In this dissertation, I investigate the fault-tolerant trajectory tracking control problem of four-wheel independent drive (FWID) electric cars under actuator failures. With the rapid development of intelligent transportation systems, the four-wheel independent drive electric car has become a major technical carrier of autonomous driving due to its fast torque response, compact drivetrain architecture, and superior potential for coordinated control. However, the large number of in-wheel motors increases the possibility of actuator faults, which may seriously degrade the trajectory tracking accuracy and jeopardize vehicle stability. Therefore, it is of great significance to develop an effective fault-tolerant tracking control strategy to guarantee the safe operation of the FWID electric car. In my research, I focus on both control algorithm design and reference trajectory generation, aiming at achieving accurate path following and stable vehicle motion under various fault conditions.
To describe the vehicle dynamic behavior under actuator failures, I first establish a seven-degree-of-freedom (7-DOF) vehicle dynamics model considering longitudinal, lateral, yaw, and four-wheel rotational dynamics. In this model, the actuator fault characteristics of in-wheel motors are represented by a multiplicative fault gain matrix \(k_i \,(i = fl, fr, rl, rr)\), which directly reflects the ratio between the actual motor torque output and the desired torque command. I further discuss typical failure modes of permanent magnet synchronous motors widely used in FWID electric cars, including inter-turn short-circuit faults, eccentricity faults, and demagnetization faults. The first two fault modes often lead to complete motor shutdown (\(k_i = 0\)), while demagnetization results in partial loss of torque capability (\(0 < k_i < 1\)). One critical issue is that when both wheels on the same side fail completely, it is impossible to generate an additional yaw moment through the torque difference between the left and right wheels. To solve this problem, I innovatively introduce a front-wheel compensation steering angle with a fault-triggering mechanism, which can dynamically adjust the actual front steering angle according to the fault degree. The trigger factor is defined as:
\[
\nu =
\begin{cases}
1, & \exists\, k_i<1, \quad i = fl, fr, rl, rr \\
0, & \text{otherwise}
\end{cases}
\]
The actual front wheel steering angle is expressed as \(\delta = \delta_f + \nu \Delta\delta\), in which \(\delta_f\) is the reference driver steering input and \(\Delta\delta\) is the compensation angle computed by the fault-tolerant controller. By doing so, the FWID electric car can effectively regulate its attitude under severe fault conditions, noticeably enhancing the vehicle capacity of fault accommodation. Combining the above-mentioned fault modeling with reasonable simplifications such as small steering angle approximation and linear tire model, I formulate the state-space representation of lateral and yaw motion for the FWID electric car:
\[
\dot{X} = \left(\frac{1}{I_z}B_y B_z + B_w\right) X + \frac{1}{I_z R_w} B_x K U + \Delta\delta B_u – \frac{2C_f\delta_f}{I_z} B_c
\]
In this equation, \(X = [v_y,\, \omega_z]^T\) denotes the state vector composed of lateral velocity and yaw rate, and \(U = [u_{fl},\, u_{fr},\, u_{rl},\, u_{rr}]^T\) is the motor torque command vector. The coefficient matrices are derived in detail in my study. The model fully characterizes the influence of actuator fault positions and degrees on the vehicle motion, thus laying a solid foundation for the subsequent controller design.
Based on the established 7-DOF dynamic model, I propose a hierarchical fault-tolerant tracking control framework to maintain the trajectory tracking accuracy and vehicle stability of the FWID electric car simultaneously when the motor actuators fail.
In the upper layer, the longitudinal speed tracking is realized by a PI controller, producing the total required torque \(T_d\). For the lateral and yaw motion, I design a super-twisting sliding mode controller (STSMC). Since the FWID electric car is typically a first-order dynamic system, the super-twisting algorithm is highly suitable because it only requires the sliding surface information without the derivative of sliding variables, which perfectly matches the measurable states of a vehicle. Meanwhile, STSMC is a second-order sliding mode control method that integrates the sign function term in a continuous manner, thereby greatly suppressing the chattering phenomenon existing in conventional sliding mode control. Moreover, the algorithm guarantees that both the sliding variable and its derivative remain on the sliding surface during the whole adjustment process, which leads to faster convergence behavior and stronger robustness against system uncertainties and external disturbances.
