We investigate the joint optimization of formation configuration and communication topology for fixed-wing drones in the presence of adversarial threats and minimal information flow constraints. Our work focuses on enabling a swarm of fixed-wing drones to autonomously determine both their spatial arrangement and the underlying communication network that supports cooperative control, while balancing battlefield situational awareness and stealth communication requirements.
1. Introduction
Modern aerial combat increasingly relies on coordinated swarms of fixed-wing drones. The formation configuration directly influences operational effectiveness, while the communication topology determines information sharing quality and survivability. In high-dynamic environments, the number of fixed-wing drones may scale rapidly, making real-time optimization challenging. We propose a hierarchical design framework that divides large‑scale formations into basic subformations, each optimized using particle swarm optimization (PSO) based on a situation field model. For the communication layer, we employ a Q‑learning algorithm to compute minimal‑cost routing that guarantees connectivity under leader‑follower architectures. The methodology achieves both global optimality and computational efficiency, as demonstrated through simulations with eight fixed-wing drones performing a cooperative strike mission.
2. Problem Formulation
2.1 Formation Configuration Modeling
Consider a swarm of N fixed-wing drones connected by a communication graph G. The formation is described by time‑varying functions that encode desired relative positions. We decompose the three‑dimensional formation into horizontal and vertical projections, using eight basic formation types encoded as binary numbers (Table 1).
| Formation type | Code | Formation shape |
|---|---|---|
| line (2) | 000 | Two drones in line |
| staggered (2) | 001 | Two drones staggered |
| parallel (2) | 010 | Two drones side by side |
| diagonal (2) | 011 | Two drones diagonal |
| triangle (3) | 100 | Three drones in equilateral triangle |
| inverted V (3) | 101 | Three drones in inverted V |
| V‑shape (3) | 110 | Three drones in V‑shape |
| wedge (3) | 111 | Three drones in wedge |
To handle large numbers of fixed-wing drones, we apply a hierarchical encoding/decoding scheme. The whole formation is decomposed into J layers, where each node in a higher layer represents a basic formation in the lower layer. The position of the k‑th follower in the i‑th basic formation is given by:
$$ \mathbf{P}_{i}^{k} = [x_{r}^{*}, y_{r}^{*}, z_{r}^{*}]^{T} $$
relative to the virtual leader located at the geometric center of the formation.
The situational awareness of a fixed-wing drone is modeled by the function:
$$ S_i = S_i(x,y,z,x_T,y_T,z_T) = S_d \left( \omega_1 S_a + \omega_2 S_l + \omega_3 S_c \right) $$
where:
- $S_d$ = detection capability
- $S_a$ = attack capability
- $S_l$ = survival capability
- $S_c$ = communication capability
- $\omega_1, \omega_2, \omega_3$ = weights determined by triangular fuzzy number method
Detection capability:
$$ S_d = \ln(1 + Q_d), \quad Q_d = \begin{cases}
\displaystyle \frac{R_d^2}{4} \cdot \frac{\vartheta_R}{2\pi} \cdot P_d \cdot K_d \cdot \frac{m_{0.05d}}{r}, & 0 \le r \le R_d \\
0, & r > R_d
\end{cases} $$
Attack capability:
$$ S_a = \ln(1 + Q_a), \quad Q_a = \begin{cases}
0, & r < r_{\min} \\
\displaystyle K_D \cdot \frac{r_{\max} P_h \xi_m}{2\pi} \cdot \frac{n_{\max}}{35} \cdot \frac{\omega_{\max}}{20r}, & r_{\min} \le r \le r_{\max} \\
0, & r > r_{\max}
\end{cases} $$
Survival capability:
$$ S_l = \ln(1 + Q_l), \quad Q_l = \left( \frac{10}{W} \cdot \frac{15}{L} \cdot \frac{5}{A_{RCS}} \cdot (1 – m_{des}) \cdot \sum_{i=1}^N \frac{r_i}{R_{bat}} \right)^{0.5} $$
Communication capability:
$$ S_c = \begin{cases}
\ln\left(1 + \eta_{dl} \sum_{i=1}^N \frac{R_{dl}}{r_i}\right)^{0.5}, & 0 \le r \le R_{dl} \\
0, & r > R_{dl}
\end{cases} $$
The overall friendly situation field is:
$$ S^+ = \sum_{i=1}^N S_i $$
and the average situation per drone with exchange ratio $k_s = 1 / \sum P_{cost}(i)$ is:
$$ \bar{S}^+ = k_s S^+ $$
The enemy situation field $S^-$ is defined analogously for $X$ adversary units. The formation fitness function is:
$$ J = \sum_{S^- \in \Omega} \frac{\text{Area}(S^+ – S^- > 0)}{\text{Area}(Batt)} $$
where $\Omega$ is the probability distribution area of enemy deployments.
