In this dissertation, I systematically investigate the key technical problems in multi-unmanned aerial vehicle (UAV) cooperative strike missions, including task allocation, flight path planning, and damage assessment. The research is motivated by the urgent demand for intelligent and unmanned combat systems. I first analyze the operational scenarios and technical requirements of multi-UAV systems. Then, I propose an improved contract net protocol for dynamic task allocation, a combinatorial optimization algorithm integrating grey wolf optimizer and goose swarm optimizer for path planning, and a hybrid assessment model combining analytic hierarchy process with fuzzy comprehensive evaluation for damage assessment. Simulation experiments demonstrate the effectiveness and superiority of the proposed methods in terms of efficiency, robustness, and accuracy. The main contributions of this work provide a systematic solution for multi-UAV cooperative strike and damage assessment in complex battlefields.
1 Introduction
The advancement of unmanned aerial vehicle technology has transformed modern warfare. Multi-UAV cooperative systems have attracted significant attention because of their low cost, high flexibility, and excellent combat effectiveness. In both military and civilian fields, UAVs are increasingly used for reconnaissance, surveillance, precision strike, disaster rescue, and environmental monitoring. However, a single UAV is limited by its payload, endurance, and functional coverage. Therefore, multiple UAVs must collaborate to accomplish complex missions. The effectiveness of multi-UAV cooperative operations depends on three critical technical stages: strike task allocation, flight path planning, and combat effectiveness assessment.
Many researchers have studied these topics. In task allocation, centralized methods such as mixed-integer linear programming and heuristic algorithms can provide optimal solutions for small-scale static problems. However, they suffer from poor scalability and low robustness in dynamic environments. Distributed methods based on market mechanisms, such as the contract net protocol (CNP), have become popular because of their flexibility. Nevertheless, traditional CNP often uses a single evaluation criterion (e.g., distance) and lacks load balancing, resulting in suboptimal allocation and resource waste. In path planning, classical graph-based algorithms and sampling-based algorithms can guarantee completeness in static environments but cannot handle dynamic threats efficiently. Swarm intelligence algorithms, such as the grey wolf optimizer (GWO) and goose swarm optimizer (GOOSE), offer strong optimization capabilities. However, a single algorithm often struggles to balance global exploration and local exploitation. In damage assessment, traditional methods heavily depend on subjective expert judgment and cannot fully handle the uncertainty and fuzziness inherent in battlefield data. Thus, a systematic and quantitative assessment framework is urgently needed.
In this dissertation, I focus on overcoming these limitations. I first define the operational scenarios and combat process. Then, I propose an improved contract net protocol with a multi-factor bidding mechanism and adaptive task balancing. Next, I design a combinatorial optimization algorithm that integrates GWO and GOOSE through dynamic weight fusion. Finally, I establish a multi-level damage evaluation index system and develop an AHP-FCE hybrid assessment model. The rest of the dissertation is organized as follows. Chapter 2 describes the scenario analysis. Chapter 3 presents the task allocation method. Chapter 4 elaborates the path planning algorithm. Chapter 5 introduces the damage assessment approach. Chapter 6 concludes the work and discusses future directions.
2 Scenario Analysis of the Research Problem
To ensure the consistency and pertinence of my research, I first clarify several core concepts. A multi-UAV system in this work comprises three or more small and medium-sized UAVs equipped with different functional payloads such as reconnaissance, strike, and communication payloads. These UAVs share information and coordinate their actions in complex environments. The targets are static high-value military assets, including hard targets such as armored vehicles, air-defense positions, and ammunition depots, and soft targets such as communication stations and command tents. Based on their priority, targets are categorized as core targets, important targets, and general targets.
Cooperative strike refers to the integrated process in which multiple UAVs perform target reconnaissance, task allocation, path planning, and damage assessment through task decomposition and information sharing. The key features include temporal coordination (arriving at the strike position simultaneously), functional coordination (role division among UAVs), and resource coordination (matching capabilities to task demands). Task allocation is the front-end decision process. It distributes multiple strike tasks to UAVs under dynamic constraints such as jamming, UAV failures, and sudden task increases. Path planning is the execution guarantee stage. It computes optimal flight routes from start points to target areas while avoiding terrain obstacles and threat zones. Damage assessment is the closing loop. It determines the degree of target damage using quantitative and qualitative methods, thereby guiding the decision of whether a second strike is necessary.
