In my master’s research, I focused on an important stability problem encountered by a particular family of intelligent electric vehicles. With the electrification of road transportation, conventional vehicle architectures are being replaced by highly integrated electric chassis architectures. Among them, a corner-module architecture electric vehicle integrates a driving motor, a steering motor, a brake actuator, and often a suspension connection into a single wheel-side module. This architecture is usually described as a four-wheel-independent steering and four-wheel-independent driving electric vehicle. Such an electric vehicle can independently control the steering angle, driving torque, and braking torque at every wheel. Therefore, a corner-module architecture electric vehicle is able to perform unconventional maneuvers such as point turns, transverse parking, diagonal driving, and active drift-like avoidance.
However, the extra degrees of freedom of a corner-module architecture electric vehicle also expose a challenging control problem. During high-speed emergency obstacle avoidance, the steering demand can easily exceed the tire adhesion capacity, particularly when the road is wet or covered by snow. If the front wheels are over-steered, the front tire side forces saturate. The vehicle then develops a large undesired yaw motion and sideslip, and the trajectory deviates severely from the driver’s intended path. In more dangerous cases, the roll angle increases rapidly, wheel lift-off may occur, and the electric vehicle can roll over. Therefore, stability control for such an electric vehicle under extreme steering conditions is not only a classical vehicle dynamics problem but also a practical safety concern for future autonomous electric vehicles.
The purpose of my thesis was to propose a novel differential oblique steering method for corner-module architecture electric vehicles. The key idea is to use the four-wheel independent steering capability to actively adjust the body attitude. Instead of suppressing vehicle sideslip completely, the controller deliberately builds a controlled tail-swing motion. The vehicle travels along the road with a body attitude that is rotated relative to the path, while the tires remain closer to their linear side-force region. I named this maneuver differential oblique steering. It can be understood as an active drift-like cornering motion, but it is formulated in a deterministic way so that path tracking and roll stability are both guaranteed by a constrained model predictive controller.
1. Vehicle Dynamics Modeling for the Corner-Module Electric Vehicle
To develop a reliable stability controller, I first established a comprehensive dynamics model of the corner-module architecture electric vehicle. The model is used as a virtual test platform in the control validation. It should also be accurate enough to describe the coupling between the lateral motion, yaw motion, roll motion, and wheel steering dynamics.
1.1 Twelve-Degree-of-Freedom Vehicle Model
I used a twelve-degree-of-freedom model for the entire electric vehicle. The model includes the longitudinal motion, lateral motion, yaw motion, roll motion, pitch motion, vertical motion of the sprung mass, and the rotational motion and steering motion of the four wheels. The governing equations for the vehicle body are divided into longitudinal dynamics, lateral dynamics, yaw dynamics, and roll dynamics.
The longitudinal, lateral, and yaw equations can be expressed as:
$$
m(\dot{V}_{x}-r V_{y}) = \sum_{i=1}^{4}F_{xi}\cos\delta_{i} – \sum_{i=1}^{4}F_{yi}\sin\delta_{i} – F_{\text{res}}
$$
$$
m(\dot{V}_{y}+r V_{x}) = \sum_{i=1}^{4}F_{xi}\sin\delta_{i} + \sum_{i=1}^{4}F_{yi}\cos\delta_{i}
$$
$$
\begin{aligned}
I_{z}\dot{r} &= a\sum_{i=1}^{2}\left(F_{xi}\sin\delta_{i} + F_{yi}\cos\delta_{i}\right) \\
&\quad – b\sum_{i=3}^{4}\left(F_{xi}\sin\delta_{i} + F_{yi}\cos\delta_{i}\right) \\
&\quad + \frac{d}{2}\sum_{\text{left}}\left(F_{xi}\cos\delta_{i} – F_{yi}\sin\delta_{i}\right) \\
&\quad – \frac{d}{2}\sum_{\text{right}}\left(F_{xi}\cos\delta_{i} – F_{yi}\sin\delta_{i}\right)
\end{aligned}
$$
Here, \(m\) denotes the total mass of the electric vehicle, \(V_x\) and \(V_y\) are the longitudinal and lateral velocity components at the vehicle center of gravity, and \(r\) is the yaw rate. The subscript \(i\) indicates the left front, right front, left rear, and right rear wheel modules respectively. Furthermore, \(\delta_i\) is the steering angle of the corresponding wheel, \(F_{xi}\) and \(F_{yi}\) are its longitudinal and lateral tire forces, \(a\) and \(b\) denote the front and rear semi-wheelbases, \(d\) denotes one-half of the track width, and \(F_{\text{res}}\) is the aerodynamic drag.
