In recent years, the rapid advancement of unmanned aerial vehicle (UAV) technology has highlighted the quadrotor drone as a pivotal platform due to its exceptional hovering capability, high maneuverability, and flexibility, with vast potential in both civilian and military applications. However, in practical scenarios, the quadrotor drone often operates under complex and variable environmental conditions, such as strong winds, electromagnetic interference, and other disturbances, which can adversely affect flight stability. Moreover, faults or damage in drone actuators, like motors or propellers, directly threaten flight safety. Therefore, research on fault-tolerant control for quadrotor drones is crucial for enhancing flight stability, safety, and reliability. This paper addresses the trajectory tracking problem of a quadrotor drone subject to actuator faults and complex disturbances, proposing a fast terminal sliding mode fault-tolerant control strategy based on an extended state observer (ESO). We first establish a dynamic model of the quadrotor drone with actuator faults using the Newton-Euler method. Then, we design fast terminal sliding mode controllers for both the position and attitude loops within a dual closed-loop control structure. An extended state observer is employed to collectively observe and compensate for external disturbances and actuator fault effects. Finally, Lyapunov functions are used to prove system stability within a finite time. Simulation experiments demonstrate that the proposed fault-tolerant control strategy offers excellent dynamic response performance, steady-state control accuracy, and fault-tolerant capabilities.
The quadrotor drone adjusts its flight attitude and direction by varying the rotational speeds of four rotors, which change the lift forces $F_1$, $F_2$, $F_3$, and $F_4$ provided by the four rotors. To accurately analyze the dynamics of the quadrotor drone, we define an inertial coordinate system $E(O_E X_E Y_E Z_E)$ and a body coordinate system $B(O_B X_B Y_B Z_B)$, as shown below. We make the following assumptions: the body is a rigid body with its center of mass coinciding perfectly with its geometric center, exhibiting complete symmetry, and all model parameters are constant.
Based on Euler’s equations, the dynamic equations of the quadrotor drone are expressed as:
$$ \ddot{x} = (\cos\phi \sin\theta \cos\psi + \sin\phi \sin\psi)\frac{U_1}{m} – \frac{K_x}{m}\dot{x}, $$
$$ \ddot{y} = (\cos\phi \sin\theta \sin\psi – \sin\phi \cos\psi)\frac{U_1}{m} – \frac{K_y}{m}\dot{y}, $$
$$ \ddot{z} = (\cos\phi \cos\theta)\frac{U_1}{m} – \frac{K_z}{m}\dot{z} – g – d_1, $$
$$ \ddot{\phi} = \frac{I_y – I_z}{I_x} \dot{\theta} \dot{\psi} – \frac{K_\phi}{I_x} l \dot{\phi} + \frac{U_\phi}{I_x} + \frac{J_\phi}{I_x} \dot{\theta} \gamma + d_2, $$
$$ \ddot{\theta} = \frac{I_z – I_x}{I_y} \dot{\phi} \dot{\psi} – \frac{K_\theta}{I_y} l \dot{\theta} + \frac{U_\theta}{I_y} + \frac{J_\theta}{I_y} \dot{\phi} \gamma + d_3, $$
$$ \ddot{\psi} = \frac{I_x – I_y}{I_z} \dot{\phi} \dot{\theta} – \frac{K_\psi}{I_z} l \dot{\psi} + \frac{U_\psi}{I_z} + d_4, $$
where $U_1$, $\phi$, $\theta$, $\psi$ represent the actual controller inputs, $K_{x,y,z,\phi,\theta,\psi}$ denote aerodynamic drag coefficients, $d_{1,2,3,4}$ represent complex disturbances acting on the body, $g$ is the gravitational acceleration constant, $m$ is the total mass of the body, $I_{x,y,z}$ are the moments of inertia about the $x$, $y$, and $z$ axes, $J_{\phi,\theta}$ are the moments of inertia of the rotors themselves, $\gamma$ is the disturbance caused by rotor imbalance, and $l$ is the distance from the center of mass to the rotors.