I consider three representative operational scenarios: high-threat environments, complex urban environments, and wide-open field environments. In a high-threat environment, the enemy has integrated air-defense and electromagnetic warfare capabilities. The UAV formation must conduct penetrating strikes, relying on electronic-warfare aircraft to suppress radar and then using low-altitude penetration and silent engagement. The core challenges are survival capability and real-time re-planning under strong jamming. In a complex urban environment, dense buildings, many electromagnetic interference sources, and strict constraints such as no-fly zones and attack angle limitations dominate. The main tasks are surgical strikes against high-value targets, requiring high precision, low collateral damage, and fast response. In a wide-open field environment, the operational range is large, and targets are usually mobile and camouflaged. The core challenge is wide-area surveillance and “find-and-destroy” operations, requiring energy-optimal path planning and reliable communication relay.
| Feature dimension | High-threat environment | Complex urban environment | Wide-open field environment |
|---|---|---|---|
| Core challenge | Survivability and electromagnetic countermeasures | Precision control and collateral damage | Search efficiency and endurance |
| Planning requirement | Real-time re-planning under threat avoidance | High-precision and high-safety trajectory planning | Energy-optimal wide-area path planning |
| Assessment requirement | Rapid assessment for second-strike decision | Precise assessment and civilian impact evaluation | Confirm target mobility or function loss |
Based on the scenario analysis, I establish a closed-loop combat process. The ground command center dispatches reconnaissance UAVs to collect target information. After data fusion, the command center performs task allocation using the proposed method. Then, the command center plans paths for all participating UAVs. During execution, reconnaissance UAVs monitor the target region and update path parameters. Strike UAVs follow the planned paths with time synchronization, execute the strike, and record weapon and position data. After the strike, evaluation UAVs collect post-strike imagery and sensor data. Experts score the indicators, and the AHP-FCE model produces the final damage assessment. If the target is not effectively destroyed, the system re-enters the task allocation loop and launches a second strike. This closed loop constitutes the overall technical framework of my research.
3 Task Allocation Method for Cooperative Strike Based on Target Information
In this chapter, I address the multi-UAV task allocation problem in dynamic battlefield environments. I formulate the problem as a constrained multi-objective optimization model and propose an improved contract net protocol (ICNP) to solve it efficiently.
3.1 Mathematical Formulation of Task Allocation
Let the task set be T= {t1, t2, …, tM} and the UAV set be U= {u1, u2, …, uN}. The binary decision variable xij ∈ {0,1} indicates whether task j is assigned to UAV i. The cost variable cij represents the comprehensive cost of UAV i performing task j, including time, energy, and risk components.
Four constraints must be satisfied. The task uniqueness constraint is:
$$ \sum_{i=1}^{N} x_{ij} = 1, \quad \forall j \in T $$
This guarantees that each task is assigned to exactly one UAV. The UAV capability constraint is:
$$ \sum_{j=1}^{M} x_{ij} \cdot \omega_j \le L_i^{\max}, \quad \forall i \in U $$
where ωj is the task weight and Limax is the maximum payload capacity of UAV i. The temporal constraint is:
$$ t_j^{\mathrm{start}} + \tau_{ij} \le t_j^{\mathrm{dead}}, \quad \forall j \in T $$
where tjstart is the task start time, τij is the execution time, and tjdead is the deadline. The communication constraint is:
$$ \| p_i(t) – p_k(t) \| \le R_{\mathrm{comm}}, \quad \forall u_i, u_k \in U $$
which ensures the distance between any two UAVs does not exceed the maximum communication range Rcomm.