The roll motion is of particular importance for the proposed differential oblique steering controller because the activation of a large body sideslip can increase the lateral load transfer. The roll equation used in the electric vehicle model is:
$$
I_{xs}\ddot{\rho} = m_s g h_s \sin\rho – \frac{d}{2}\sum_{i=1,3}F_{si} + \frac{d}{2}\sum_{i=2,4}F_{si} – m_s h_s a_y\cos?
$$
For the sake of compactness, I implemented the full nonlinear roll motion of the corner-module electric vehicle using suspension forces that depend on the relative displacement and velocity between the sprung mass and unsprung masses. Each suspension force is written as:
$$
F_{si} = k_{si}\Delta z_i + c_{si}\Delta \dot{z}_i
$$
where \(k_{si}\) and \(c_{si}\) are the suspension stiffness and damping coefficients, and \(\Delta z_i\) is the relative vertical displacement at the corresponding corner.
1.2 Magic Formula Tire Model for the Electric Vehicle
The tire force calculation strongly influences the fidelity of the electric vehicle model. Since the proposed differential oblique steering strategy often operates near the tire nonlinear region, I used a simplified version of the Magic Formula tire model. The lateral tire force is represented as:
$$
F_{y} = D\sin\left[C\arctan\left\{B\alpha – E\left(B\alpha – \arctan(B\alpha)\right)\right\}\right]
$$
where \(\alpha\) is the tire slip angle. The coefficients \(B\), \(C\), \(D\), and \(E\) depend on the vertical tire load. The tire model parameters used in the electric vehicle simulation model are summarized below.
| Parameter | Value | Description |
|---|---|---|
| \(a_0\) | 1.6 | Shape coefficient for side force model |
| \(a_1\) | -34 | Stiffness factor coefficient |
| \(a_2\) | 1250 | Load dependency coefficient |
| \(a_3\) | 2320 | Camber/curvature factor |
| \(a_4\) | 12.8 | Curvature factor coefficient |
| \(a_6\) | -0.0053 | Vertical-load curvature coefficient |
| \(a_7\) | 0.1925 | Vertical-load curvature coefficient |
In order to correctly represent the braking and driving longitudinal forces on low-friction roads, I used the longitudinal Magic Formula expression:
$$
F_{x} = D_{x}\sin\left[C_{x}\arctan\left\{B_{x}\lambda – E_{x}\left(B_{x}\lambda – \arctan(B_{x}\lambda)\right)\right\}\right]
$$
where \(\lambda\) is the longitudinal slip ratio. The combined tire force was constrained with a friction ellipse to prevent the controller from asking for friction outside the available adhesion circle.
1.3 Wheel-Side Steering System and Hub Motor Models
Since the corner-module architecture electric vehicle uses steer-by-wire actuators, I also modeled the wheel-side steering system. The steering actuator is a DC brush motor connected to the steering axis through a reduction gear. The dynamics of the complete steering module can be written as:
$$
(J_{w} + k^{2}J_{m})\ddot{\delta}_{w} + (B_{w} + k^{2}B_{m})\dot{\delta}_{w} + T_{e} + T_{F} = k T_{\text{act}}
$$
where \(J_{w}\) and \(J_{m}\) are the wheel-side moment of inertia and motor rotor inertia, \(B_{w}\) and \(B_{m}\) are the corresponding damping coefficients, \(k\) is the gear reduction ratio, \(T_e\) is the aligning torque, and \(T_F\) is the Coulomb friction torque.
