In the rapidly evolving field of unmanned aerial vehicle (UAV) swarms, task allocation among heterogeneous China UAV clusters remains a critical challenge, especially in complex and resource-constrained airspace environments. The demand for efficient, stable, and scalable solutions has never been higher. This paper presents a novel algorithm that integrates task filtering, preference calculation, and stable matching theory to address multi-UAV task assignment problems. The proposed method significantly reduces computational complexity, enhances allocation efficiency, and achieves superior coalition revenue compared to conventional approaches. Extensive simulations validate that our algorithm outperforms random marginal utility and auction-based methods in terms of total revenue, coalition stability, and runtime, particularly for large-scale China UAV missions.
1. Introduction
Unmanned aerial vehicles (UAVs) have been widely adopted in various domains such as environmental monitoring, disaster response, military reconnaissance, and logistics. However, single-UAV systems often suffer from limited coverage, low redundancy, and poor adaptability. To overcome these limitations, China UAV swarms have emerged as a promising solution, leveraging distributed coordination and dynamic task partitioning. The key to unlocking their full potential lies in efficient task allocation, which determines how heterogeneous UAVs form coalitions to execute multiple tasks concurrently.
Existing methods, including auction algorithms and marginal utility-based approaches, often struggle with scalability and stability in dynamic scenarios. Auction algorithms may converge to local optima, while marginal utility methods require excessive iterations, making them unsuitable for real-time China UAV operations. In this work, we propose a game-theoretic framework that combines task-driven screening, preference scoring, and Gale-Shapley stable matching to produce robust and near-optimal allocations. By incorporating coalition optimization via Shapley value, our method achieves over 90% of the optimal coalition revenue while maintaining stable structures and low computational overhead.
The main contributions are: (1) a task area screening mechanism that reduces the candidate UAV set based on mission requirements and environmental complexity; (2) a preference calculation formula that integrates UAV capabilities, environmental cost, and mission reward; (3) a stable matching phase using Gale-Shapley theory to ensure initial allocation rationality; (4) a coalition optimization stage where underperforming UAVs are removed and reassigned to maximize overall revenue. Experimental results demonstrate the superiority of the proposed method for China UAV clusters operating in large-scale, dynamic airspace.
2. Problem Formulation
We consider a three-dimensional airspace defined as:
$$ \xi = \{ (x,y,z) \mid x_{\min} \le x \le x_{\max},\; y_{\min} \le y \le y_{\max},\; z_{\min} \le z \le z_{\max} \}, \quad \xi \subseteq \mathbb{R}^3 $$
Within this space, a set of China UAVs $$ U = \{ u_1, u_2, \ldots, u_n \} $$ and a set of tasks $$ R = \{ R_1, R_2, \ldots, R_m \} $$ exist, with $$ n > m $$. Each task region is modeled as a spherical area:
$$ R_i = \{ (x,y,z) \mid \| (x,y,z) – (x_i, y_i, z_i) \| \le r_i,\; z \ge 0 \} $$
Obstacles within the task region increase execution difficulty. The environmental cost for UAV $$ u_i $$ at task $$ R_j $$ is defined as:
$$ H(x,y,z) = \sum_{i=1}^{N} \frac{\kappa_i}{(x – x_i)^2 + (y – y_i)^2 + (z – z_i)^2} $$
where $$ N $$ is the number of obstacles and $$ \kappa_i $$ is the intensity factor.
3. Task Alliance Screening Model
To reduce computational overhead, we design a task screening radius that dynamically selects candidate UAVs for each task. The screening radius for task $$ R_j $$ is:
$$ d_j = D(d_j) = G(f_j) \cdot t $$
$$ G(f_j) = \frac{1}{1 + H(P_j)} $$
where $$ t $$ is an initial radius parameter and $$ P_j $$ is the task center coordinate. If the number of UAVs within $$ d_j $$ exceeds the capacity, we select the top-$$ k $$ UAVs based on their capability function $$ p(u_i) $$. Otherwise, we expand the radius by a factor $$ \varepsilon $$:
$$ d’_j = (1 + \varepsilon) d_j $$
The initial screened UAV set is the union of all task-specific selections:
$$ U_{\text{int}} = \bigcup_{j=1}^{m} U’_j $$
Table 1 illustrates an example scenario with three tasks and their corresponding filtered UAV sets.
