Drone technology has undergone transformative advancements in recent years, enabling the deployment of large-scale drone swarms for complex missions such as cooperative reconnaissance, target strike, and command relay. However, these swarms are frequently subjected to disturbances including severe weather conditions, electromagnetic interference, and hostile air defense strikes, which degrade their performance and mission completion capability. To ensure successful task execution, drone swarms must possess a high degree of resilience, defined as the ability to anticipate, withstand, adapt to, and rapidly recover from disruptive events. In this paper, we present a comprehensive modeling and resilience assessment framework for multi-task payload-driven drone swarms, addressing critical gaps in existing research regarding the coupling between communication topology and task coordination, as well as the quantitative characterization of collapse intervals during attack scenarios.
Our work makes three primary contributions. First, we develop a hierarchical communication network model driven by multi-task payloads, which captures both the communication links between drones and the collaborative relationships among different task payloads. Second, we propose quantitative performance functions tailored to three typical mission scenarios: reconnaissance, strike, and command. Third, we introduce a relay-centric recovery strategy that enhances swarm resilience under electromagnetic interference, and we formulate a resilience evaluation method that explicitly accounts for the collapse interval. Through extensive simulations, we demonstrate that the proposed recovery strategy achieves 16.5%, 29.3%, and 21.2% improvement in mean resilience for reconnaissance, strike, and command missions, respectively, compared to traditional recovery approaches.
1. Hierarchical Network Model for Drone Swarms
Modern drone swarms consist of heterogeneous unmanned aerial vehicles (UAVs) equipped with various payloads such as electro-optical sensors, synthetic aperture radars, jamming devices, or precision-guided munitions. The effective execution of cooperative tasks requires seamless communication among drones and the proper coordination of their payloads. To capture both aspects, we propose a two-layer network model comprising a communication layer and a task payload layer.
1.1 Communication Layer
The communication layer is modeled as an undirected unweighted graph \(G = (V, E)\), where the node set \(V\) represents individual drones and the edge set \(E\) denotes bidirectional communication links. The network is generated with an initial fully connected core of \(n_0\) drones. As new drones join, they connect to existing nodes based on a probability that accounts for both node degree and physical distance:
$$
P(i \rightarrow W_t) = \frac{(k_j + \epsilon) F(d_{i \rightarrow j})}{\sum_{l \in W_t} (k_l + \epsilon) F(d_{i \rightarrow l})}
$$
where \(k_j\) is the degree of drone \(j\), \(\epsilon\) is a small positive bias to avoid isolation, and \(F(d)\) is the distance-dependent connectivity function:
$$
F(d_{i \rightarrow j}) =
\begin{cases}
1, & d_{i \rightarrow j} < r_c \\
\frac{r_c – d_{i \rightarrow j}}{r_c (1-\eta)}, & r_c \le d_{i \rightarrow j} < \frac{r_c}{\eta} \\
0, & d_{i \rightarrow j} \ge \frac{r_c}{\eta}
\end{cases}
$$
Here, \(r_c\) is the communication range and \(\eta\) is a distance decay parameter. To prevent excessive degree concentration, we impose a maximum degree constraint \(k_{\max}\). Each drone adaptively adjusts its local connections using the following criterion:
$$
\chi_i = \frac{\sum_{j \in \Gamma_i} k_j}{\sum_{j} k_j}, \quad \text{if } \chi_i < \theta
$$
where \(\Gamma_i\) is the set of neighbors of drone \(i\) and \(\theta\) is a threshold. If the condition is met, the drone initiates a reconnection process by removing one of its links and establishing a new one according to the probability function above, thereby maintaining network efficiency and robustness.
1.2 Task Payload Layer
Each drone in the communication layer is mapped to a node in the task payload layer, representing its carried payload. Edges in this layer denote cooperative task relationships. If two drones collaborate on \(q\) distinct tasks (e.g., a reconnaissance drone sharing target data with a strike drone), there exist \(q\) parallel edges between them. Thus, the task payload layer is a multi-edge, undirected network that captures the multi-tasking nature of modern drone swarms.
1.3 Interlayer Coupling
The coupling between the communication and task payload layers is one-to-one: every drone node in the communication layer has a corresponding payload node in the task layer. When two drones are directly or indirectly connected in the communication layer, their corresponding payload nodes are also connected in the task layer. This architecture enables the swarm to simultaneously support multiple mission threads while maintaining a unified communication backbone.
2. Performance Quantification for Multi-Mission Scenarios
To evaluate swarm effectiveness under different mission contexts, we define three composite performance measures: reconnaissance performance, strike performance, and command performance. Each measure integrates relevant network metrics and task-specific factors.