The hub motor model used in the electric vehicle is a second-order lag representation of the torque response:
$$
\frac{T_{m}(s)}{T_{m}^{*}(s)} = \frac{1}{1 + 2\zeta s + \tau^{2}s^{2}}
$$
This simplified motor model can reflect the finite response time of the in-wheel motor while avoiding overly detailed electrical modeling.
1.4 Verification of the Electric Vehicle Model
I verified the proposed model against a Carsim vehicle model under a steering-wheel step input. The vehicle speed was set to 40 km/h and the road friction coefficient was 0.85. I compared the sideslip angle, yaw rate, lateral velocity, roll angle, and trajectory. The comparison results showed that the dynamic responses of my Simulink model were highly consistent with the Carsim responses.
| Comparison Variable | Simulink Model | Carsim Model | Trend Consistency |
|---|---|---|---|
| Yaw rate | Smooth convergence | Smooth convergence | High |
| Vehicle sideslip angle | Small peak overshoot | Small peak overshoot | High |
| Lateral velocity | Positive during turn | Positive during turn | High |
| Roll angle | Monotonic rise and return | Monotonic rise and return | High |
The validated model provided a solid baseline for the subsequent development of the differential oblique steering controller for the corner-module electric vehicle.
2. Differential Oblique Steering Angle Allocation for the Electric Vehicle
After establishing the vehicle model, I investigated different steering strategies for the corner-module architecture electric vehicle. Traditional front-wheel steering uses only the front axle to generate lateral force. In an emergency, because the lateral acceleration requirement is high, the rear tires are not sufficiently utilized. Four-wheel steering improves this situation by adding rear-wheel steering, but the reduction of roll risk is still limited. I therefore proposed differential oblique steering to exploit the full potential of the corner-module architecture electric vehicle.
2.1 Mechanism of Differential Oblique Steering
Differential oblique steering is different from conventional four-wheel steering. In a conventional high-speed four-wheel steering electric vehicle, the rear wheels usually steer in phase with the front wheels, but with a smaller angle. This configuration reduces the vehicle sideslip angle and improves direction stability. However, when the required lateral acceleration is close to the adhesion limit, the tire slip angles at all wheels increase beyond the linear range. Once the front or rear axle reaches saturation, maintaining the intended path becomes almost impossible.
In contrast, differential oblique steering deliberately assigns a larger steering angle to the rear wheels and a smaller angle to the front wheels. The body sideslip angle is intentionally increased in a controlled manner. The electronic vehicle therefore behaves like a pendulum that rotates around an instantaneous center close to the vehicle. The body attitude angle is used as an additional controllable state. This enlarges the equivalent virtual wheelbase under the perspective of roll dynamics, thus reducing the roll moment due to the reduced effective lateral acceleration arm.
Another important property of differential oblique steering is the improved tire force distribution. Because all four wheels are steerable, the lateral force demand is distributed among all four tires. When the rear axle steers aggressively, the tire side-slip angle at the front axle can be reduced. Consequently, the front tires remain more controllable and the electric vehicle is able to track a path at a higher entry speed.