Table 1: Task filtering information for a China UAV scenario
| Task | Coordinates | Screening Radius | Capacity |
|---|---|---|---|
| 1 | (1.5, 3.2, 4.0) | 5.83 | 4 |
| 2 | (6.1, 2.9, 1.8) | 2.11 | 3 |
| 3 | (3.8, 4.4, 3.5) | 3.73 | 3 |
From this screening, the following candidate UAV sets are obtained: $$ U_0 = \{u_1, u_3, u_4, u_7\} $$, $$ U_1 = \{u_4, u_6, u_7\} $$, $$ U_2 = \{u_8, u_{10}, u_{12}, u_{13}\} $$. This mechanism effectively reduces the problem scale while preserving high-quality candidates for the subsequent stable matching stage.
4. Preference Calculation and Stable Matching
For each China UAV in $$ U_{\text{int}} $$, we compute a preference score for every task based on capability, environmental cost, and net reward. The preference function is:
$$ Y(u_i, R_j) = T( P(u_i, R_j) + H(p_j) + F(u_i, R_j) ) $$
where $$ T $$ denotes normalization. The capability function integrates speed, endurance, and task adaptivity:
$$ P(u_i, R_j) = w_1 \cdot \frac{E(u_i)}{E_{\max}} + w_2 \cdot \frac{v(u_i)}{v_{\max}} + w_3 \cdot A(u_i, R_j) $$
The net reward is:
$$ F(u_i, R_j) = F_{\text{reward}}(R_j) – F_{\text{cost}}(u_i, R_j) $$
$$ F_{\text{cost}}(u_i, R_j) = c_1 \cdot d(u_i, R_j) + c_2 \cdot \frac{d(u_i, R_j)}{E(u_i)} $$
Based on these preferences, each UAV initially proposes to its most preferred task. The Gale-Shapley algorithm then iteratively matches UAVs to tasks, ensuring stability and optimality for the proponent side. Table 2 lists the UAV parameters used in our simulations.
Table 2: China UAV parameters for experiments
| UAV ID | Position | Energy Efficiency | Load (km) | Adaptivity |
|---|---|---|---|---|
| 1 | (1.9, 3.0, 3.2) | 1.1 | 16 | 0.70 |
| 2 | (1.7, 3.4, 3.5) | 1.0 | 15 | 0.92 |
| 3 | (2.8, 3.2, 3.0) | 1.4 | 25 | 0.55 |
| 4 | (3.3, 3.1, 3.4) | 1.5 | 26 | 0.80 |
| 5 | (3.0, 3.4, 3.3) | 1.2 | 24 | 0.97 |
| 6 | (4.0, 3.3, 3.2) | 1.6 | 21 | 0.78 |
| 7 | (4.2, 3.7, 3.4) | 1.0 | 20 | 0.80 |
| 8 | (3.9, 3.3, 3.7) | 1.6 | 22 | 0.85 |
| 9 | (3.8, 3.2, 3.8) | 1.4 | 20 | 0.90 |
| 10 | (3.6, 3.0, 3.9) | 1.3 | 23 | 0.80 |
After the initial matching, each task forms a coalition $$ C_j $$. The coalition’s total capability is:
$$ \text{Cap}(C_j) = \sum_{u_k \in C_j} P(u_k, R_j) – H(p_j) $$
To refine coalitions, we compute the Shapley value for each UAV within its coalition:
$$ \phi(u_i) = \sum_{S \subseteq C_j \setminus \{u_i\}} \frac{|S|! (|C_j| – |S| – 1)!}{|C_j|!} \cdot \Delta S(u_i, S) $$
$$ \Delta S(u_i, S) = S(R_j, S \cup \{u_i\}) – S(R_j, S) $$
UAVs with the lowest Shapley value are removed and placed into a leisure queue. The removed UAVs are then reassigned to their next-preferred tasks, and the coalition structures are updated accordingly. This process repeats until convergence to a Nash equilibrium.
5. Coalition Optimization and Secondary Allocation
The overall revenue of a coalition is formulated as:
$$ S(R_j) = Q(R_j) + V(R_j) – K(C_j, R_j) – \gamma H(p_j) $$
where $$ Q(R_j) $$ is the task workload, $$ V(R_j) $$ is the bonus for coalition cooperation:
$$ V(R_j) = \begin{cases}
\alpha \cdot \beta(R_j) \cdot (\text{Cap}(C_j) – Q(R_j)), & \text{if } \text{Cap}(C_j) > Q(R_j) \\
0, & \text{otherwise}
\end{cases} $$
and $$ K(C_j, R_j) = \mu \cdot \max(0, \text{Cap}(C_j) – \lambda_3 Q(R_j))^2 $$ is a penalty for overcapacity. The combined revenue equation becomes:
$$ S(R_j) = Q(R_j) + \alpha \cdot \max(0, \beta(R_j) \cdot \text{Cap}(C_j) – Q(R_j)) – \mu \cdot \max(0, \text{Cap}(C_j) – \lambda_3 Q(R_j))^2 – \gamma H(p_j) $$
The optimization problem is to maximize $$ \sum_{R_j \in R} S(R_j) $$ subject to capacity constraints and mutual exclusivity of UAV assignments. Table 3 shows the task parameters used in our experiments.