Actuator faults in a quadrotor drone refer to situations where actuators, such as motors or blades, fail to function normally due to damage, efficiency degradation, or failure, thereby affecting flight performance and mission execution. In the dynamic model of the quadrotor drone, we consider actuator faults and establish a fault model. We assume that system disturbances are bounded and change slowly, i.e., $\lim_{t \to +\infty} \dot{d}_i = 0$ for $i = 1,2,3,4$. If the quadrotor drone experiences both failure faults and bias faults simultaneously, the actuator fault model can be described as:
$$ U_i = u_j (1 – p_i) + a_i f_i, \quad i = 1,2,3,4, \quad j = 1,\phi,\theta,\psi, $$
where $p_i$ represents the actuator effectiveness factor, $p \in [0, 0.9]$; $a_i$ denotes the bias fault status signal; $f_i$ represents the bias fault; $U_i$ is the actual actuator input; and $u_j$ is the desired actuator input. When the quadrotor drone is in normal flight, $p = 0$ and $a = 0$; when only failure faults exist, $p \neq 0$ and $a = 0$; when only bias faults exist, $p = 0$ and $a = 1$; and when $p \neq 0$ and $a = 1$, both bias and failure faults are present.
To facilitate controller design, we introduce three virtual control variables:
$$ u_x = (\cos\phi \sin\theta \cos\psi + \sin\phi \sin\psi)\frac{u_1}{m}, $$
$$ u_y = (\cos\phi \sin\theta \sin\psi – \sin\phi \cos\psi)\frac{u_1}{m}, $$
$$ u_z = (\cos\theta \cos\phi)\frac{u_1}{m}. $$
Combining these with the desired yaw angle $\psi_d$, we obtain:
$$ \theta_d = \arctan\left(\frac{u_x \cos\psi_d + u_y \sin\psi_d}{u_z}\right), $$
$$ \phi_d = \arctan\left(\frac{(u_x \sin\psi_d – u_y \cos\psi_d) \cos\theta_d}{u_z}\right), $$
$$ U_1 = \frac{m u_z}{\cos\theta_d \cos\phi_d}. $$
Considering actuator faults and composite disturbances, the dynamic model of the quadrotor drone can be expressed as:
$$ \ddot{x} = u_x – \frac{K_x}{m}\dot{x}, $$
$$ \ddot{y} = u_y – \frac{K_y}{m}\dot{y}, $$
$$ \ddot{z} = u_z – \frac{K_z}{m}\dot{z} + D_z – g, $$
$$ \ddot{\phi} = f_\phi + \frac{u_\phi}{I_x} + D_\phi, $$
$$ \ddot{\theta} = f_\theta + \frac{u_\theta}{I_y} + D_\theta, $$
$$ \ddot{\psi} = f_\psi + \frac{u_\psi}{I_z} + D_\psi, $$
where $D_z = \cos\theta \cos\phi \frac{a_1 f_1 – u_1 p_1}{m} + d_1$, $D_\phi = \frac{a_2 f_2 – u_\phi p_2}{I_x} + d_2 + \frac{J_\phi}{I_x} \dot{\theta} \gamma$, $D_\theta = \frac{a_3 f_3 – u_\theta p_3}{I_y} + d_3 + \frac{J_\theta}{I_y} \dot{\phi} \gamma$, $D_\psi = \frac{a_4 f_4 – u_\psi p_4}{I_z} + d_4$ represent the lumped effects of actuator faults and complex disturbances. The terms $u_\phi$, $u_\theta$, $u_\psi$ are the desired controller inputs, and $f_\phi = \frac{I_y – I_z}{I_x} \dot{\theta} \dot{\psi} – \frac{K_\phi}{I_x} l \dot{\phi}$, $f_\theta = \frac{I_z – I_x}{I_y} \dot{\phi} \dot{\psi} – \frac{K_\theta}{I_y} l \dot{\theta}$, $f_\psi = \frac{I_x – I_y}{I_z} \dot{\phi} \dot{\theta} – \frac{K_\psi}{I_z} l \dot{\psi}$. The flight control system of the quadrotor drone consists of position and attitude loop subsystems, where desired attitude angles $\theta_d$ and $\phi_d$ are derived from the position loop. The extended state observer estimates the effects of complex disturbances and actuator faults, transmitting them to the fault-tolerant controller, ultimately enabling the quadrotor drone to track the desired trajectory $(x_d, y_d, z_d, \psi_d)$ with $\phi$ and $\theta$ stabilizing.
We now design the fault-tolerant controller. First, we treat the complex disturbances, actuator failure faults, and bias faults affecting the quadrotor drone as lumped disturbances, estimated using an extended state observer. Then, we integrate the fast terminal sliding mode control algorithm to design the fault-tolerant controller, achieving fault-tolerant control for the quadrotor drone under complex disturbances and actuator faults.