2.2 Mathematical Model for the Differential Oblique Steering Maneuver
I derived a geometry-based relation for the differential oblique steering mode. The schematic relation between wheelbase, turning radius, and body sideslip can be approximated by:
$$
\tan \delta_{f} \approx \frac{a}{R} + \tan \beta
$$
$$
\tan \delta_{r} \approx \tan \beta – \frac{b}{R}
$$
where \(R\) is the radius of the vehicle trajectory at the center of gravity. Subtracting the two expressions gives:
$$
\tan \delta_{r} = \tan \delta_{f} – \frac{a+b}{R}
$$
In my control framework, I used this relation to convert the desired body sideslip angle and trajectory curvature into front and rear steering commands:
$$
\delta_{f} = \beta^{*} + \frac{a}{R}, \quad \delta_{r} = \beta^{*} – \frac{b}{R}
$$
For implementation on the real four-wheel steering actuator system of the electric vehicle, the final front and rear axle angles are converted into individual wheel angles using the Ackermann geometry:
$$
\begin{aligned}
\delta_{fl} &= \frac{\tan\delta_{f}}{1 – \frac{B}{2L}(\tan\delta_{f} – \tan\delta_{r})} \\
\delta_{fr} &= \frac{\tan\delta_{f}}{1 + \frac{B}{2L}(\tan\delta_{f} – \tan\delta_{r})} \\
\delta_{rl} &= \frac{\tan\delta_{r}}{1 – \frac{B}{2L}(\tan\delta_{f} – \tan\delta_{r})} \\
\delta_{rr} &= \frac{\tan\delta_{r}}{1 + \frac{B}{2L}(\tan\delta_{f} – \tan\delta_{r})}
\end{aligned}
$$
The proposed angle allocation law can also be expressed in the unified form:
$$
\delta_{r} = G_{\delta}\delta_{f} + G_{r}r + G_{d}
$$
For the conventional four-wheel steering mode, I used the coefficients derived from a zero-sideslip steady-state condition:
| Mode | \(G_\delta\) | \(G_r\) | \(G_d\) |
|---|---|---|---|
| Rear-axle follow-up 4WS | \(-k_f/k_r\) | Function of vehicle speed and axle stiffness | 0 |
| Differential oblique steering | 1 | 0 | \(L/R\) |
This framework allows a seamless transition between the two steering modes by interpolating the coefficients with a switching factor.
2.3 Feasibility Validation of the Proposed Steering Allocation
I validated the four-wheel steering and differential oblique steering allocation models by simulation. In a single-lane-change maneuver at a speed of 36 km/h, the conventional four-wheel steering electric vehicle showed good tracking ability. The vehicle sideslip angle remained small, and the lateral error was limited. In a second test, I applied a sinusoidal desired sideslip angle to the differential oblique steering allocation law. The resulting front and rear wheel angles remained within the actuator limits and followed the expected pattern, which confirmed the feasibility of the four-wheel angle allocation scheme.
According to the comparison between the two modes, I concluded that differential oblique steering should be used only when the driving task is demanding, such as on a low-friction road or during an emergency obstacle avoidance maneuver. In normal driving, a conventional four-wheel steering strategy is more comfortable for the driver. This led me to design a supervisory switching strategy for the electric vehicle.
3. Stability Control Framework for the Electric Vehicle under Extreme Steering
The complete control architecture that I developed is composed of three layers. The upper layer is the steering-mode decision layer. The middle layer is a roll-stability-oriented steering-angle constraint layer. The lower layer is a model predictive path-tracking controller. The lower controller calculates the optimal front steering angle command, while the rear steering angle is determined according to the selected mode. The resulting control system coordinates path following and roll stability in real time.
3.1 Roll Stability Steering-Angle Constraint Controller
I first considered how the road friction coefficient influences the allowable body sideslip angle. The total lateral force generated by the four tires is limited by:
$$
F_{yf} + F_{yr} \le \mu mg
$$
Assuming that both axles operate in their approximately linear range, the lateral forces are:
$$
F_{yf} = k_{f}\left(\beta + \frac{a}{V_x}r – \delta_f\right)
$$
$$
F_{yr} = k_{r}\left(\beta – \frac{b}{V_x}r – \delta_r\right)
$$
Combining these equations gives the maximum allowable sideslip angle:
$$
\beta_{\max} = \frac{\mu mg + k_{f}\delta_f + k_{r}\delta_r – \frac{k_f a – k_r b}{V_x}r}{k_f + k_r}
$$
In the control framework, I used this bound as a dynamic constraint on the body sideslip angle of the electric vehicle. If the planned sideslip angle exceeds the bound, the controller will avoid applying excessive steering commands.