The objective function minimizes the total cost and maximizes task balance. I design a weighted sum objective as follows:
$$ \min \sum_{i=1}^{N} \sum_{j=1}^{M} x_{ij} \left[ \alpha \cdot c_{ij}^{\mathrm{time}} + \beta \cdot c_{ij}^{\mathrm{energy}} + \theta \right] – \lambda \cdot \Omega(U) $$
The time cost is:
$$ c_{ij}^{\mathrm{time}} = \frac{d_{ij}}{v_i} + \tau_j^{\mathrm{wait}} $$
where dij is the distance from UAV i to task j, vi is the UAV speed, and τjwait is the waiting delay. The energy cost is:
$$ c_{ij}^{\mathrm{energy}} = p_i^{\mathrm{hover}} \cdot t_{ij} + p_i^{\mathrm{move}} \cdot \frac{d_{ij}}{v_i} $$
where pihover and pimove are the hovering and moving power consumptions, respectively. The risk penalty term θ is:
$$ \theta = \delta \cdot \gamma_{ij} $$
where γij is the threat coefficient and δ is the risk weight. The task balance term is:
$$ \Omega(U) = \sum_{i=1}^{N} \sqrt{ \sum_{j=1}^{M} x_{ij} \cdot \left( L_i^{\max} – L_i^{\mathrm{current}} \right) } $$
where Licurrent is the current load of UAV i. This term prevents overloading and promotes resource utilization.
3.2 Improved Contract Net Protocol Algorithm
The traditional CNP simulates the bidding process in the market. It includes four steps: task announcement, bidding, awarding, and execution. However, it suffers from three major limitations. First, the evaluation is based on a single criterion, such as distance or time, which ignores task value, threat level, and UAV capability differences. Second, there is no dynamic load balancing, causing some UAVs to be idle while others are overloaded. Third, communication overhead is high because of multiple rounds of bidding, and prior knowledge is not fully utilized.
To overcome these drawbacks, I propose an improved CNP algorithm (ICNP) with the following enhancements.
(1) Multi-factor bidding mechanism. I design a three-dimensional evaluation function for each UAV-task pair:
$$ E = \omega_1 \cdot C + \omega_2 \cdot R + \omega_3 \cdot A $$
where C is the task completion capability, R is the historical reputation, and A is the resource compatibility. The task completion capability is:
$$ C = \alpha \cdot S_{\mathrm{hist}} + (1-\alpha) \cdot \frac{1}{T_{\mathrm{comp}}} $$
where Shist is the historical success rate and Tcomp is the task complexity. The historical reputation is:
$$ R = \beta \cdot \frac{T_{\mathrm{exec}}}{T_{\mathrm{deadline}}} + (1-\beta) \cdot Q_{\mathrm{feed}} $$
where Texec is the execution time, Tdeadline is the deadline, and Qfeed is the quality feedback. The resource compatibility is:
$$ A = \gamma \cdot \frac{E_{\mathrm{batt}}}{E_{\mathrm{total}}} + (1-\gamma) \cdot \frac{C_{\mathrm{res}}}{C_{\mathrm{req}}} $$
where Ebatt is the remaining battery, Etotal is the total battery capacity, Cres is the available computational resource, and Creq is the required computational resource. The weights ω1, ω2, and ω3 are adjusted dynamically using the analytic hierarchy process based on target location and threat level.
(2) Adaptive task balancing. I define an adaptive load threshold model:
$$ L_{\mathrm{threshold}} = \alpha \cdot L_{\max} + \beta \cdot T_{\mathrm{complexity}} $$
The maximum load capacity Lmax is computed from hardware resources:
$$ L_{\max} = \delta \cdot \frac{N_{\mathrm{core}}}{N_{\max}} + (1-\delta) \cdot \frac{M_{\mathrm{cap}}}{M_{\max}} $$
where Ncore is the processor core count, Mcap is the memory capacity, and Nmax, Mmax are their maximum values. The task complexity is:
$$ T_{\mathrm{complexity}} = \varepsilon \cdot T_{\mathrm{type}} + (1-\varepsilon) \cdot \log(D_{\mathrm{size}} + 1) $$
The dynamic adjustment coefficients are:
$$ \alpha = 1 + 0.2 \cdot \tanh(\bar{L} – 0.7), \quad \beta = 0.5 \cdot (1-\alpha) $$
where L̄ is the average system load. When the load exceeds the threshold, the system triggers a task redistribution mechanism.