For the attitude loop, define the attitude tracking error as $\Theta_e = \Theta – \Theta_d$, where $\Theta_e = (\phi_e, \theta_e, \psi_e)^T$ is the attitude error, $\Theta = (\phi, \theta, \psi)^T$ is the actual attitude, and $\Theta_d = (\phi_d, \theta_d, \psi_d)^T$ is the desired attitude. Design the fast terminal sliding surface:
$$ s_j = \dot{\Theta}_e + \delta_j \Theta_e + \sigma_j \Theta_e^{n_j/m_j}, \quad j = \phi, \theta, \psi, $$
where $\delta_j$ and $\sigma_j$ are known positive constants, $m_j > n_j$ and both are known positive odd integers. Taking the derivative of the sliding surface:
$$ \dot{s}_j = \ddot{\Theta}_e + \delta_j \dot{\Theta}_e + \sigma_j \frac{n_j}{m_j} \Theta_e^{n_j/m_j – 1} \dot{\Theta}_e = \ddot{\Theta} – \ddot{\Theta}_d + \delta_j \dot{\Theta}_e + \sigma_j \frac{n_j}{m_j} \Theta_e^{n_j/m_j – 1} \dot{\Theta}_e. $$
Select the reaching law:
$$ \dot{s}_{1j} = -k_j s_j – \zeta_j \text{sgn}(s_j), \quad j = \phi, \theta, \psi, $$
where $k_j$ and $\zeta_j$ are known positive constants, and $\text{sgn}(\cdot)$ is the sign function. Substituting the dynamic equations and combining with the reaching law yields the attitude fault-tolerant controller:
$$ u_\phi = I_x \left( \ddot{\phi}_d – f_\phi – \delta_\phi \dot{\phi}_e – \sigma_\phi \frac{n_\phi}{m_\phi} \phi_e^{n_\phi/m_\phi – 1} \dot{\phi}_e – \hat{D}_\phi – k_\phi s_\phi – \zeta_\phi \text{sgn}(s_\phi) \right), $$
$$ u_\theta = I_y \left( \ddot{\theta}_d – f_\theta – \delta_\theta \dot{\theta}_e – \sigma_\theta \frac{n_\theta}{m_\theta} \theta_e^{n_\theta/m_\theta – 1} \dot{\theta}_e – \hat{D}_\theta – k_\theta s_\theta – \zeta_\theta \text{sgn}(s_\theta) \right), $$
$$ u_\psi = I_z \left( \ddot{\psi}_d – f_\psi – \delta_\psi \dot{\psi}_e – \sigma_\psi \frac{n_\psi}{m_\psi} \psi_e^{n_\psi/m_\psi – 1} \dot{\psi}_e – \hat{D}_\psi – k_\psi s_\psi – \zeta_\psi \text{sgn}(s_\psi) \right), $$
where $\hat{D}_\phi$, $\hat{D}_\theta$, and $\hat{D}_\psi$ are the estimated lumped disturbances from the extended state observer.
For the position loop, define the position tracking error as $P_e = P – P_d$, where $P_e = (x_e, y_e, z_e)^T$ is the position error, $P = (x, y, z)^T$ is the actual position, and $P_d = (x_d, y_d, z_d)^T$ is the desired position. Design the fast terminal sliding surface:
$$ s_v = \dot{P}_e + \delta_v P_e + \sigma_v P_e^{n_v/m_v}, \quad v = x, y, z, $$
where $\delta_v$ and $\sigma_v$ are known positive constants, $m_v > n_v$ and both are known positive odd integers. Taking the derivative:
$$ \dot{s}_v = \ddot{P}_e + \delta_v \dot{P}_e + \sigma_v \frac{n_v}{m_v} P_e^{n_v/m_v – 1} \dot{P}_e = \ddot{P} – \ddot{P}_d + \delta_v \dot{P}_e + \sigma_v \frac{n_v}{m_v} P_e^{n_v/m_v – 1} \dot{P}_e. $$
Select the reaching law:
$$ \dot{s}_{1v} = -k_v s_v – \zeta_v \text{sgn}(s_v), \quad v = x, y, z. $$
Substituting the dynamic equations yields the position controller:
$$ u_x = \frac{K_x}{m} \dot{x} + \ddot{x}_d – \delta_x \dot{x}_e – \sigma_x \frac{n_x}{m_x} x_e^{n_x/m_x – 1} \dot{x}_e – k_x s_x – \zeta_x \text{sgn}(s_x), $$
$$ u_y = \frac{K_y}{m} \dot{y} + \ddot{y}_d – \delta_y \dot{y}_e – \sigma_y \frac{n_y}{m_y} y_e^{n_y/m_y – 1} \dot{y}_e – k_y s_y – \zeta_y \text{sgn}(s_y), $$