In addition to the sideslip angle, I designed a roll-angle-dependent constraint for the four-wheel steering command. The roll dynamics are written in the following compact form:
$$
\dot{\mathbf{x}}_{\rho} = A_{\rho}\mathbf{x}_{\rho} + B_{\rho}\boldsymbol{\delta}^{*}
$$
where \(\mathbf{x}_{\rho} = [\rho,\dot{\rho}]^{T}\) and \(\boldsymbol{\delta}^{*}\) is the vector of target wheel steering angles. The safety constraint is:
$$
|\rho(t)| \le \rho_{\lim}
$$
The value of \(\rho_{\lim}\) depends on the vehicle type. For the passenger electric vehicle studied in this research, I used a conservative roll limit of about \(5^\circ\) because the high-speed maneuver involves both lateral acceleration and sudden path transitions. The table below lists typical roll-angle thresholds for several vehicle families.
| Vehicle Type | Roll Angle Threshold (deg) |
|---|---|
| Passenger car | 35–45 |
| SUV | 30–40 |
| Bus | 25–35 |
| Heavy truck | 20–30 |
| High-performance car | 40–50 |
The roll-angle-constraint controller compares the predicted roll angle with the limit. When the roll angle is close to its threshold, the allowable changes in the front and rear wheel angles are reduced. This behavior prevents the electric vehicle from entering the rollover danger region.
3.2 Fuzzy Steering-Mode Switching Controller
Because the road condition and the severity of the obstacle avoidance event are variable, the electric vehicle cannot remain permanently in differential oblique steering mode. Therefore, I developed a fuzzy-logic-based switching controller. The first input is the maximal absolute tire slip angle of the four wheels. The second input is the road curvature of the planned path. The output is a continuous switching coefficient \(\lambda\), which lies between zero and one.
When \(\lambda=0\), the rear steering angle is computed according to the conventional four-wheel steering mode. When \(\lambda=1\), the rear steering angle is computed according to the differential oblique steering mode. Intermediate values are obtained by interpolation:
$$
\begin{aligned}
G_{\delta} &= (1-\lambda)G_{\delta,1} + \lambda G_{\delta,2} \\
G_{r} &= (1-\lambda)G_{r,1} + \lambda G_{r,2} \\
G_{d} &= (1-\lambda)G_{d,1} + \lambda G_{d,2}
\end{aligned}
$$
The fuzzy inference rules are shown in the following table.
| Rule | Tire Slip Angle \(\alpha\) | Curvature \(\kappa\) | Output \(\lambda\) |
|---|---|---|---|
| 1 | Linear region | Small | 0 (4WS mode) |
| 2 | Nonlinear region | Small | 0 (4WS mode) |
| 3 | Saturated region | Small | 1 (Differential oblique steering mode) |
| 4 | Linear region | Large | 1 (Differential oblique steering mode) |
| 5 | Nonlinear region | Large | 1 (Differential oblique steering mode) |
| 6 | Saturated region | Large | 1 (Differential oblique steering mode) |
I used triangular and trapezoidal membership functions for the input sets and the output sets. The fuzzy controller made the mode-switching process smooth because it avoided hard switching between two very different steering laws.
3.3 MPC Path-Tracking Controller for Differential Oblique Steering
The path-following problem of the differential oblique steering electric vehicle is solved by a model predictive controller. I selected four state variables for the tracking controller:
$$
\mathbf{x} = \left[\beta,\; r,\; e_{y},\; e_{\varphi}\right]^{T}
$$
where \(\beta\) is the body sideslip angle, \(r\) is the yaw rate, \(e_y\) is the lateral displacement error relative to the reference path, and \(e_{\varphi}\) is the heading angle error. The continuous-time state equation is:
$$
\begin{aligned}
\dot{\beta} &= \frac{k_{f}+k_{r}}{mV_{x}}\beta + \left(\frac{ak_f – bk_r}{mV_{x}^{2}} – 1\right)r \\
&\quad – \frac{k_f}{mV_{x}}\delta_{f} – \frac{k_r}{mV_{x}}\delta_{r}
\end{aligned}
$$
$$
\begin{aligned}
\dot{r} &= \frac{ak_f – bk_r}{I_{z}}\beta – \frac{a^{2}k_f + b^{2}k_r}{I_{z}V_{x}}r \\
&\quad + \frac{ak_f}{I_{z}}\delta_{f} – \frac{bk_r}{I_{z}}\delta_{r}
\end{aligned}
$$
$$
\dot{e}_{y} = V_{x}\beta + V_{x}e_{\varphi}
$$
$$
\dot{e}_{\varphi} = r – \kappa V_{x}
$$
Here, \(\kappa\) is the reference road curvature. In the differential oblique steering mode, the rear steering angle is linked to the front steering angle by the mode allocation law. Therefore, the independent control input is chosen as \(u = \delta_{f}\), while \(\delta_r\) is generated according to the mode-dependent allocation rule.