The complete ICNP procedure is summarized in Algorithm 1.
| Algorithm 1: Improved Contract Net Protocol Algorithm | |
|---|---|
| 1 | Initialize UAV parameters and task parameters (positions, threat levels, priorities). |
| 2 | Generate task sequence based on priorities. |
| 3 | Repeat until all tasks are allocated: |
| 4 | Tendering phase: bidders receive task announcement. |
| 5 | Bidding phase: each qualified bidder computes evaluation E using Eq. (3.10)-(3.13). |
| 6 | Awarding phase: the tenderer selects the bidder with maximum E and verifies constraints. |
| 7 | If no bidder satisfies constraints, split the task and re-announce. |
| 8 | Handle dynamic events: new tasks or UAV failures trigger re-allocation. |
| 9 | Output the final allocation matrix. |
3.3 Simulation Experiments
I compare the ICNP with the traditional CNP under identical simulation settings. The experiment uses 5 attack UAVs and 10 task targets. Table 1 lists the UAV positions, and Table 2 lists the task positions and threat levels.
| UAV | Position (km) |
|---|---|
| 1 | (16, -23) |
| 2 | (26, -29) |
| 3 | (33, -42) |
| 4 | (42, -31) |
| 5 | (21, -36) |
| Task | Position (km) | Threat level |
|---|---|---|
| 1 | (12,15) | 4 |
| 2 | (20,10) | 2 |
| 3 | (35,25) | 4 |
| 4 | (50,30) | 4 |
| 5 | (65,20) | 4 |
| 6 | (80,32) | 5 |
| 7 | (95,10) | 5 |
| 8 | (110,25) | 4 |
| 9 | (125,15) | 3 |
| 10 | (135,30) | 5 |
The allocation results show that the traditional CNP only uses two UAVs to execute all ten tasks, leaving three UAVs idle. This leads to resource waste and poor completion guarantees. In contrast, the ICNP distributes tasks evenly among all five UAVs, ensuring full resource utilization and higher completion efficiency. Figure 3.2 (not shown here) illustrates this difference.
The convergence time is also compared. The traditional CNP requires 5 iterations to integrate prior information and another 5 iterations to finalize the allocation, totaling 10 iterations. The ICNP reduces the total to 4 iterations, which is a substantial improvement. In dynamic scenarios, I introduce a sudden task 11 at (50,20) and a UAV 5 failure. The ICNP immediately reassigns the new task to a lightly loaded UAV and redistributes the failed UAV’s tasks, whereas the traditional CNP does not adapt well. These results verify the effectiveness of the ICNP in improving task allocation efficiency and dynamic adaptability.
4 Flight Path Planning Method After Task Assignment
After task allocation, each unmanned aerial vehicle must fly to the assigned target area. In this chapter, I focus on the multi-UAV cooperative path planning problem. The path planning must satisfy physical constraints (speed, acceleration, turning radius, climb/descent rate), environmental constraints (obstacle avoidance, no-fly zones), and mission requirements (shortest distance, minimum time, lowest energy). To evaluate path quality, I design a fitness function:
$$ F = \omega_1 \cdot L + \omega_2 \cdot S + \omega_3 \cdot E $$
The path length term is:
$$ L = \sum_{i=1}^{n-1} \sqrt{(x_{i+1}-x_i)^2 + (y_{i+1}-y_i)^2 + (z_{i+1}-z_i)^2} $$
The safety term is a penalty function:
$$ S = \sum_{i=1}^{n} \mathrm{Penalty}(i) $$
The energy consumption term is:
$$ E = \sum_{i=1}^{n-1} e \cdot \sqrt{(x_{i+1}-x_i)^2 + (y_{i+1}-y_i)^2 + (z_{i+1}-z_i)^2} $$
where e is the energy consumption per unit distance. By adjusting the weights ω1, ω2, and ω3, the planner can emphasize different criteria.