In my design, I construct two sliding surfaces, respectively:
\[
\begin{cases}
s_1 = c_1 e_y + e_{v_y} \\
s_2 = c_2 e_\varphi + e_\omega
\end{cases}
\]
where \(e_y\), \(e_{v_y}\), \(e_\varphi\), and \(e_\omega\) are the tracking errors of lateral displacement, lateral velocity, yaw angle, and yaw rate. The positive constants \(c_1\) and \(c_2\) represent the weight factors. The super-twisting reaching law is designed as:
\[
\begin{cases}
\dot{s}_i = -\lambda_i |s_i|^{\frac{1}{2}} \operatorname{sgn}(s_i) + \upsilon_i,\quad i=1,2 \\
\dot{\upsilon}_i = -\alpha_i \operatorname{sgn}(s_i)
\end{cases}
\]
The adaptive gains are updated according to:
\[
\dot{\lambda}_i =
\begin{cases}
\frac{1}{2} r_i^{\frac{1}{2}} w_i, & \text{if } s_i \neq 0 \\
0, & \text{otherwise}
\end{cases}
\]
To further reduce the chattering amplitude, I replace the standard sign function with an approximate arctangent function \(\operatorname{sgn}(x) \approx \frac{2}{\pi}\arctan(kx)\), leading to a smoother control response. The derived intermediate control laws are expressed as:
\[
\begin{aligned}
V_{m1} = &-\lambda_1 |s_1|^{\frac{1}{2}} \operatorname{sgn}(s_1) – \int \alpha_1 \operatorname{sgn}(s_1) dt – c_1 e_{v_y} + \dot{v}_{yd} + v_x \omega_z \\
&- \frac{1}{I_z} B_{y1} B_{z1} + \frac{2C_f\delta_f}{I_z} B_{c1} \\
V_{m2} = &-\lambda_2 |s_2|^{\frac{1}{2}} \operatorname{sgn}(s_2) – \int \alpha_2 \operatorname{sgn}(s_2) dt – c_2 e_\varphi + \dot{\omega}_{zd} \\
&- \frac{1}{I_z} B_{y2} B_{z2} + \frac{2C_f\delta_f}{I_z} B_{c2}
\end{aligned}
\]
In the above expressions, \(V_{m1}\) and \(V_{m2}\) are the intermediate control variables for lateral and yaw motions. The stability of the closed-loop system is rigorously proved through Lyapunov theory. I construct the Lyapunov function as:
\[
V(\eta, \lambda, \alpha) = V_0(\eta) + \frac{1}{2} r^{-1}(\lambda – \lambda^*)^2
\]
with \(V_0(\eta) = \eta^T P \eta\) and \(\eta = [|s|^{1/2}\operatorname{sgn}(s),\, \upsilon]^T\) being a positive definite matrix. Through careful algebraic derivation, I prove that the derivative of the Lyapunov function satisfies \(\dot{V} \leq -n V^{1/2}\), which means that the designed controller guarantees finite-time convergence of the tracking errors. The finite settling time is further bounded by \(t_s = \frac{2}{n}V^{1/2}(0)\).