For MPC implementation, the continuous-time model is discretized into:
$$
\mathbf{x}(k+1) = A_{d}\mathbf{x}(k) + B_{d}u(k) + d_{d}(k)
$$
The prediction model is then augmented with the control increment:
$$
\Delta u(k) = u(k) – u(k-1)
$$
The objective function of the MPC controller is:
$$
J = \sum_{i=1}^{N_p} \left\| \boldsymbol{\eta}(k+i|k) – \boldsymbol{\eta}_{\text{ref}}(k+i|k) \right\|_{Q}^{2}
+ \sum_{j=0}^{N_c-1} \left\| \Delta u(k+j|k) \right\|_{R}^{2} + \rho \varepsilon^{2}
$$
where \(\boldsymbol{\eta}\) is the controlled output vector, \(Q\) and \(R\) are weighting matrices, and \(\varepsilon\) is a slack variable used to soften constraints.
To avoid excessive steering and roll risk, the following constraints are imposed inside the optimization:
$$
\begin{aligned}
u_{\min} &\le u(k+j) \le u_{\max} \\
\Delta u_{\min} &\le \Delta u(k+j) \le \Delta u_{\max} \\
|\beta(k+i)| &\le \beta_{\max} \\
|\rho(k+i)| &\le \rho_{\lim}
\end{aligned}
$$
The resulting quadratic programming problem is solved at every sampling time. The first optimal control increment is applied to the electric vehicle model. The flow is repeated in a receding-horizon manner.
4. Simulation Results and Analysis
In this section, I describe the simulation results that were used to verify the differential oblique steering stability controller. The vehicle model was tested in two extreme scenarios. The first scenario was a high-speed U-turn on medium-friction road. The second scenario was a high-speed S-turn on low-friction road. In both scenarios, I compared three modes: front-wheel steering, four-wheel steering, and the proposed differential oblique steering.
4.1 High-Speed U-Turn on a Medium-Friction Road
The first simulation scenario represented an emergency obstacle avoidance maneuver on a road with friction coefficient 0.55. The vehicle speed was maintained at 80 km/h. The reference path was a U-shaped curve with a radius of 100 m. The differential oblique steering MPC controller tracked the reference path successfully. The front-wheel steering electric vehicle lost stability and departed from the intended path. The four-wheel steering electric vehicle was able to finish the maneuver, but its lateral error reached a peak value of about 2.9 m. The differential oblique steering electric vehicle reduced the peak lateral error to about 0.8 m. This corresponds to an improvement of 72.41% over the four-wheel steering mode.
