Agricultural drones, also termed agricultural UAVs, have revolutionized precision farming through aerial pesticide spraying. The downward airflow generated by rotors atomizes pesticides into fine mist, enhancing coverage efficiency while reducing operator exposure. However, these agricultural UAVs face significant challenges during operation:
$$ \begin{cases}
\dot{x} = (U_1/m)(\cos\phi\sin\theta\cos\psi + \sin\phi\sin\psi) – C_1x/m + d_x \\
\dot{y} = (U_1/m)(\cos\phi\sin\theta\sin\psi – \sin\phi\cos\psi) – C_2y/m + d_y \\
\dot{z} = (U_1/m)(\cos\phi\cos\theta) – g – C_3z/m + d_z \\
\ddot{\phi} = lU_2/I_1 – C_4\dot{\phi}/I_1 \\
\ddot{\theta} = lU_3/I_2 – C_5\dot{\theta}/I_2 \\
\ddot{\psi} = lU_4/I_3 – C_6\dot{\psi}/I_3
\end{cases} $$
| Parameter | Description | Typical Value |
|---|---|---|
| $m$ | Total mass | 2 kg |
| $l$ | Rotor-to-center distance | 0.2 m |
| $I_1,I_2$ | Roll/Pitch inertias | 0.02 kg·m² |
| $I_3$ | Yaw inertia | 0.04 kg·m² |
| $C_{1-3}$ | Drag coefficients | 0.01 N·s/m |
| $C_{4-6}$ | Rotational drag coefficients | 0.012 N·m·s |
Agricultural UAVs exhibit underactuated dynamics requiring dual-loop control architecture. The position outer loop controller employs adaptive sliding mode control with saturation functions to mitigate chattering:
$$ \mathbf{U}_P = -\lambda\mathbf{E} – \mathbf{\hat{\Theta}} – k\cdot\text{sat}(\mathbf{s}/\sigma_1) – \eta\mathbf{s} $$
$$ \dot{\mathbf{\hat{\Theta}}} = \gamma \mathbf{s} \quad \text{with} \quad \mathbf{\hat{\Theta}} = \text{Proj}(\mathbf{\hat{\Theta}}) $$
$$ \text{sat}(s_i) = \begin{cases}
\text{sgn}(s_i) & |s_i| \geq \sigma_1 \\
s_i/\sigma_1 & |s_i| < \sigma_1
\end{cases} $$
The attitude inner loop controller ensures finite-time convergence through integral sliding surfaces and exponential reaching laws:
$$ \mathbf{s} = \dot{\mathbf{e}} + \lambda\mathbf{e} + \Delta\int\mathbf{e} dt $$
$$ \mathbf{U}_B = -\mathbf{s} – K\cdot\text{sat}(\mathbf{s}/\sigma_2) – \epsilon\mathbf{s} – \lambda\dot{\mathbf{B}}_d + \lambda\beta\mathbf{B} – \Delta\mathbf{e} $$
Lyapunov stability analysis proves global convergence for the agricultural drone system:
$$ V = \frac{1}{2}\mathbf{s}_P^T\mathbf{s}_P + \frac{1}{2\gamma}\mathbf{\tilde{\Theta}}^T\mathbf{\tilde{\Theta}} + \frac{1}{2}\mathbf{s}_B^T\mathbf{s}_B $$
$$ \dot{V} \leq -k\|\mathbf{s}_P\| – \eta\|\mathbf{s}_P\|^2 – K\|\mathbf{s}_B\| – \epsilon\|\mathbf{s}_B\|^2 < 0 $$
| Control Parameter | Symbol | Value |
|---|---|---|
| Adaptive gain | $\gamma$ | 1.0 |
| Sliding coefficient | $\lambda$ | 30 |
| Chattering gain | $\eta$ | 0.2 |
| Position gain | $k$ | 4.0 |
| Attitude gain | $K$ | 25 |
| Integral coefficient | $\Delta$ | 20 |
Field experiments confirm the agricultural UAV maintains stable hover (position error < 0.15m) under wind disturbances. Trajectory tracking performance demonstrates the controller’s robustness:
$$ \text{Position RMS Error} = \sqrt{\frac{1}{T}\int_0^T \|\mathbf{P}_d – \mathbf{P}\|^2 dt < 0.2\text{m}} $$
Agricultural UAVs implementing this control scheme show 40% reduction in trajectory deviation compared to conventional PID during spraying operations. The adaptive mechanism effectively compensates for payload variations up to 30% mass change, crucial for agricultural drones during chemical discharge.
The dual-loop architecture provides three key advantages for agricultural UAV applications: 1) Adaptive compensation of spray-induced mass variations 2) Wind disturbance rejection during low-altitude operations 3) Vibration suppression from turbulent crop-rotor interactions. These advancements significantly enhance spraying precision while reducing chemical drift in precision agriculture. Future work will investigate swarm coordination for large-scale agricultural drone deployments.