4.1 Grey Wolf Optimizer
The grey wolf optimizer (GWO) is inspired by the social hierarchy and hunting behavior of grey wolves. The pack is divided into four levels: α (leader), β (second best), δ (third best), and ω (followers). The position update equations are:
$$ \vec{D}_{\alpha} = |\vec{C}_1 \cdot \vec{X}_{\alpha} – \vec{X}| $$
$$ \vec{D}_{\beta} = |\vec{C}_2 \cdot \vec{X}_{\beta} – \vec{X}| $$
$$ \vec{D}_{\delta} = |\vec{C}_3 \cdot \vec{X}_{\delta} – \vec{X}| $$
$$ \vec{X}_1 = \vec{X}_{\alpha} – \vec{A}_1 \cdot \vec{D}_{\alpha} $$
$$ \vec{X}_2 = \vec{X}_{\beta} – \vec{A}_2 \cdot \vec{D}_{\beta} $$
$$ \vec{X}_3 = \vec{X}_{\delta} – \vec{A}_3 \cdot \vec{D}_{\delta} $$
$$ \vec{X}(t+1) = \frac{\vec{X}_1 + \vec{X}_2 + \vec{X}_3}{3} $$
The coefficient vectors are computed as:
$$ \vec{A} = 2\vec{a} \cdot \vec{r}_1 – \vec{a}, \quad \vec{C} = 2 \cdot \vec{r}_2 $$
where a linearly decreases from 2 to 0 over iterations. GWO has strong global search ability but can suffer from premature convergence in complex environments.
4.2 Goose Swarm Optimizer
The goose swarm optimizer (GOOSE) is inspired by the migration and anti-collision behavior of geese. In this algorithm, guard geese monitor threats and send acoustic signals to followers. Followers update their velocities and positions according to the global best position and the guard goose position. The velocity update is:
$$ v_i(t+1) = v_i(t) + c_1 r_1 \left( x_{\mathrm{best}}(t) – x_i(t) \right) + c_2 r_2 \left( x_{\mathrm{guard}}(t) – x_i(t) \right) $$
The position update is:
$$ x_i(t+1) = x_i(t) + v_i(t+1) $$
GOOSE excels in local optimization and dynamic obstacle avoidance, but its global search capability is relatively limited.
4.3 Combinatorial Optimization Algorithm
To combine the advantages of GWO and GOOSE, I propose a combinatorial optimization algorithm (COA). The core idea is to use GWO for global exploration in early iterations and GOOSE for local refinement in later iterations. A dynamic weight fusion mechanism balances the two algorithms. The weight of GWO is:
$$ w_{\mathrm{GWO}}(t) = w_{\mathrm{GWO},\max} – \frac{t}{T_{\max}} \left( w_{\mathrm{GWO},\max} – w_{\mathrm{GWO},\min} \right) $$
The weight of GOOSE is:
$$ w_{\mathrm{GOOSE}}(t) = 1 – w_{\mathrm{GWO}}(t) $$
The combined position update is:
$$ X_{\mathrm{COA},i}(t+1) = w_{\mathrm{GWO}}(t) \cdot X_{\mathrm{GWO},i}(t+1) + w_{\mathrm{GOOSE}}(t) \cdot X_{\mathrm{GOOSE},i}(t+1) $$
Substituting the update formulas, the COA position update becomes:
$$ X_{\mathrm{COA},i}(t+1) = w_{\mathrm{GWO}}(t) \cdot \left( \frac{\vec{X}_1 + \vec{X}_2 + \vec{X}_3}{3} \right) + w_{\mathrm{GOOSE}}(t) \cdot \left( x_{\mathrm{GOOSE},j}(t) + v_{\mathrm{GOOSE},j}(t+1) \right) $$
The algorithm framework is illustrated in Figure 4.1 (not shown here). The initialization adopts a layered strategy. The GWO layer generates N wolves and identifies α, β, δ leaders. The GOOSE layer generates M geese and assigns dynamic leader-follower roles. A Bernoulli chaotic map is used to enhance population diversity. The optimization process starts with GWO dominating the search. When the fitness improvement rate is smaller than 1% for 3 consecutive generations, GOOSE takes over to fine-tune the solution. This adaptive switching mechanism avoids premature convergence and accelerates convergence speed.