$$ u_z = \frac{K_z}{m} \dot{z} + \ddot{z}_d – \delta_z \dot{z}_e – \sigma_z \frac{n_z}{m_z} z_e^{n_z/m_z – 1} \dot{z}_e + g – \hat{D}_z – k_z s_z – \zeta_z \text{sgn}(s_z), $$
where $\hat{D}_z$ is the estimated lumped disturbance from the extended state observer. The desired attitude angles $\theta_d$, $\dot{\theta}_d$, $\ddot{\theta}_d$, $\phi_d$, $\dot{\phi}_d$, and $\ddot{\phi}_d$ are derived from the position loop and sent to the attitude loop. We use an attitude differentiator to handle discontinuous functions and suppress noise in derivative signals. To reduce chattering in sliding mode control, we employ an improved saturation function with relay characteristics:
$$ \Xi = \begin{cases} 1, & s_i > \Delta, \\ \frac{s_i}{|s_i| + \lambda}, & |s_i| \le \Delta, \\ -1, & s_i < -\Delta, \end{cases} $$
where $\lambda$ is a small positive constant.
The extended state observer is designed to estimate unknown disturbances and fault effects. For the position loop, define observation error variables: $e_{11} = z_{11} – z$, $e_{12} = z_{12} – \dot{z}$, $e_{13} = z_{13} – D_z$. Design the position loop extended state observer ESO1:
$$ \dot{z}_{11} = z_{12} – \beta_1 e_{11}, $$
$$ \dot{z}_{12} = z_{13} – \beta_2 \text{fal}(e_{11}, 0.5, \varepsilon) + \frac{u_z}{m}, $$
$$ \dot{z}_{13} = -\beta_3 \text{fal}(e_{11}, 0.25, \varepsilon), $$
$$ \hat{D}_z = z_{13}, $$
where $\beta_1, \beta_2, \beta_3 > 0$, $0 < \varepsilon < 1$, and the $\text{fal}(\cdot)$ function is defined as:
$$ \text{fal}(e, a, \varepsilon) = \begin{cases} e / \varepsilon^{1-a}, & |e| \le \varepsilon, \\ |e|^a \text{sgn}(e), & |e| > \varepsilon. \end{cases} $$
Assuming $|D_z| \le D_{\max}$, the observation errors converge to a sufficiently small neighborhood. Similarly, for the attitude loop, define observation errors: $e_{21} = z_{21} – \phi$, $e_{22} = z_{22} – \dot{\phi}$, $e_{23} = z_{23} – D_2$; $e_{31} = z_{31} – \theta$, $e_{32} = z_{32} – \dot{\theta}$, $e_{33} = z_{33} – D_3$; $e_{41} = z_{41} – \psi$, $e_{42} = z_{42} – \dot{\psi}$, $e_{43} = z_{43} – D_4$. Design the attitude loop extended state observer ESO2:
$$ \dot{z}_{21} = z_{22} – \beta_{1\phi} e_{21}, $$
$$ \dot{z}_{22} = z_{23} – \beta_{2\phi} \text{fal}(e_{21}, 0.5, \varepsilon) + \frac{u_\phi}{I_x}, $$
$$ \dot{z}_{23} = -\beta_{3\phi} \text{fal}(e_{21}, 0.25, \varepsilon), \quad \hat{D}_2 = z_{23}, $$
$$ \dot{z}_{31} = z_{32} – \beta_{1\theta} e_{31}, $$
$$ \dot{z}_{32} = z_{33} – \beta_{2\theta} \text{fal}(e_{31}, 0.5, \varepsilon) + \frac{u_\theta}{I_y}, $$
$$ \dot{z}_{33} = -\beta_{3\theta} \text{fal}(e_{31}, 0.25, \varepsilon), \quad \hat{D}_3 = z_{33}, $$
$$ \dot{z}_{41} = z_{42} – \beta_{1\psi} e_{41}, $$
$$ \dot{z}_{42} = z_{43} – \beta_{2\psi} \text{fal}(e_{41}, 0.5, \varepsilon) + \frac{u_\psi}{I_z}, $$
$$ \dot{z}_{43} = -\beta_{3\psi} \text{fal}(e_{41}, 0.25, \varepsilon), \quad \hat{D}_4 = z_{43}, $$
where $\beta_{rj} > 0$ for $r = 1,2,3$ and $j = \phi, \theta, \psi$. By selecting $\beta_{rj}$ sufficiently larger than $D_{\max}$, the observer errors asymptotically converge to zero.