In the lower layer, I establish a quadratic programming (QP) problem to optimally distribute the control efforts among the four in-wheel motors and the front-wheel compensation steering angle. The intermediate control variables are extended to \(\Psi = [V_{m1}, V_{m2}, T_d]^T\), which should satisfy the following equality constraint:
\[
\Psi = M \xi
\]
Here, the control vector is \(\xi = [u_{fl}, u_{fr}, u_{rl}, u_{rr}, \Delta\delta]^T\) and the matrix \(M\) is defined as:
\[
M = \frac{1}{R_w I_z}
\begin{bmatrix}
B_{x11}k_{fl} & B_{x12}k_{fr} & B_{x13}k_{rl} & B_{x14}k_{rr} & B_{u11} \\
B_{x21}k_{fl} & B_{x22}k_{fr} & B_{x23}k_{rl} & B_{x24}k_{rr} & B_{u12} \\
I_z k_{fl} & I_z k_{fr} & I_z k_{rl} & I_z k_{rr} & 0
\end{bmatrix}
\]
The objective function of the optimization problem is formulated by considering the tire workload rate, which is an important indicator reflecting the vehicle stability margin. Since the longitudinal tire force is much larger than the lateral tire force, I choose the following cost function:
\[
J_1 = \sum_{i} \frac{F_{xi}^2}{(\mu F_{zi})^2} = \sum_{i} \frac{u_i^2}{R_w^2 (\mu F_{zi})^2}
\]
Meanwhile, to make the optimization process more robust when the equality constraint cannot be strictly satisfied due to severe actuator failures, I introduce a slack term reflecting the tracking accuracy of the equality constraint into the cost function. The final QP problem is written as:
\[
\min_{\xi} \quad J_2 = \|W\xi\|_2^2 + \zeta \|W_w (M\xi – \Psi)\|_2^2
\]
\[
\text{s.t.} \quad \xi_{\min} \leq \xi \leq \xi_{\max}
\]
The upper and lower bounds in the constraint are derived by taking the intersection of the mechanical torque limit, the friction circle constraint, and the compensation angle limit. Specifically, the motor torque constraint is:
\[
|u_i| \leq \min\left\{ k_i T_{\max},\; \frac{R_w}{k_i}\sqrt{(\mu F_{zi})^2 – F_{yi}^2} \right\}
\]
The weight matrices in the QP problem are carefully selected to balance the tracking performance and the smoothness of control inputs. By solving this optimization problem in real time, the most appropriate torque command for each healthy wheel and the compensation steering angle for the front wheels can be obtained.
Simulation studies based on the CarSim and MATLAB/Simulink platform are carried out to examine the effectiveness of my proposed fault-tolerant tracking control strategy. The vehicle parameters utilized in the simulation environment are listed in the following table:
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| Vehicle mass | m | 1230 | kg |
| Yaw moment of inertia | I_z | 1343 | kg·m² |
| Distance from CG to front axle | l_f | 1.04 | m |
| Distance from CG to rear axle | l_r | 1.56 | m |
| Wheelbase | L | 2.6 | m |
| Half track width | d_h | 1.48 | m |
| Front tire cornering stiffness | C_f | 66 | kN/rad |
| Rear tire cornering stiffness | C_r | 63 | kN/rad |
| Tire radius | R_w | 0.325 | m |
The control parameters of my STSMC are listed below.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| k_p | 200 | k_i | 60 |
| γ1 | 0.53 | γ2 | 4.35 |
| c1 | 1.23 | c2 | 6.88 |
| k1 | 100 | k2 | 50 |
| β1 | 0.25 | β2 | 3.93 |
| ε1 | 0.13 | ε2 | 0.01 |
| ω1 | 0.46 | ω2 | 4.84 |
| ϑ | 0.03 | ζ | 1.26 |
| a1 | 10.3 | a2 | 1.43 |
| a3 | 0.58 |
I first conduct the single-lane-change simulation at a speed of 20 m/s. The reference trajectory includes one lane-change maneuver with a lateral displacement of about 3 m. The target path is planned such that the most demanding steering action occurs around 4 s. Consequently, I assume that the actuator fault occurs at the 4-th second, exactly at the maximum steering angle. Two fault scenarios are investigated: complete failure of the left front wheel, and complete failure of both left-side wheels. For comparison, I also evaluate the modified sliding mode fault-tolerant control (MSM-FTC), the adaptive fast terminal sliding mode fault-tolerant control (AFTSM-FTC), and the control system without fault tolerance (w/o FTC).
