## 5 Conclusions  
This paper has presented two efficient algorithms: CD algorithm and CR algorithm, which constitute a novel CA system for multiple cooperative UAVs aiming to detect and resolve threats by generating an optimal trajectory with an overall minimum cost in 3D airspace. The CD module analyzes the spatial-temporal information composing a set of discrete 4D trajectories to generate the intuitionistic representation of detected conflicts. The CR algorithm integrates with the CD portion and solves the detected threats through DDOA and causal analysis. The DDOA provides new feasible alternative trajectories for each UAV involved in an encounter with a local optimization scope, and it generates alternative avoiding trajectories by an objective function (integrating track adjustment, cost, distance, and time) in consideration of several constraints (i.e., performance, state, and distance). The causal analysis explores the emergent dynamics between the alternative trajectories generated by DDOA and the surrounding traffic. It has numerous advantages such as splitting the scenario to separate clusters, reducing the size of solution space, and exploring the global optimal solution. Based on the quantitative simulation results, the proposed CA system has been validated to be feasible and effective in resolving conflicts for multiple UAVs and has high scalability for different traffic densities; the efficiency decreases as the value of conflict volume increases, and increases as the sense range increases; the causal analysis is effective for the selection of an optimal resolution trajectory.  
Figure 11: Variation of efficiency with \(R_{\mathit{cf}}\) and sense range for the traffic density of 20 UAVs.  
Future research will be dedicated to: (1) using a heuristic-based algorithm to improve our proposed approach, which could tackle the collision avoidance problem of more UAVs in high-density scenarios, while it also may require more computation time; (2) making a comprehensive review of the existing best performing methods that consider UAV factors and integrating them to our system in order to improve its performance; (3) considering several disturbances (e.g., wind) to improve the current system logic in order to hold the complex field situations; (4) integrating UAVs into(manned) general aviation to operate in a non-segregated airspace.  
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (71601181), the Military Scientific Research Project (162017160500A21 XXX), and the State Key Laboratory of Management and Control for Complex Systems-Open Project (20160109).  
[PERSON] and [PERSON] designed the distributed dynamic optimization approach and causal analysis, conducted the simulations of the core algorithms and co-wrote the initial manuscript. Besides, [PERSON] helped improve the system design and put forward several construction suggestions. The final manuscript was read and approved by all authors.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l}
3D & Three dimensional \\
4D & Four dimensional \\ ADS-B & Automatic Dependent Surveillance Broadcast \\ ASAS & Airborne Separation Assurance System \\ CA & Collision avoidance \\ CD & Conflict detection \\ CPA & Closet point of approach \\ CR & Conflict resolution \\ DDOA & Distributed dynamic optimization approach \\ NP & Non-deterministic polynomial \\ TCAS & Traffic Alert and Collision Avoidance System \\ TMA & Terminal Maneuvering Area \\ UAV & Unmanned aerial vehicle \\ \end{tabular}