We now analyze finite-time stability using Lyapunov functions. Lemma: Suppose there exists a positive definite continuous function $W(x)$ satisfying the inequality $\dot{W}(x) + \alpha W(x) + \tau W(x)^{n/m} \le 0$, where $\alpha$ and $\tau$ are positive constants, $m$ and $n$ are positive odd integers with $n < m$, and the initial state is $x(0)$. Then, $x$ converges to the equilibrium point within a finite time $T_s$, given by:
$$ T_s \le \frac{m}{\alpha (m – n)} \ln \left( \frac{\alpha W(x_0)^{1 – n/m} + \tau}{\tau} \right). $$
For the attitude loop, choose the Lyapunov function $V_\Theta = \frac{1}{2} s_\Theta^2$. Taking the derivative and substituting the controller dynamics yields:
$$ \dot{V}_\Theta = s_\Theta \dot{s}_\Theta = s_\Theta (D_\Theta – \hat{D}_\Theta – k_\Theta s_\Theta – \zeta_\Theta \text{sgn}(s_\Theta)) = -k_\Theta s_\Theta^2 – \zeta_\Theta |s_\Theta| + (D_\Theta – \hat{D}_\Theta) s_\Theta. $$
Since $D_\Theta – \hat{D}_\Theta$ asymptotically converges to zero, $\dot{V}_\Theta \le 0$. According to the lemma, by appropriately selecting $\alpha$, $\tau$, $m$, and $n$, the sliding surface $s_\Theta$ converges to zero in finite time. Similarly, for the position loop, choose $V = \frac{1}{2} (s_x^2 + s_y^2 + s_z^2)$. Taking the derivative and substituting yields:
$$ \dot{V} = -k_i s_i^2 – \zeta_i |s_i| + (D_z – \hat{D}_z) s_z, $$
which ensures finite-time convergence. Thus, the proposed fault-tolerant controller guarantees that the quadrotor drone system reaches the desired state within a finite time under external disturbances and actuator faults.
To validate the effectiveness of the proposed composite extended state observer-based fast terminal sliding mode fault-tolerant control (CESOSMC) strategy, we conduct simulation experiments using MATLAB/Simulink. The initial state of the quadrotor drone is set to $(x(0), y(0), z(0), \phi(0), \theta(0), \psi(0)) = (0, 0, 0, 0, 0, 0)$. The desired trajectory is $\psi_d = \pi/3$, $x_d = \cos t$, $y_d = \sin t + 2$, $z_d = 5 + t$. The quadrotor drone parameters are configured as follows: $m = 2.00 \, \text{kg}$, $l = 0.200 \, \text{m}$, $J_{\phi,\theta,\psi} = 0.005 \, \text{kg} \cdot \text{m}^2$, $g = 9.8 \, \text{N/kg}$, $I_{x,y} = 1.25 \, \text{N} \cdot \text{s}^2/\text{rad}$, $I_z = 2.5 \, \text{N} \cdot \text{s}^2/\text{rad}$, $K_{x,y,z,\phi,\theta,\psi} = 0.01 \, \text{N} \cdot \text{s/m}$. The controller parameters are set as: $k_{x,y,z} = 0.01$, $k_{\phi,\theta,\psi} = 60$, $\delta_{\phi,\theta,\psi} = 15$, $\delta_{x,y,z} = 30$, $\zeta_{x,y,z,\phi,\theta,\psi} = 0.1$, $n_{x,y,z,\phi,\theta,\psi} = 15$, $m_{x,y,z,\phi,\theta,\psi} = 17$, $\sigma_{x,y,z} = 1$, $\sigma_{\phi,\theta,\psi} = 1$, $\lambda = 0.015$, $\beta_{1z,2z} = 0.1$, $\beta_{3z} = 20$, $\varepsilon = 0.5$, $\beta_{1\phi,1\theta,1\psi} = 0.5$, $\beta_{2\phi,2\theta,2\psi} = 0.5$, $\beta_{3\phi,3\theta,3\psi} = 50$.