2.1 Performance Factors
Three fundamental factors are introduced:
| Factor | Symbol | Definition | Range |
|---|---|---|---|
| Area Factor | \(R_S(t)\) | Ratio of current coverage area to initial coverage area | [0,1] |
| Focus Factor | \(R_A(t)\) | Ratio of overlapping coverage area to total coverage area | [0,1] |
| Time Factor | \(R_T\) | Ratio of payload operational duration to total mission time | [0,1] |
The area factor \(R_S(t)\) measures the swarm’s spatial coverage efficiency. A single drone covers a circle of radius \(r_c\), and the union of all active drones’ coverage forms the total area. The focus factor \(R_A(t)\) quantifies the degree of overlap: high overlap indicates concentrated effort (e.g., for precision strikes), while low overlap indicates wide-area surveillance. The time factor \(R_T\) accounts for the duty cycle of payloads; a payload that operates for \(L\) seconds out of a total mission time \(T\) yields \(R_T = L/T\).
2.2 Reconnaissance Performance
Reconnaissance missions aim to gather maximum information from a target area. The performance function combines area and time factors, weighted by the network’s connectivity metric \(L_S(t)\):
$$
P_C(t) = \frac{R_S^{(C)}(t) \cdot R_T^{(C)} \cdot L_S(t)}{L_S(t)}
$$
Here, the superscript \((C)\) denotes the subset of drones dedicated to reconnaissance. The connectivity metric \(L_S(t)\) is the size of the largest connected component normalized by total swarm size. A well-connected swarm ensures that detected information is disseminated effectively.
2.3 Strike Performance
Strike missions require coordinated attacks on high-value targets, demanding both wide coverage and high overlap. The strike performance is defined as:
$$
P_D(t) = \frac{R_S^{(D)}(t) + R_A^{(D)}(t)}{2} \cdot X(t)
$$
where \(X(t)\) is the network efficiency:
$$
X(t) = \frac{1}{N(N-1)} \sum_{i \neq j} \frac{1}{d_{ij}(t)}
$$
Network efficiency measures the reciprocal of shortest path distances; higher efficiency means faster coordination among strike drones.
2.4 Command Performance
Command and control missions rely on timely message delivery. The performance function accounts for the number of recipients, message decay over time, and payload duty cycle:
$$
P_Z(t) = R_T^{(Z)} \cdot \frac{\sum_{i} \nu_i(t) M_i(t) \cdot \delta_{d,i}}{\sum_{i} M_i(t)}
$$
Here, \(\nu_i(t)\) is the number of drones that receive message \(M_i(t)\) by time \(t\), and \(\delta_{d,i}\) is an exponential decay factor capturing the diminishing value of delayed information.
3. Attack Model and Resilience Evaluation
3.1 Integrated Attack Model
We model four types of attacks: random electromagnetic interference, hub drone attacks, relay drone attacks, and local drone attacks. The probability that drone \(i\) is targeted in stage \(l\) is:
$$
w_{i,l} = \frac{ \psi D_{i,l} + (1-\psi) \tau }{ \sum [\psi D_{i,l} + (1-\psi) \tau ] }
$$
where \(\psi \in \{0,1,2,3\}\) selects the topology attribute \(D_{i,l}\) (degree, betweenness, clustering coefficient, or constant), and \(\tau\) is a singularity avoidance constant. The four attack modes correspond to \(\psi=0\) (random), \(\psi=1\) (hub with highest degree), \(\psi=2\) (relay with highest betweenness centrality), and \(\psi=3\) (local with highest clustering coefficient).
3.2 Failure Propagation and Recovery
When a drone fails, its communication links are removed, and its corresponding payload node becomes inactive. Isolated drones (no communication links) are considered failed as well. The failure cascades through the coupled layers, potentially destroying task coordination edges. Recovery begins after a predefined delay. We propose a relay-priority recovery strategy that calculates the betweenness centrality of each surviving drone:
$$
I_{i,k} = \frac{\sum_{s \neq t \in V_k} \sigma_{st}(i)}{\sum_{s \neq t \in V_k} \sigma_{st}}
$$
Drones with higher \(I_{i,k}\) are restored first—they reestablish communication links within their range, rapidly rebuilding the backbone of the network. This is in contrast to traditional degree-priority recovery that restores high-degree hubs first.
3.3 Resilience Metric
We adopt the linear resilience formulation from the literature, decomposing resilience into degradation and recovery phases:
$$
R = \alpha \cdot \delta_d \sigma_d \rho_d + \beta \cdot \delta_r \sigma_r \rho_r
$$
where \(\alpha + \beta = 1\), \(\alpha=0.4\), \(\beta=0.6\). The six components are defined as:
| Phase | Process Factor | State Factor | Time Factor |
|---|---|---|---|
| Degradation | \(\delta_d = \frac{\int_{t_d}^{t_r} y(t) dt}{(t_r – t_d) y_0}\) | \(\sigma_d = \frac{y_{\min}}{y_0}\) | \(\rho_d = \frac{\Delta (t_r – t_d)}{B}\) |
| Recovery | \(\delta_r = \frac{\int_{t_r}^{t_s} y(t) dt}{(t_s – t_r) y_0}\) | \(\sigma_r = \frac{y_s}{y_0}\) | \(\rho_r = \frac{\Delta (t_s – t_r)}{B}\) |
Here, \(y(t)\) is the mission performance function (one of \(P_C, P_D, P_Z\)), \(y_0\) is the initial steady-state performance, \(y_{\min}\) is the minimum during degradation, and \(y_s\) is the final stabilized performance after recovery. The time constant \(B\) is the reference time horizon, and \(\Delta=0.8\) controls the time penalty. This metric quantitatively captures both the depth and duration of performance loss, as well as the speed and extent of recovery.