For the single-wheel fault scenario, the simulation results show that the proposed method has the smallest lateral displacement error among all the compared algorithms. Without fault-tolerant control, the FWID electric car severely deviates from the desired trajectory after the fault occurs, with a maximum lateral error of 1.46 m, indicating a potential collision risk. In contrast, my strategy maintains the vehicle close to the reference trajectory with a maximum lateral error of only 0.0546 m. The yaw rate tracking result also demonstrates that my controller achieves the quickest recovery and the smallest error amplitude. The torque distribution results of the proposed method do not show any obvious chattering, which is superior to the MSM-FTC algorithm. The quantitative comparison results for this scenario are listed below.
| Strategy | eymax (m) | eyRMSE (m) | eωmax (rad/s) | eωRMSE (rad/s) | Δεy (%) | Δεω (%) |
|---|---|---|---|---|---|---|
| w/o FTC | 1.46 | 0.716 | 0.032 | 0.0106 | – | – |
| MSM-FTC | 0.391 | 0.158 | 0.0153 | 0.002 | 77.93 | 81.13 |
| AFTSM-FTC | 0.214 | 0.108 | 0.008 | 0.0016 | 84.92 | 84.91 |
| STSM-FTC | 0.0546 | 0.0232 | 0.0029 | 5.37e-5 | 96.76 | 99.49 |
In the more challenging scenario where both left wheels completely fail at 4 s, the performance of all control strategies degrades to some extent due to the loss of ability to generate corrective yaw moment through torque differences. The w/o FTC strategy exhibits the largest tracking error and even loses stability during the lane-change process. The conventional MSM-FTC also shows noticeable performance degradation, with a maximum lateral error of 1.48 m and excessive yaw rate oscillations. The AFTSM-FTC and my proposed method still achieve acceptable tracking behavior, which confirms the benefit of the adaptive mechanism. Among all the tested strategies, my method again achieves the smallest lateral error and the quickest transient recovery. The front-wheel compensation angle is automatically enlarged by the fault-triggering mechanism in this severe fault scenario, demonstrating its considerable effectiveness. The quantitative results are presented below.
| Strategy | eymax (m) | eyRMSE (m) | eωmax (rad/s) | eωRMSE (rad/s) | Δεy (%) | Δεω (%) |
|---|---|---|---|---|---|---|
| w/o FTC | 2.549 | 1.056 | 0.0357 | 0.0117 | – | – |
| MSM-FTC | 1.48 | 0.58 | 0.0181 | 0.0056 | 45.08 | 52.14 |
| AFTSM-FTC | 0.675 | 0.332 | 0.0153 | 0.0044 | 68.56 | 62.39 |
| STSM-FTC | 0.120 | 0.0671 | 0.0075 | 0.0012 | 93.65 | 89.74 |
The quantitative analysis clearly indicates that my proposed strategy reduces the RMS lateral displacement error by 85.32% compared to MSM-FTC in the single-side fault case, and by 79.79% compared to the adaptive fast terminal sliding mode approach. These results validate that the proposed super-twisting sliding mode fault-tolerant tracking controller can effectively improve the trajectory tracking accuracy and robustness of the FWID electric car, especially under serious actuator failure conditions.
Considering that the reference trajectory for the fault-tolerant tracking controller is usually the output of the trajectory planning module in autonomous driving systems, I further investigate the trajectory planning problem for FWID electric cars in typical urban road environments. I propose an improved rapidly-exploring random tree (RRT) trajectory planning algorithm to address the shortcomings of the classic RRT algorithm, such as blind search, unsmooth path, and difficulty to integrate traffic rules. In the improved method, I introduce a heuristic search strategy, where the target point, the road centerline, or a random point is selected as the sampling point according to different random numbers. This design comprehensively balances the exploration efficiency and the global search capability. The expansion rule of a new node \(q_{new}\) is expressed as:
\[
q_{new} = q_{min} + \frac{s_1(q_{rand} – q_{min})}{d(q_{min}, q_{rand})} + \frac{s_2(q_{goal} – q_{min})}{d(q_{min}, q_{goal})}
\]
Furthermore, I design a driver-behavior cost function to select the optimal parent node. The cost function considers not only the distance between nodes, but also the slope of the connecting line and the lateral offset from the road centerline:
\[
J = \omega_1 d(q_c, q_f) + \omega_2 \operatorname{ang}(q_c, q_f) + \omega_3 \sum_{i=1}^{n} d(q_c, C_i)
\]
where \(C_i\) represents the coordinates of the \(i\)-th centerline and \(n\) is the total number of centerlines. The redundant node optimization strategy is then applied to the initially generated nodes by checking whether a straight line connecting two non-adjacent nodes intersects an obstacle. This iterative process effectively removes unnecessary intermediate nodes and greatly shortens the planned path. Finally, a spline curve smoothing algorithm is adopted to further improve the curvature continuity of the trajectory.
