Recent advances in drone technology have significantly improved Unmanned Aerial Vehicle (UAV) control systems, yet payload-induced nonlinearities remain challenging. Conventional strategies like PID control struggle with unbalanced load disturbances due to strong nonlinear coupling. We address this limitation through synergistic integration of Long Short-Term Memory (LSTM) networks and Model Predictive Control (MPC). Our LSTM-MPC framework enhances attitude control precision by predicting dynamic responses and optimizing control inputs in real-time, substantially improving flight stability for critical applications like precision agriculture and aerial surveying.
Dynamic Modeling of UAV with Payload Disturbance
We establish the quadrotor’s attitude dynamics in body-fixed coordinates, where payload imbalance introduces torque disturbances and inertia variations. The coupled system’s rotational inertia becomes:
$$J_C = J_Q + m_L(\|d_L\|^2I_3 – d_Ld_L^T)$$
where \(J_Q\) denotes UAV inertia, \(m_L\) is payload mass, and \(d_L\) represents payload displacement. Gravity-induced disturbance torque is:
$$M_L = d_L m_L g$$
The complete attitude dynamics under unbalanced load are:
$$
\begin{cases}
\dot{\varphi}_C = [M_x + M_{Lx} – (J_{Cy} – J_{Cz})\dot{\theta}\dot{\psi}]/J_{Cx} \\
\dot{\theta}_C = [M_y + M_{Ly} – (J_{Cz} – J_{Cx})\dot{\varphi}\dot{\psi}]/J_{Cy} \\
\dot{\psi}_C = [M_z + M_{Lz} – (J_{Cx} – J_{Cy})\dot{\varphi}\dot{\theta}]/J_{Cz}
\end{cases}
$$
where \(\varphi\), \(\theta\), \(\psi\) represent roll, pitch, and yaw angles respectively. This formulation captures the critical nonlinear couplings exacerbated by asymmetric loading in drone technology applications.
LSTM-MPC Architecture Design
Our architecture combines temporal pattern recognition and predictive optimization. The LSTM network processes 10-dimensional input vectors to forecast attitude states:
| Input Features | Output Predictions |
|---|---|
|
|
MPC then solves the finite-horizon optimization:
$$J = \sum_{k=0}^{n-1} [(y(k) – y_{ref}(k))^T Q (y(k) – y_{ref}(k)) + u(k)^T R u(k)]$$
subject to actuator constraints. The hybrid structure operates through:
- LSTM prediction of attitude trajectory
- MPC computation of optimal control sequence
- Double feedback correction:
- Prediction error compensation
- Reference tracking adjustment
Experimental Validation
We trained the LSTM with 140 samples (70% training, 30% testing), achieving high prediction fidelity:
| Attitude | R² (Train) | RMSE (Test) | MAE (Test) |
|---|---|---|---|
| Roll | 0.9926 | 0.0148 rad | 0.0127 rad |
| Pitch | 0.9853 | 0.0202 rad | 0.0149 rad |
| Yaw | 0.9934 | 0.0134 rad | 0.0115 rad |
MATLAB simulations with 0.9kg payload at (0.15m, 0.15m, 0.05m) demonstrated superior tracking:
| Control Strategy | Roll RMSE | Pitch RMSE | Yaw RMSE |
|---|---|---|---|
| Fuzzy PID | 0.0121 rad | 0.0229 rad | 0.0021 rad |
| MPC | 0.0120 rad | 0.0195 rad | 0.0018 rad |
| LSTM-MPC | 0.0104 rad | 0.0171 rad | 0.0016 rad |
Real-world validation used an F450 Unmanned Aerial Vehicle carrying 0.6kg payload. During 60-second tests, our strategy maintained:
- Roll error: 3.91%
- Pitch error: 5.31%
- Yaw error: 1.10%
Conclusion
Our LSTM-MPC framework significantly enhances quadrotor resilience against payload disturbances. Key innovations include:
- LSTM-based disturbance prediction for anticipatory compensation
- MPC’s constrained optimization under dynamic couplings
- Dual-loop error correction architecture
This approach reduced attitude RMSE by 11.11-25.33% compared to conventional methods in drone technology applications. Future work will extend this framework to multi-UAV systems carrying variable payloads, further advancing Unmanned Aerial Vehicle capabilities in complex operational environments.