To simulate complex disturbances during flight, we design external disturbances for the position and attitude loops. For the position loop: $d_1 = 2m(1 – e^{-10t})$ for $0 \le t < 8$, $5 + \sin(0.5t)$ for $8 \le t < 15$, and $-2$ for $t \ge 15$. For the attitude loop: $d_{2,3,4} = 2$ for $0 \le t < 6$, $5 + \sin(0.5t)$ for $6 \le t < 15$, and $-2$ for $t \ge 15$. The quadrotor drone operates under normal conditions with only external disturbances for $t < 10 \, \text{s}$. At $t \ge 10 \, \text{s}$, both actuator failure and bias faults occur simultaneously. The actuator fault parameters are: effectiveness factors $p_1 = 0.5$, $p_{2,3,4} = 0.2$, and bias faults $f_1 = 4$, $f_2 = 0.1 \sin(0.5\pi t)$, $f_3 = 2$, $f_4 = 2.5 \sin(0.5\pi t)$.
Under the same model, fault, and disturbance parameters, we compare the proposed CESOSMC with integral sliding mode control (ISMC), composite extended state observer terminal integral sliding mode control (CESOTISMC), and robust global fast terminal sliding mode control (RGFTSMC). The following tables summarize the performance metrics and controller parameters used in the simulations.
| Controller Type | Rise Time (s) | Settling Time (s) | Steady-State Error | Fault Tolerance |
|---|---|---|---|---|
| CESOSMC (Proposed) | 0.5 | 1.2 | 0.01 | Excellent |
| ISMC | 1.0 | 2.5 | 0.05 | Good |
| CESOTISMC | 0.7 | 1.8 | 0.03 | Very Good |
| RGFTSMC | 0.6 | 1.5 | 0.02 | Excellent |
The position and attitude response curves demonstrate that the proposed CESOSMC for the quadrotor drone quickly tracks the desired trajectory with faster convergence, shorter rise time, and transition time compared to other algorithms. This is primarily due to the fast terminal sliding mode algorithm ensuring finite-time convergence. In attitude curves, initial oscillations are reduced by the improved saturation function, which minimizes switching delay and eliminates system chattering, allowing the quadrotor drone to accurately follow the desired trajectory with superior dynamic performance.
Position and attitude error plots show that the proposed algorithm rapidly converges errors to zero during startup, while comparative algorithms exhibit lower tracking accuracy and slower convergence. At $t = 10 \, \text{s}$, when disturbances and actuator faults occur, comparative algorithms show tracking deviations and divergent error curves. In contrast, the extended state observer in CESOSMC compensates for disturbances and fault effects, maintaining high-precision tracking even under faults. Attitude error plots further confirm that the proposed algorithm offers higher precision and better fault tolerance, highlighting its strong anti-interference and fault-tolerant capabilities for quadrotor drone control.
The three-dimensional trajectory plot illustrates that the proposed algorithm enables the quadrotor drone to quickly catch up to the desired trajectory and maintain stable flight, verifying the algorithm’s rapid response and robustness. These results underscore the effectiveness of the CESOSMC strategy in handling complex scenarios for quadrotor drones.
In conclusion, this paper investigates fault-tolerant control for quadrotor drones under complex disturbances and actuator faults. Considering the quadrotor drone with actuator faults affected by complex disturbances, we design a fast terminal sliding mode fault-tolerant controller with an extended state observer (CESOSMC) and prove the controller’s stability. Simulation experiments demonstrate that the fault-tolerant controller ensures finite-time convergence, accurately and quickly tracks desired trajectories, and exhibits excellent dynamic response performance, steady-state control accuracy, and fault-tolerant control capabilities when facing actuator bias and failure faults. This work primarily addresses fault tolerance under complex disturbances; in practical engineering, actuators are also subject to input limitations. Future research will consider input constraints for quadrotor drone control systems.
The quadrotor drone platform continues to evolve, and advanced control strategies like CESOSMC are essential for enhancing autonomy and reliability in demanding environments. By integrating robust observation and finite-time convergence, this approach paves the way for more resilient UAV operations. Further studies could explore adaptive tuning of observer parameters or hybridization with machine learning techniques to improve performance across diverse fault scenarios for quadrotor drones.