4. Simulation Results and Analysis
4.1 Experimental Setup
We simulate a swarm of 100 drones with \(r_c=50\), \(\eta=0.6\), \(\epsilon=0.4\), \(\Delta=0.8\), \(\alpha=0.4\), \(\beta=0.6\). The network is built using the probabilistic connectivity model, yielding a degree distribution that closely follows an exponential decay \(y = 0.43 e^{-0.36x}\), characteristic of exponential random networks. Such networks are robust to random failures but vulnerable to targeted attacks.
4.2 Performance Sensitivity
We compare the sensitivity of our proposed performance functions against simple metrics like coverage area and network efficiency. Under random electromagnetic interference, the coverage area metric remains nearly flat until 30% of drones are disabled, whereas our reconnaissance and strike performance functions decline monotonically from the very first attack. This confirms that the composite functions capture mission-critical dependencies more accurately.
4.3 Resilience Under Various Attacks
For each mission type and each attack mode, we evaluate the performance trajectory over 100 time steps. Attacks begin at t=10 and recovery starts at t=50. The following table summarizes the mean resilience improvement of our relay-priority recovery over the traditional degree-priority recovery (as referenced in the literature) for attack proportions of 10%, 30%, and 50%.
| Mission | Attack Type | Resilience Improvement (%) |
|---|---|---|
| Reconnaissance | Random EM | 9.2 |
| Hub | 42.9 | |
| Relay | 7.9 | |
| Local | 57.0 | |
| Strike | Random EM | 24.3 |
| Hub | 16.9 | |
| Relay | 24.7 | |
| Local | 18.9 | |
| Command | Random EM | 14.4 |
| Hub | 21.4 | |
| Relay | 12.8 | |
| Local | 17.5 |
The results show that the relay-priority strategy yields significant improvements across all scenarios. Notably, reconnaissance missions benefit most from relay restoration because reconnaissance networks rely on high-betweenness nodes to bridge spatially separated sub-clusters. In contrast, command missions, which rely on a few hub nodes for central coordination, show moderate improvements. The strike mission gains are especially pronounced under random EM interference, where the relay strategy helps re-establish the overlapping coverage critical for coordinated attacks.
4.4 Collapse Interval Analysis
When attack proportions exceed 50%, the swarm enters a collapse interval where performance drops to near zero and recovery becomes marginal. We analyze the resilience values under 60% to 100% attack proportions for random electromagnetic interference. The following table shows that even with the best recovery strategy, resilience degrades rapidly beyond 70% attack:
| Mission | Attack % | Resilience (Random Recovery) | Resilience (Relay-Priority Recovery) |
|---|---|---|---|
| Reconnaissance | 60 | 0.0227 | 0.0445 |
| 70 | 0.0222 | 0.0209 | |
| 80 | 0.0073 | 0.0100 | |
| 90 | 0.0020 | 0.0040 | |
| 100 | 0.0000 | 0.0000 | |
| Strike | 60 | 0.0685 | 0.0689 |
| 70 | 0.0551 | 0.0624 | |
| 80 | 0.0343 | 0.0412 | |
| 90 | 0.0060 | 0.0247 | |
| 100 | 0.0000 | 0.0000 | |
| Command | 60 | 0.0859 | 0.0944 |
| 70 | 0.0477 | 0.0450 | |
| 80 | 0.0170 | 0.0170 | |
| 90 | 0.0025 | 0.0039 | |
| 100 | 0.0000 | 0.0000 |
The collapse interval reveals that when more than 70% of drones are disabled, the network fragments into isolated clusters with minimal cross-connectivity. In such regimes, even sophisticated recovery strategies cannot restore meaningful functionality because the number of surviving nodes is too small to form a connected backbone. This underscores the importance of proactive resilience measures (e.g., redundancy and diversity) rather than relying solely on reactive recovery.
5. Conclusion
In this work, we have presented a comprehensive framework for modeling and assessing the resilience of multi-task payload-driven drone swarms. By constructing a two-layer network that couples communication topology with task payload collaboration, we capture the essential dynamics of modern drone technology. Our proposed performance functions—reconnaissance, strike, and command—integrate area coverage, focus, timeliness, and network efficiency, providing a nuanced evaluation of mission effectiveness under stress. The relay-priority recovery strategy, which prioritizes the restoration of high-betweenness relay nodes, consistently outperforms traditional degree-based recovery across all attack types and mission scenarios, achieving mean resilience improvements of 16.5% to 29.3%. Furthermore, our collapse interval analysis offers quantitative insights into the boundaries of recoverability, highlighting the critical need for preemptive design to avoid catastrophic performance loss. These findings advance the understanding of resilience in drone swarms and provide actionable guidelines for engineers and operators seeking to enhance the robustness of autonomous systems in contested environments. Future work will extend the model to heterogeneous swarms with time-varying communication ranges and incorporate machine learning algorithms for adaptive recovery scheduling.