For dynamic obstacles commonly found in urban road scenarios, I also propose a re-planning strategy based on obstacle velocity information. By mapping the planar coordinates \((x, y)\) and time \(t\) to a three-dimensional space, dynamic obstacles can be represented as static obstacles sweeping along their velocity direction during a certain time horizon. The relationship between time and distance is:
\[
t = d(\Psi_i, \Psi_j) / v
\]
In the three-dimensional planning space, the search-tree expansion process continues until the target region is reached. When the predicted dynamic obstacle interferes with the previously planned trajectory, a re-planning procedure is triggered at the collision point. The obtained three-dimensional trajectory can be projected onto the \(XY\) plane to obtain the corresponding planar path for the FWID electric car.
To evaluate the performance of my improved RRT algorithm, I simulate two typical urban traffic scenarios: straight-road driving with obstacles and left-turn at an intersection. The simulation road includes three lanes with a lane width of 4 m, following the corresponding urban road design code. In the straight-road scenario, the vehicle moves at a set speed of 30 km/h along a 90 m long road segment with two static obstacles. The classic RRT algorithm produces many messy redundant search branches and irregular planned paths, which seriously deviates from human driving behavior and consumes a large amount of computational resources. In contrast, my improved RRT algorithm plans a smooth path that closely follows the road centerline, automatically selects the lane with fewer obstacles, and respects the traffic rules. In the left-turn scenario, the improved algorithm similarly demonstrates significantly better planning quality.
For the quantitative analysis, I conduct 50 repeated trials for both algorithms in each scenario. The averaged results show that in the straight-road situation, the planning time of the improved RRT is reduced by 53.54% compared with the classic RRT, while the path length is shortened by 12.59%. In the left-turn case, the planning time is reduced by 34.75% and the path length by 14.01%. These results demonstrate the superior efficiency and trajectory quality of my proposed trajectory planning method.
| Scenario | Algorithm | Planning time (s) | Path length (m) | Node number |
|---|---|---|---|---|
| Straight road | Classic RRT | 2.63 | 108.74 | 180 |
| Improved RRT | 1.22 | 95.05 | 42 | |
| Left-turn intersection | Classic RRT | 1.87 | 87.66 | 143 |
| Improved RRT | 1.22 | 75.38 | 37 |
I also test the dynamic obstacle avoidance performance of the proposed method. In a straight-road scenario, two slow-moving vehicles travel at 3 m/s in front of the host FWID electric car. The host vehicle at 8 m/s needs to safely overtake both moving obstacles. The re-planning is triggered 15 times during the driving process, and the final trajectory successfully avoids all dynamic obstacles and reaches the desired endpoint at 6.22 s. In a left-turn scenario, three vehicles with different velocities approach the intersection from different directions, and the planner triggers five re-planning processes. The final trajectory guarantees collision-free navigation. These tests confirm that the improved RRT-based planner is capable of handling complex and highly dynamic urban traffic environments.
After obtaining a planned trajectory from the improved RRT algorithm, I further validate the fault-tolerant trajectory tracking control strategy under more realistic urban road conditions. The simulation scenario is set as a three-lane straight road of 200 m length. The vehicle initial position is \((0,\,-4)\) and the destination is \((200,\,-2)\). Four static obstacles are placed at positions \((50,\,-4)\), \((60,\,0)\), \((150,\,4)\) and \((160,\,0)\). The reference trajectory includes a double-lane-change maneuver within the first 60 m, demanding a total lateral displacement of about 8 m. This trajectory is considerably more challenging than the previously tested single-lane-change maneuver, since the vehicle needs to change two lanes within the same longitudinal distance.