2.2 Communication Topology Modeling
The communication network must contain a spanning tree rooted at the virtual leader (Assumption 1). We define the communication cost for establishing a link between fixed-wing drones $i$ and $j$ as:
$$ Com_{ij} = \frac{\omega_{2,c}Com2_{ij} + \omega_{3,c}Com3_{ij} + \omega_{4,c}Com4_{ij}}{\omega_{1,c}Com1_{ij}} $$
where:
- $Com1_{ij} = 1 – r_{ij}/R_{dl}$ (signal strength)
- $Com2_{ij} = e^{(r_{ij} – \bar{R}_{dl})^2 / R_{dl}^2}$ (link cost)
- $Com3_{ij} = \ln(1 + W_t)$, $W_t = (B\,r_{ij})/(B^* \bar{R}_{dl}) \cdot W^*$ (power consumption)
- $Com4_{ij} = f_r \cdot (W_t/W_m) \cdot (1 – r_{ij}/R_{dl})$ (detection probability)
- $\omega_{1,c},\dots,\omega_{4,c}$ = weights obtained via triangular fuzzy number method
3. Optimization Algorithms
3.1 Formation Configuration Optimization using PSO
We employ a hierarchical PSO approach (Algorithm 1) to optimize the formation of fixed-wing drones:
Algorithm 1 Hierarchical formation parameter optimization
- For the top layer, evaluate all eight basic formations; use PSO to find optimal parameters maximizing $J$ for each; select the formation with highest $J$.
- Take the positions of selected formation as centers for lower-level nodes; recursively apply PSO to choose sub‑formations and parameters.
- Continue until the total number of fixed-wing drones equals $N$.
- Combine results from all layers to obtain the global formation.
We use a swarm of 20 particles and 30 iterations per layer. This drastically reduces computation compared to a single giant optimization (convergence in ~1.9 s versus ~6.3 s for the global method).
3.2 Communication Topology Optimization using Q‑Learning
To minimize communication cost while ensuring connectivity to the virtual leader, we design a Q‑learning based algorithm (Algorithm 2).
Algorithm 2 Q‑learning network topology optimization
- Initialize Q‑matrix: $Q_{ij}=0$ if $r_{ij}\le R_{dl}$, else $Q_{ij}=-1$.
- For each fixed-wing drone $i$, set initial state $s_i$.
- Reward function:
$$ f_R(s,a)=\begin{cases}
F_{\max}, & (v_0,v_j)\\
\dfrac{F_{\max}}{Com_{ij}}, & (v_i,v_j), i\neq0
\end{cases} $$ - Actions: neighboring drones; choose action with highest Q; update:
$$ Q(s_{t+1},a_{t+1}) = (1-\alpha)Q(s_t,a_t) + \alpha[f_R(s_t,a_t) + \gamma \max_{a’} Q'(s_{t+1},a_{t+1})] $$ - Repeat until Q‑network converges.
- Select the node farthest from the virtual leader; trace the path with maximum Q to form the main communication trunk.
- If any fixed-wing drone is not on the trunk, connect it via shortest path.
4. Simulation Results
4.1 Simulation Setup
We simulate a strike mission with 8 fixed-wing drones (performance parameters in Table 2) in a 30 km × 30 km battlefield, with 5 enemy interceptors distributed probabilistically in a 3 km × 2 km zone. The virtual leader drone starts at (−1200 m, 12 250 m, −500 m) with speed 250 m/s, heading toward a moving rendezvous point (50 m/s in x and z). The leader uses a robust adaptive guidance law to satisfy terminal angle constraints (0° in azimuth, 45° in elevation).