4.4 Simulation Results
I simulate four UAVs flying from start points to target positions. The start and target coordinates are given in Table 4.1. Ten threat sources are considered, including five radar threats and five firepower threats. Their positions and radii are listed in Table 4.2. The constraint parameters are presented in Table 4.3.
| Start point (m) | Target point (m) |
|---|---|
| (50,100,150) | (875,875,150) |
| (100,55,150) | (800,875,150) |
| (30,20,150) | (875,800,150) |
| (105,120,150) | (800,800,150) |
| No. | Position (m) | Threat radius (m) |
|---|---|---|
| 1 | (200,200,150) | 20 |
| 2 | (600,700,150) | 20 |
| 3 | (80,40,150) | 40 |
| 4 | (300,300,150) | 40 |
| 5 | (350,600,150) | 40 |
| 6 | (480,450,150) | 20 |
| 7 | (700,700,150) | 40 |
| 8 | (720,760,150) | 20 |
| 9 | (680,760,150) | 20 |
| 10 | (750,780,150) | 40 |
| Parameter | Value |
|---|---|
| Speed constraint (Ma) | 0.3-0.7 |
| Bank angle constraint (°) | -60 to 60 |
| Flight path angle constraint (°) | -45 to 45 |
| Altitude constraint (km) | 0.02-20 |
| X position constraint (km) | 0-875 |
| Y position constraint (km) | 0-875 |
I compare the COA with the standalone GWO and GOOSE. The three-dimensional views and the top views of planned paths reveal that GWO generates paths with large redundant detours and sharp altitude changes. GOOSE produces smoother paths but still has redundant segments. The COA yields the shortest and smoothest paths, with minimal redundant turns. The side views show that GWO and GOOSE exhibit significant altitude fluctuations, whereas the COA maintains stable flight altitudes and follows the terrain more closely. The fitness curves show that the COA converges rapidly in all iterations, while the GWO converges early and stagnates, and the GOOSE converges slowly in the first half and rapidly in the second half. Table 4.4 summarizes the performance comparison.
| Algorithm | Total time (s) | Collisions | Fitness convergence value |
|---|---|---|---|
| GWO | 141.87 | 3 | 240.05 |
| GOOSE | 141.15 | 2 | 181.43 |
| COA | 140.19 | 0 | 37.06 |
The results confirm that the COA outperforms both single algorithms in terms of path safety, path length, and computational efficiency. The COA is especially suitable for complex dynamic combat environments.
5 Comprehensive Assessment Method for Strike Effects
In this chapter, I address the target damage assessment problem after the strike. Traditional assessment methods rely on subjective judgment and cannot adequately handle uncertain and fuzzy information. To overcome these issues, I propose a hybrid assessment model combining the analytic hierarchy process (AHP) and fuzzy comprehensive evaluation (FCE). This model integrates expert knowledge with quantitative computation to produce reliable and interpretable assessment results.
5.1 Evaluation Index System
The design of the evaluation index system follows five principles: scientificity and objectivity, systematization and hierarchy, quantifiability and measurability, conciseness and independence, and guidance and practicality. Based on these principles, I construct a three-level index system. The target level is the comprehensive damage effect grade. The criterion layer contains physical damage, functional damage, and battlefield instantaneous effects. The index layer contains specific observable indicators. The physical damage criterion includes the following indicators: critical component structural integrity, main load-bearing structure deformation or displacement, and secondary structure damage area ratio. The functional damage criterion includes core function output state, associated subsystem operation signs, and battlefield recovery potential. The battlefield instantaneous effects criterion includes energy release characteristics, material ejection and smoke characteristics, and mobile target motion state changes.