The initial and target speeds are both set to 20 m/s. The fault is activated at 0.25 s when the steering wheel angle reaches its maximum value. In the single-wheel fault scenario, my proposed controller gives the smallest tracking error among all compared methods. The maximum lateral displacement error is only 0.365 m, while the RMS value is 0.246 m. In contrast, the vehicle without fault-tolerant control has a maximum error of 5.368 m, which is unacceptable in real traffic. The torque distribution of my method is smooth and does not contain high-frequency components. The quantitative indicators under the planned trajectory are summarized below.
| Strategy | eymax (m) | eyRMSE (m) | eωmax (rad/s) | eωRMSE (rad/s) | Δεy (%) | Δεω (%) |
|---|---|---|---|---|---|---|
| w/o FTC | 5.368 | 2.838 | 0.0787 | 0.0253 | – | – |
| MSM-FTC | 5.034 | 2.710 | 0.0470 | 0.0111 | 4.51 | 27.15 |
| AFTSM-FTC | 2.224 | 1.283 | 0.0406 | 0.0095 | 54.79 | 62.45 |
| STSM-FTC | 0.365 | 0.246 | 0.0299 | 0.0084 | 91.32 | 66.80 |
For the more severe single-side wheel failure scenario, my method is still able to track the planned trajectory with a maximum lateral error of only 0.768 m. The compensation steering angle is automatically enlarged in this case, proving the effectiveness of the proposed fault-triggered mechanism. The quantitative indicators are shown in Table 7.
| Strategy | eymax (m) | eyRMSE (m) | eωmax (rad/s) | eωRMSE (rad/s) | Δεy (%) | Δεω (%) |
|---|---|---|---|---|---|---|
| w/o FTC | 10.821 | 5.162 | 0.0922 | 0.0283 | – | – |
| MSM-FTC | 8.188 | 4.498 | 0.0778 | 0.0197 | 12.86 | 30.39 |
| AFTSM-FTC | 3.344 | 2.559 | 0.0815 | 0.0236 | 50.43 | 16.61 |
| STSM-FTC | 0.768 | 0.607 | 0.0482 | 0.0134 | 88.24 | 52.65 |
In order to investigate the performance of the proposed fault-tolerant control strategy under more realistic hardware conditions, I carry out experiments on a real FWID electric car platform. The experimental platform is equipped with four permanent magnet synchronous in-wheel motors, a steering-by-wire system, a hydraulic braking system, and a centimeter-level integrated navigation module. The control algorithm is implemented in C++ and deployed on the vehicle control unit, with a control period of 0.05 s. The fundamental parameters of the experiment platform are listed below.
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| Platform mass | m | 894 | kg |
| Yaw moment of inertia | I_z | 1000 | kg·m² |
| Distance from CG to front axle | l_f | 1.01 | m |
| Distance from CG to rear axle | l_r | 1.24 | m |
| Wheelbase | L | 2.25 | m |
| Front tire cornering stiffness | C_f | 30 | kN/rad |
| Rear tire cornering stiffness | C_r | 25 | kN/rad |
| Tire radius | R_w | 0.325 | m |
| Half track width | d_h | 1.48 | m |
Since the in-wheel motors of the experimental platform cannot operate in the reverse direction, the motor torque command is constrained in the interval \([0,\,20]\) Nm, and the compensation angle is limited within \([-0.1,\,0.1]\) rad. The experimental scenario is a closed bidirectional two-lane road, in which the initial and target positions are predefined and three static obstacles are placed along the path. The initial and desired vehicle speed are set to 5 m/s for safety reasons. The trajectory in the experiment is generated offline using my improved RRT planner. The reference trajectory mainly consists of two consecutive lane-change segments with opposite directions, which requires the vehicle to continuously switch its attitude. The actuator faults are triggered at the 4-th second of the experiment by multiplying the control signal with a step function, so as to simulate the sudden loss of motor driving capability.