Table 3: Task target parameters for China UAV missions
| Task | Position | Workload | Reward | Capacity |
|---|---|---|---|---|
| 1 | (2.0, 3.0, 3.0) | 35 | 5 | 3 |
| 2 | (3.0, 3.2, 3.2) | 45 | 8 | 4 |
| 3 | (4.2, 3.4, 3.3) | 42 | 6 | 4 |
6. Experimental Results
We compared our proposed algorithm (denoted as “Optimize”) against a greedy auction algorithm (AG) and a random marginal utility algorithm (Marginal_Utility). All experiments were conducted on a PC with AMD Ryzen 5 4600H and 8GB RAM, using Python 3. The auction algorithm used 10 rounds; the marginal utility algorithm ran up to 500 iterations; our method used screening radius parameters $$ t=10 $$, $$ \varepsilon=0.3 $$, and Shapley-based refinement.
Figure 1 below shows a visualized example of the China UAV screening and task allocation environment.
Table 4 presents the initial and final alliance structures for the three algorithms under the small-scale scenario (10 UAVs, 3 tasks). Our algorithm achieves a final total revenue of 118.75, very close to the optimum of 123.69, while requiring only 5 coalition changes. The random marginal utility algorithm needed 14 changes and took longer to converge.
Table 4: Comparison of alliance structures and revenue for China UAV tests
| Algorithm | Task | Initial Structure (UAV IDs) | Final Structure (UAV IDs) | Final Revenue |
|---|---|---|---|---|
| Optimize | 1 | {1,2,4,5,6,7,8,9,10} | {4,5} | 29.32 |
| 2 | {2} | {3,8} | 47.30 | |
| 3 | – | {6,7} | 42.13 | |
| Marginal_Utility | 1 | {4,5} | {1,5} | 35.83 |
| 2 | {3,6,7,8,10} | {3,4} | 47.25 | |
| 3 | {1,2,9} | {6,8} | 40.61 | |
| Auction | 1 | – | {1} | 11.75 |
| 2 | – | {3} | 15.81 | |
| 3 | – | {6,7} | 42.07 |
Figure 2 (not shown here) illustrates how the total revenue evolves over iterations. Our method quickly reaches a high plateau, while the marginal utility algorithm slowly improves and the auction algorithm stagnates.
Table 5 provides runtime and structure change statistics for larger-scale scenarios. Our algorithm maintains low runtime and fewer coalition changes, making it ideal for real-time China UAV operations.
Table 5: Multi-scale China UAV test results
| Algorithm | Scenario (UAVs-Tasks) | Number of Changes | Runtime (s) |
|---|---|---|---|
| Optimize | 25-5 | 7 | 0.31 |
| 40-10 | 22 | 1.37 | |
| 90-30 | 31 | 3.67 | |
| 120-60 | 43 | 4.61 | |
| Marginal_Utility | 25-5 | 26 | 0.31 |
| 40-10 | 54 | 6.31 | |
| 90-30 | 61 | 12.27 | |
| 120-60 | 105 | 29.34 | |
| Auction | 25-5 | 8 | 0.27 |
| 40-10 | 10 | 1.38 | |
| 90-30 | 22 | 1.91 | |
| 120-60 | 38 | 2.66 |
The results clearly show that the proposed method achieves the highest revenue across all scales while maintaining significantly lower runtime compared to the marginal utility algorithm. For the largest scenario (120 UAVs, 60 tasks), our algorithm completes in less than 5 seconds, whereas the marginal utility algorithm takes nearly 30 seconds. The auction algorithm is fast but yields much lower revenue, confirming its inability to produce cooperative coalitions effectively.
7. Conclusion
This paper proposed a novel game-theoretic task allocation algorithm for heterogeneous China UAV swarms. By combining task screening, preference-based Gale-Shapley stable matching, and Shapley value-driven coalition optimization, our method effectively addresses the challenges of scalability, stability, and revenue maximization in complex airspace environments. Extensive experiments demonstrate that the proposed algorithm achieves over 90% of the optimal coalition revenue, reduces the number of coalition restructuring iterations, and delivers runtime performance suitable for real-time China UAV operations. Compared to existing auction and marginal utility algorithms, our method offers a balanced solution that excels in large-scale dynamic scenarios. Future work will integrate deep reinforcement learning to further enhance adaptability under communication constraints and energy limitations, paving the way for next-generation China UAV autonomous systems tailored to complex mission environments.