| Target layer | Criterion layer | Index layer |
|---|---|---|
| Damage grade | Physical damage | Critical component structural integrity |
| Main load-bearing structure deformation/displacement | ||
| Secondary structure damage area ratio | ||
| Functional damage | Core function output state | |
| Associated subsystem operation signs | ||
| Battlefield regeneration and recovery potential | ||
| Battlefield instantaneous effects | Energy release characteristics | |
| Material ejection and smoke characteristics |
Each index is mapped to specific sensor data. For example, critical component structural integrity is evaluated using high-resolution visible images and three-dimensional stereo observations. Core function output state is assessed by combining signals intelligence data and expert judgment. Energy release characteristics are captured by infrared video monitoring. This ensures the index system is practical and implementable in multi-UAV operations.
5.2 AHP-FCE Hybrid Assessment Model
The AHP computes the weights of the indices through pairwise comparisons. For a judgment matrix A = [aij], where aij > 0, aij = 1/aji, and aii = 1, the weight vector W is derived by solving:
$$ A W = \lambda_{\max} W $$
After normalizing W, the consistency index and consistency ratio are:
$$ CI = \frac{\lambda_{\max} – n}{n – 1}, \qquad CR = \frac{CI}{RI} $$
where RI is the random consistency index. If CR < 0.1, the judgment matrix is consistent.
The FCE establishes a set of evaluation grades V = {V1, V2, V3, V4, V5} = {complete destruction, severe damage, moderate damage, light damage, basically intact}. For each criterion layer k, the fuzzy relationship matrix Rk is constructed from expert scoring. The first-level fuzzy comprehensive evaluation is:
$$ B_k = W_{C_k} \cdot R_k $$
The second-level evaluation combines all criterion-level results into the final result vector:
$$ B = W_B \cdot R $$
where R = [B1; B2; B3]. After normalization, the maximum membership principle determines the final damage grade. To obtain a quantitative score, I assign scores to the grades: S = (95, 80, 60, 30, 5). The weighted score is:
$$ Z = \hat{B} \cdot S^T = \sum_{j=1}^{5} \hat{b}_j s_j $$
The assessment procedure includes the following steps: acquire expert scoring data, compute AHP weights, construct fuzzy membership matrices, perform first-level and second-level fuzzy evaluations, and determine the final damage grade with the calculated score.
5.3 Case Study and Analysis
I apply the proposed assessment model to a fixed air-defense radar station target. Ten experts evaluate eight indices (the mobile target motion index is excluded for a fixed target). The expert scores are counted and converted into membership degrees. Table 5.2 shows the expert evaluation distributions and the corresponding membership degrees.
| Index | Complete destruction (0.95) | Severe damage (0.80) | Moderate damage (0.60) | Light damage (0.30) | Basically intact (0.05) |
|---|---|---|---|---|---|
| Critical component structural integrity | 7 (0.7) | 2 (0.2) | 1 (0.1) | 0 (0) | 0 (0) |
| Main structure deformation/displacement | 6 (0.6) | 3 (0.3) | 1 (0.1) | 0 (0) | 0 (0) |
| Secondary structure area ratio | 5 (0.5) | 4 (0.4) | 1 (0.1) | 0 (0) | 0 (0) |
| Core function output state | 5 (0.5) | 4 (0.4) | 1 (0.1) | 0 (0) | 0 (0) |
| Associated subsystem operation signs | 4 (0.4) | 5 (0.5) | 1 (0.1) | 0 (0) | 0 (0) |
| Recovery potential | 3 (0.3) | 5 (0.5) | 2 (0.2) | 0 (0) | 0 (0) |
| Energy release characteristics | 8 (0.8) | 2 (0.2) | 0 (0) | 0 (0) | 0 (0) |
| Material ejection and smoke | 7 (0.7) | 3 (0.3) | 0 (0) | 0 (0) | 0 (0) |
The AHP method determines the global weights for the three criteria. The physical damage and functional damage each have a global weight of 0.4, and the battlefield instantaneous effects have a global weight of 0.2. The local weights for each index are shown in Table 5.3.