More importantly, the peak body roll angle was reduced from about 3.45° for four-wheel steering to approximately 1.09° for differential oblique steering. The roll angle reduction reached 68.26%. This result indicates that the active tail-swing motion in differential oblique steering can successfully attenuate roll motion during high-speed cornering.
| U-Turn Scenario | Front-Wheel Steering | Four-Wheel Steering | Differential Oblique Steering |
|---|---|---|---|
| Path tracking success | Failed | Completed with overshoot | Successful |
| Peak lateral error | Large divergence | ≈ 2.9 m | ≈ 0.8 m |
| Peak roll angle | Rollover risk | ≈ 3.45° | ≈ 1.09° |
| Path tracking improvement | — | Baseline | 72.41% improvement |
| Roll reduction | — | Baseline | 68.26% reduction |
4.2 High-Speed S-Turn on a Low-Friction Road
The second simulation scenario used a low-friction road with \(\mu=0.3\). The vehicle speed was again fixed at 80 km/h. The reference path was an S-shaped curve. The front-wheel steering vehicle lost adhesion almost immediately after the first steering reversal. The four-wheel steering electric vehicle could approximately follow the path but exhibited a large lateral error with a peak value of about 7.21 m. The differential oblique steering electric vehicle achieved a peak lateral error of about 2.83 m. Compared with the four-wheel steering mode, the path-tracking error was reduced by 60.75%.
In terms of roll stability, the peak roll angle of the four-wheel steering electric vehicle was about 2.75 degrees. The differential oblique steering electric vehicle reduced this peak to approximately 1.09 degrees, giving a reduction of 60.36%. Therefore, the proposed electric vehicle control strategy effectively enhanced both the path-following capability and the anti-roll stability of the corner-module architecture electric vehicle.
| S-Turn Scenario | Front-Wheel Steering | Four-Wheel Steering | Differential Oblique Steering |
|---|---|---|---|
| Path tracking success | Failed completely | Marginal success | Successful |
| Peak lateral error | Diverged | ≈ 7.21 m | ≈ 2.83 m |
| Peak roll angle | Unstable | ≈ 2.75° | ≈ 1.09° |
| Path tracking improvement | — | Baseline | 60.75% improvement |
| Roll reduction | — | Baseline | 60.36% reduction |
From the simulation results, I observed that differential oblique steering required a larger body sideslip angle than conventional four-wheel steering. This is expected because the electric vehicle intentionally rotates its body to change the path angle. Nevertheless, the roll angle remained smaller, which confirms that the geometric enlargement of the effective wheelbase is advantageous for roll stability.
5. Controller-in-the-Loop Verification of the Electric Vehicle Controller
Offline simulation results cannot fully capture the effect of communication delays, sampling periods, and hardware quantization. To further validate the differential oblique steering controller, I built a controller-in-the-loop testing platform. The controller-in-the-loop platform consists of a dSPACE MicroAutoBox, a PXI real-time simulator, CAN communication interfaces, power supplies, and host computers. The proposed MPC controller was compiled and executed on the dSPACE hardware. The nonlinear electric vehicle model was compiled into a dynamic-link library and executed on the PXI real-time target.
5.1 Setup of the Controller-in-the-Loop Platform
In the real-time environment, the electric vehicle model runs on the PXI machine while the steering controller runs on the dSPACE processor. The two parts communicate through a CAN bus. I set the CAN communication baud rate to 500 kbit/s and the sampling period of the vehicle model to 1 ms. The controller sampling period was set to 10 ms to approximate the real implementation constraints.
Tables below summarize the CAN signals sent between the vehicle model and the controller.
| Signal | Description | Unit | Start Bit | Length |
|---|---|---|---|---|
| \(e_\beta\) | Sideslip angle error | rad | 0 | 16 bits |
| \(e_r\) | Yaw rate error | rad/s | 16 | 16 bits |
| \(e_d\) | Lateral displacement error | m | 32 | 16 bits |
| \(e_\varphi\) | Heading error | rad | 48 | 16 bits |
| Signal | Description | Unit | Start Bit | Length |
|---|---|---|---|---|
| \(\delta_{fl}\) | Left front wheel steering angle | rad | 0 | 16 bits |
| \(\delta_{fr}\) | Right front wheel steering angle | rad | 16 | 16 bits |
| \(\delta_{rl}\) | Left rear wheel steering angle | rad | 32 | 16 bits |
| \(\delta_{rr}\) | Right rear wheel steering angle | rad | 48 | 16 bits |
The human-machine interface was programmed in LabVIEW. It displayed the vehicle trajectory, sideslip angle, yaw rate, roll angle, and wheel steering angles in real time. Data were logged for post-processing and comparison with offline simulation results.
