Surveying drones face significant challenges in maintaining formation stability during intermittent communication blackouts caused by signal interference or electromagnetic jamming. This work proposes a novel event-triggered control strategy enabling cooperative tracking in denied environments while minimizing communication overhead. The core innovation integrates an error compensation mechanism with dynamic event triggering to address leader-follower synchronization under directed communication topologies.
The surveying UAV dynamics with small-angle approximation are modeled as:
$$
\begin{cases}
\dot{x}_i = u_i \\
\dot{y}_i = v_i \\
\dot{z}_i = w_i \\
\dot{u}_i = -g\theta_i + \frac{f_{d,x}}{m_i} \\
\dot{v}_i = g\phi_i + \frac{f_{d,y}}{m_i} \\
\dot{w}_i = \frac{f_{d,z} – f_i}{m_i} \\
\dot{\phi}_i = p_i \\
\dot{\theta}_i = q_i \\
\dot{\psi}_i = r_i \\
\dot{p}_i = \frac{\tau_{i,x} + \tau_{d,x}}{J_{i,x}} \\
\dot{q}_i = \frac{\tau_{i,y} + \tau_{d,y}}{J_{i,y}} \\
\dot{r}_i = \frac{\tau_{i,z} + \tau_{d,z}}{J_{i,z}}
\end{cases}
$$
where \(m_i\) denotes surveying drone mass, \(J\) represents inertia moments, and disturbance terms \(f_d\), \(\tau_d\) encompass wind effects during aerial surveying operations.
Control Architecture
The intermittent event-triggered controller for surveying UAVs combines three key components:
$$
u_i =
\begin{cases}
c_i K q_i(t_i^k) + \hat{u}, & t \in [t_i^k, t_i^{k+1}) \cap [T_i, T_i + \tau_i) \\
0, & t \in [T_i + \tau_i, T_{i+1})
\end{cases}
$$
where \(\hat{u} = (1+\upsilon)\bar{u}g(Kq_i(t_i^k))\) provides disturbance compensation. The adaptive gain \(c_i\) evolves as:
$$
\dot{c}_i =
\begin{cases}
a\alpha_i(t) + b\beta_i(t_i^k), & c_i < \bar{c} \\
0, & c_i \geq \bar{c}
\end{cases}
$$
with \(\dot{\alpha}_i = \sigma e^{\sigma t} \|Kq_i(t_i^k)\|^2\) and \(\beta_i = \|Kq_i\|^2\). This structure enables surveying drones to maintain formation through communication outages.
| Parameter | Surveying UAV Function | Value Range |
|---|---|---|
| \(\phi_1, \phi_2\) | Trigger sensitivity | 0.05-0.15 |
| \(\sigma\) | Convergence rate | \(\geq \gamma_3 \lambda_{\max}(P)\) |
| \(\upsilon\) | Disturbance compensation | \(\geq \max\left(\frac{\int_{T_i+\tau_i}^{T_{i+1}} \sum v_i b_i \|Kq_i\| ds}{\int_{T_{i+1}}^{T_{i+1}+\delta_1 \sum v_i b_i \|Kq_i\| ds}\right)\) |
| \(a,b\) | Adaptation weights | \(a=0.8, b=1.2\) |
Stability Analysis
The Lyapunov function proves global stability for surveying drone formations:
$$
V(t) = q^T (\bar{C}V \otimes P) q + \frac{e^{-\sigma t}}{2\sigma} \sum_{i=1}^N v_i (c_i – \bar{c})^2
$$
Time-derivative analysis during communication intervals \([T_i, T_i + \tau_i)\) yields:
$$
\dot{V} \leq -\Xi V + \varpi_{14} e^{-\sigma t} – 2\upsilon \bar{c} \bar{u} \sum_{i=1}^N v_i b_i \|Kq_i\|
$$
where \(\Xi = \gamma_3 / \lambda_{\max}(P)\). The error compensation mechanism ensures bounded divergence during communication blackouts, enabling surveying UAVs to recover formation post-blackout.
Communication Efficiency
The dual-threshold event trigger minimizes inter-drone messaging:
$$
t_i^{k+1} = \inf \left\{ t > t_i^k : \begin{array}{c} \bar{c} \|K\varepsilon_i\| > \phi_1 c_i \|Kq_i\|^2 + \phi_1 e^{-\sigma t} \\ \lor \\ \bar{c}^2 \|K\varepsilon_i\|^2 > \phi_2 c_i \|Kq_i\|^2 + \phi_2 e^{-\sigma t} \end{array} \right\}
$$
This reduces surveying UAV communication frequency by 78-85% versus periodic control while maintaining <2cm formation tracking accuracy. Key performance metrics:
| Metric | Periodic Control | Proposed Method |
|---|---|---|
| Avg. comm interval | 0.1s | 0.54s |
| Comm bandwidth | 8Mbps | 1.2Mbps |
| Steady-state error | 0.015m | 0.018m |
| Blackout recovery | 4.2s | 3.1s |
Simulation Validation
Four surveying UAVs tracking a leader under three communication blackouts (110-130s, 180-190s, 320-325s) demonstrate:
- Formation integrity maintained within \(\pm\)0.25m during blackouts
- Maximum 1.8cm steady-state position error
- 78% reduction in control updates
- Disturbance rejection for wind gusts up to 8m/s
The surveying drones achieve these metrics through the synergistic operation of the adaptive gain mechanism and error compensation, particularly crucial during electromagnetic-denied environments typical in industrial surveying applications.
Conclusion
This work establishes a robust cooperative control framework for surveying UAV swarms operating in intermittent communication environments. The integrated event-triggered mechanism and disturbance compensation enable:
$$
\begin{array}{c}
\lim_{t \to \infty} \|e_i(t)\| = 0 \\
\downarrow \\
\text{85\% comm reduction} \\
\downarrow \\
\text{2cm tracking accuracy}
\end{array}
$$
Future work will extend this framework to heterogeneous surveying drone fleets executing simultaneous mapping and inspection tasks in GNSS-denied environments.