I first carry out an experiment under the left front wheel complete failure scenario. The measured steering wheel angle shows that the compensation angle is introduced immediately after the fault occurs, which effectively reduces the required steering wheel angle during the fault period. It is noteworthy that the compensation angular direction automatically follows the actual steering direction, meaning that when the steering wheel turns right, the compensation angle is negative, and vice versa. This directional adaptivity reduces the burden for the remaining healthy wheels and contributes to better vehicle controllability. The torque responses show that after the fault occurs, the left front wheel torque drops to zero, and the remaining three wheels respond promptly to compensate for the lost driving force. The velocity of the vehicle experiences only a minor transient drop before returning to the target value. From the global trajectory result, the vehicle accurately follows the planned path despite the sudden fault at 4 s. The yaw rate response also shows a small and quickly damped disturbance after the failure, confirming effective vehicle stability regulation.
The quantitative results show that in the single-wheel failure experiment, the RMS lateral displacement error is 0.0368 m with a maximum error of 0.1168 m. The RMS yaw rate error is 0.0185 rad/s with a maximum error of 0.0652 rad/s. These results fulfill the accuracy requirements of the experimental platform and further prove the effectiveness of my proposed strategy in practical environments.
I next perform an experiment under the more severe single-side wheel failure scenario. At the 4-th second, both the left front and left rear wheels simultaneously lose their driving capability. The compensation steering angle becomes noticeably larger than that in the single-wheel fault scenario, reflecting the fault-triggering mechanism’s ability to respond proportionally to fault severity. Since no healthy wheel on the left side remains, only the two right-side wheels provide the total driving torque. The vehicle speed still converges to the target value. The planned trajectory is well tracked in this severe fault condition, and the yaw rate remains close to the desired value throughout the whole test. The quantitative results show that the RMS lateral displacement error is 0.0733 m, with a maximum error of 0.1889 m, and the RMS yaw rate error is 0.0252 rad/s. Although the response delay is slightly larger, the vehicle remains stable and controllable during the whole process.
The experimental results demonstrate that under actuator failure conditions, my proposed fault-tolerant trajectory tracking strategy can effectively guarantee both the tracking accuracy of the FWID electric car and the stability of its motion even in actual urban road-like environments. The errors in trajectory tracking remain within the safety bound, which is essential for the future commercial deployment of autonomous FWID electric cars.
Based on the above simulation and experimental results, I draw the following conclusions from my research. First, the seven-degree-of-freedom vehicle dynamics model that I build in this study can faithfully characterize the behavior of the FWID electric car under different actuator fault scenarios. The introduction of the fault-triggered front-wheel compensation steering angle remarkably enhances the adjustment capability of the vehicle when one-side wheels completely fail. Second, the hierarchical fault-tolerant tracking control strategy based on super-twisting sliding mode control and quadratic programming torque allocation performs well in balancing path following accuracy and vehicle stability. Compared with the modified sliding mode strategy and the adaptive fast terminal sliding mode approach, my proposed controller significantly reduces the lateral tracking error and the yaw rate error under both single-wheel and single-side failures. The robustness of the proposed strategy is consistently validated by simulations with different fault severities and experiment field tests. Third, the improved RRT trajectory planning method I develop for urban scenes can efficiently generate a smooth, collision-free, and human-driving-compliant reference path. Combined with the planned trajectory, the fault-tolerant tracking strategy can still maintain satisfactory accuracy and stability, demonstrating that my algorithm is suitable for real-world city driving environments and can serve as a practical solution for future autonomous FWID electric cars.
There is still room for further improvement based on the present work. In the future, I plan to investigate the integration of trajectory planning with actuator fault information so that the planning module can proactively avoid risky regions when a fault occurs. Meanwhile, more realistic fault scenarios considering communication delay and sensor noise should be incorporated to further bridge the gap between theoretical research and engineering implementation of FWID electric cars.