5.2 Controller-in-the-Loop Results for the U-Turn Condition
The controller-in-the-loop test for the U-turn condition used the same vehicle parameters and the same reference path as the offline simulation. The differential oblique steering electric vehicle still tracked the U-shaped path accurately. The four-wheel steering electric vehicle produced a peak lateral error of nearly 6 m in the real-time test, while the differential oblique steering electric vehicle maintained a peak lateral error of about 0.6 m. The roll angle was reduced from about 3.45 degrees in the four-wheel steering mode to about 1.24 degrees in differential oblique steering mode.
I observed that the real-time results were slightly deteriorated compared with offline simulation because of the CAN communication latency. However, the trends and the level of improvement remained similar. This demonstrated that the proposed MPC controller is robust enough to be implemented on an embedded electric vehicle control platform.
5.3 Controller-in-the-Loop Results for the S-Turn Condition
In the low-friction S-turn test, the behavior of the front-wheel steering electric vehicle became unstable after the first curve. The four-wheel steering electric vehicle followed the path but with a large lateral error of about 10.3 m. In comparison, the differential oblique steering electric vehicle achieved a peak lateral error of approximately 3.61 m, and its trajectory remained close to the reference path.
These real-time results confirm that the differential oblique steering allocation law and the fuzzy mode-switching logic can be executed reliably on genuine controller hardware. Moreover, the real-time tests also demonstrated that the control system is insensitive to moderate time delays, which is a crucial requirement for path-tracking controllers implemented in future electric vehicles.
6. Conclusions and Future Outlook
In this research, I studied the roll-stability control problem of a corner-module architecture electric vehicle during extreme steering on severe roads. The main contributions and conclusions of my work can be summarized as follows.
First, a twelve-degree-of-freedom vehicle model, Magic Formula tire model, steer-by-wire actuator model, and in-wheel motor model were constructed for the corner-module architecture electric vehicle. The accuracy of the complete electric vehicle model was verified against the Carsim vehicle model. The validated model can be used as a benchmark for future controller development.
Second, I proposed a differential oblique steering mode based on the four-wheel independent steering capability of the electric vehicle. Compared with traditional front-wheel steering and four-wheel steering, differential oblique steering allows the rear wheels to steer with larger angles than the front wheels, producing an intentional tail-swing motion. The differential oblique steering electric vehicle is able to track curved roads at high speed while maintaining lower roll angles because the equivalent virtual wheelbase is increased.
Third, I developed a hierarchical control architecture. The fuzzy switching layer determines when the electric vehicle should enter differential oblique steering mode. The roll-stability constraint layer prevents excessive wheel steering angles and body sideslip angles. The model predictive controller computes the optimal front steering command while honoring the vehicle dynamics and safety constraints.
Fourth, high-speed U-turn and S-turn simulations on medium-friction and low-friction roads confirmed the effectiveness of the proposed method. The differential oblique steering electric vehicle reduced the peak lateral path-tracking error by 60.75% to 72.41% and reduced the peak body roll angle by 60.36% to 68.26% compared with the conventional four-wheel steering mode.
Finally, controller-in-the-loop tests were conducted using a PXI simulator and a dSPACE controller connected through CAN communication. The hardware-in-the-loop results verified that the proposed controller can run in real time with acceptable tracking accuracy. This suggests that the differential oblique steering control strategy is feasible for practical implementation in future intelligent electric vehicles.
There are several directions that need further investigation. First, the desired body sideslip angle should be scheduled according to the driver’s visibility, road geometry, and obstacle density. Second, online estimation of the tire-road friction coefficient is necessary for real-world deployment. Third, vehicle-to-everything information could be integrated into the MPC to improve predictive capability. I believe that the differential oblique steering concept will provide a valuable reference for the stability control of next-generation corner-module architecture electric vehicles.