reduced to a small value, preventing wheel overspin. In contrast, the uncontrolled vehicle continues to demand the maximum torque from the electric motors, leading to a rapid wheel speed increase and severe slip. The HiL test therefore confirms that the proposed control law is robust to realistic hardware delays and CAN communication limitations.
7. Conclusions and Future Work
In this thesis, I designed a complete road-adhesion-aware anti-skid control framework for distributed drive electric vehicles. Starting from vehicle modeling, I constructed a high-fidelity simulation environment that integrates body dynamics, wheel rotational dynamics, magic-formula tire behavior, and in-wheel motor characteristics. The longitudinal vehicle speed estimator based on an unscented particle filter achieved a maximum estimation error below 1.2 km/h under transient acceleration and braking scenarios. The road friction estimation system used semantic segmentation, unsupervised image enhancement, and a Transformer-in-Transformer classifier to handle abnormal lighting conditions such as night and fog. The average classification accuracy reached 98.38% and the weighted temporal fusion reduced the output fluctuation standard deviation to 0.05.
The control core of the framework is a model-free adaptive sliding mode controller. It does not rely on an explicit tire model, which makes it particularly suitable for electric vehicles operating on unknown and varying road surfaces. The controller continuously estimates the pseudo-gradient and disturbance, and it generates smooth torque increments. CarSim/Simulink simulations on low-adhesion and split-adhesion roads demonstrated that the controller prevents excessive wheel slip and significantly improves the vehicle acceleration and stability. The hardware-in-the-loop tests further confirmed the practical validity under realistic real-time constraints.
There are several aspects that I plan to explore in future research. First, I intend to expand the road dataset to include snow-covered, gravel, and other mixed-surface conditions so that the visual estimator can support more diverse weather and environmental scenarios. Second, fusing the camera with radar or LiDAR could improve the robustness of the estimation system in low-visibility conditions. Third, I will investigate a full-vehicle dynamic control architecture that coordinates traction control with yaw stability control and rollover prevention for distributed drive electric vehicles. In addition, I plan to validate the control strategy on a prototype electric vehicle in real-world driving tests to account for sensor noise, communication delays, actuator failures, and other practical engineering issues.
In summary, my research contributes to the advancement of active safety systems for electric vehicles by improving road adhesion estimation and anti-skid control. The proposed approach can increase the reliability and efficiency of electric vehicles in adverse driving environments, and it provides a valuable reference for the future development of intelligent and autonomous electric vehicles.