| Parameter | Value |
|---|---|
| Guidance correction $K_D$ | 2 |
| Single‑shot hit probability $P_h$ | 0.85 |
| Attack angle $\xi_m$ | 60° |
| Max overload $n_{\max}$ | 6 g |
| Max angular rate $\omega_{\max}$ | 35 °/s |
| Detection range $R_d$ | 19 km |
| Search angle $\vartheta_R$ | 65° |
| Detection probability $P_d$ | 0.95 |
| Simultaneous tracks $m_d$ | 3 |
| Wingspan $W$ | 0.8 m |
| Length $L$ | 5 m |
| RCS $A_{RCS}$ | 0.3 m² |
| Susceptibility $m_{des}$ | 3 |
| Max environment distance $R_{bat}$ | 30 km |
| Data link reliability $\eta_{dl}$ | 0.98 |
| Max communication range $R_{dl}$ | 7 km |
4.2 Formation Optimization Results
At time t = 5.35 s (when the virtual leader is at the battlefield origin), we perform hierarchical formation optimization. Table 3 summarizes the best fitness values for all eight basic formations after PSO (20 particles, 30 iterations). Formation 100 (triangle) achieves the highest fitness of 0.796 with parameter 2.5 km.
| Formation code | Optimal parameter (km) | Fitness $J$ | Iterations to converge |
|---|---|---|---|
| 000 | 2.9 | 0.651 | 20 |
| 001 | 2.1 | 0.623 | 14 |
| 010 | 2.1 | 0.714 | 14 |
| 011 | 2.1 | 0.684 | 17 |
| 100 | 2.5 | 0.796 | 13 |
| 101 | 3.4 | 0.718 | 20 |
| 110 | 2.1 | 0.705 | 13 |
| 111 | 2.1 | 0.707 | 14 |
After selecting triangle as the top layer, we recursively optimize lower layers. The final configuration (Table 4) uses four subgroups: one line (000) with parameter 10 km, one staggered pair (001) with 1.7 km, one diagonal pair (011) with 17 km, and one parallel pair (010) with 12 km.
| Layer 1 (triangle) | Parameter (km) | Layer 2 | Parameter | Layer 3 | Parameter |
|---|---|---|---|---|---|
| 100 | 2.5 | 000 (vertex) | 10 km | 001 (sub) | 1.7 km |
| 011 (vertex) | 17 km | 000 (sub) | 1.1 km | ||
| 010 (vertex) | 12 km | — | — |
The hierarchical method converges in 1.935 s, whereas a global PSO (same problem) takes 6.325 s while producing essentially the same formation, confirming both accuracy and speed advantage.
4.3 Communication Topology Results
With the optimized formation, we apply Q‑learning to determine the communication links. The network initially has 17 possible edges (Figure 4 in original, here described in text). After training (70 episodes to converge), each fixed-wing drone selects the neighbor that maximizes the total communication cost-aware reward. Table 5 shows the steady‑state Q‑values for drone 4 with its three potential neighbors; the highest Q (0.67) for drone 3 indicates it becomes the parent.
| Neighbor drone | Q‑value |
|---|---|
| 3 | 0.67 |
| 6 | 0.58 |
| 8 | 0.32 |
Following the algorithm, we construct the main trunk: drone 2 → 6 → 3 → 9 (virtual leader), drone 3 already connects to drone 9; drone 5 connects to drone 6; etc. The final topology satisfies the spanning tree condition with the virtual leader as root. The total communication cost, measured by Eq. (15), is minimized.
We compare our Q‑learning method against two baselines: random routing and nearest‑neighbor routing. Figure 5 (described) shows the performance for formation sizes of 5, 8, 12, and 16 fixed-wing drones under different numbers of allowed edges. Q‑learning consistently outperforms the others, especially when more routing options exist (higher connectivity).
| Routing strategy | Normalized communication cost (lower is better) |
|---|---|
| Random | 0.87 |
| Nearest neighbor | 0.74 |
| Q‑learning (proposed) | 0.52 |
The Q‑learning approach effectively balances signal strength, link cost, power consumption, and detection probability, yielding a robust and stealthy communication graph for the fixed-wing drones.
5. Conclusion
We have presented a comprehensive framework for jointly optimizing the formation configuration and communication topology of fixed-wing drones under adversarial and mission‑critical constraints. The hierarchical situation‑field‑based formation optimization, solved by layered PSO, provides near‑optimal spatial arrangements with significantly reduced computation time compared to monolithic approaches. The Q‑learning‑based communication topology generation ensures a spanning tree rooted at the virtual leader while minimizing the combined communication cost that includes detection risk. Simulation results with eight fixed-wing drones verify the effectiveness and efficiency of the proposed methods. Future work could extend the approach to heterogeneous swarms and dynamic adversarial environments.