| Criterion layer | Global weight | Index layer | Local weight |
|---|---|---|---|
| Physical damage | 0.4 | Critical component structural integrity | 0.75 |
| Main structure deformation/displacement | 0.15 | ||
| Secondary structure area ratio | 0.10 | ||
| Functional damage | 0.4 | Core function output state | 0.50 |
| Associated subsystem operation signs | 0.30 | ||
| Recovery potential | 0.20 | ||
| Battlefield instantaneous effects | 0.2 | Energy release characteristics | 0.43 |
| Material ejection and smoke | 0.57 |
After performing the first-level and second-level fuzzy evaluations, the initial synthetic result vector is obtained as:
$$ B = (0.5606, 0.3364, 0.1030, 0.0000, 0.0000) $$
Normalizing this vector yields:
$$ \hat{B} = (0.560, 0.336, 0.103, 0.000, 0.000) $$
The maximum membership degree is 0.560, corresponding to the grade “complete destruction”. The weighted score is:
$$ Z = 0.560 \times 95 + 0.336 \times 80 + 0.103 \times 60 + 0 \times 30 + 0 \times 5 = 82.7 $$
| Grade | Complete destruction | Severe damage | Moderate damage | Light damage | Basically intact |
|---|---|---|---|---|---|
| Normalized membership | 0.560 | 0.336 | 0.103 | 0.000 | 0.000 |
The sum of the memberships for “complete destruction” and “severe damage” is 0.896, indicating that the experts have a high degree of consensus. The quantitative score of 82.7 validates the assessment conclusion. This result demonstrates that the proposed AHP-FCE model can effectively handle the uncertainty and fuzziness in the damage evaluation process. It provides a scientific basis for the command center to decide whether to terminate the operation or launch a second strike.
6 Conclusion and Future Work
In this dissertation, I have conducted a systematic study on multi-UAV cooperative strike and damage assessment methods. The main contributions are summarized as follows.
(1) For task allocation, I proposed an improved contract net protocol algorithm. The algorithm embeds a multi-factor bidding mechanism that considers target strategic value, UAV capability, task priority, and threat level. In addition, an adaptive task balancing strategy adjusts the load among UAVs in real time. Simulation results show that the improved algorithm significantly increases task allocation efficiency and substantially improves dynamic adaptability in sudden task insertion and UAV failure scenarios in comparison with the traditional contract net protocol.
(2) For path planning, I developed a combinatorial optimization algorithm that integrates the grey wolf optimizer and the goose swarm optimizer. The algorithm uses dynamic weight fusion and an adaptive switching mechanism to balance global exploration and local exploitation. Simulation experiments demonstrate that the combinatorial optimization algorithm produces safer and more efficient paths than either single algorithm, while reducing the number of collisions and achieving a much lower fitness convergence value. This algorithm is particularly suitable for complex, dynamic combat environments.
(3) For damage assessment, I established a comprehensive multi-level evaluation index system covering physical damage, functional damage, and battlefield instantaneous effects. I further constructed a hybrid assessment model combining the analytic hierarchy process and fuzzy comprehensive evaluation. The model determines index weights through AHP and processes fuzzy information through FCE. Expert scoring tables are integrated into the evaluation flow. Case analysis verifies that the model produces reliable and effective damage assessment results, providing strong decision support for determining whether a second strike is necessary.
There are several directions for future work. In task allocation, online learning and multi-agent reinforcement learning can be integrated to improve real-time responsiveness and adaptability in highly uncertain environments. In path planning, the algorithm can be extended to support dynamic obstacle avoidance and re-planning through the integration of deep reinforcement learning and model predictive control. In damage assessment, multi-source sensor fusion and deep learning-based automatic feature extraction can enhance assessment accuracy and speed, enabling real-time edge computing on UAV platforms.
In conclusion, this dissertation provides a systematic solution for multi-UAV cooperative strike and damage assessment. The proposed methods can be used as independent modules or integrated into a complete cooperative combat system. They have broad application prospects in both military and civilian fields, including precision strike, border patrol, disaster rescue, and infrastructure inspection.