# Real-time Conflict Resolution Algorithm for Multi-UAV Based on Model Predict Control
## 1 Introduction  
Interest in research activities related to techniques using multiple Unmanned Aerial Vehicles (UAVs) has experienced a significant increase in recent decades [1; 2]. As the application of cooperative UAVs to execute tasks has gradually increased, the common problem of maintaining a safe separation among all UAVs has aroused much attention from scholars. Therefore, conflict (detection and) resolution algorithms are needed for all the multi-UAV scenarios.  
The major problem of conflict (detection and) resolution lies in the accurate collision prediction and efficient adjustment of the flight status among conflicting UAVs [2; 3]. Many mythologies and approaches have been applied in order to this problem, among them are two main categories: numerical approaches [4; 5; 6; 7; 8; 9; 10; 11] and control approaches [12; 13; 14; 15]. As for numerical approaches, [PERSON]. [4; 5] considered the conflict resolution (CR) as a replanning problem and applied mixed-integer linear program (MILP). [PERSON] and [PERSON] implemented conflict resolution by using game theory [6]. In Ref. [7], the conflict was resolved by tuning the speed of aerial vehicles based on Monte Carlo optimization, but not all conflicts could be resolved, due to the constraints of velocity change. Other CR methods have been proposed, such as application of geometric algorithm [8], ant colony optimization algorithm [9], multi-objective evolutionary algorithms [10] and differential geometric algorithm [11]. Numerical methods can efficiently resolve the conflicts in some typical scenarios, but they find it difficult to take the actual flight status of the UAV in to account.  
Thus, other scholars have adopted control methods in solving the CR problem, a typical form among them is model predictive control (MPC). In Ref. [12], a centralized model predictive controller is designed that considers the physical limitations of the aircraft, although the timeliness of the method is not very good. A modified MPC approach combined with morphing potential field is proposed in Ref. [13], which prohibits UAVs' collision with obstacles and conflicts in real time. [PERSON] et al. [14]designed a decentralized model predictive control (DMPC) scheme for hierarchical systems, which can provide a preview of the otherwise myopic navigation functions and generate conflict-free trajectories, but without considering the priorities of aircrafts in the system. Meanwhile, all the methods mentioned above focused on resolving current conflicts, while ignoring subsequent conflicts.  
In this paper, an improved distributed nonlinear MPC (DNMPC) framework for autonomous UAVs is proposed to resolve the conflicts of flight trajectories that implement decentralized CR based on the communication between the conflicting UAVs. This proposed method is motivated by two main properties: reliable prediction of the potential conflicts and constraint handling for resolving the predicted conflicts by managing the current inputs and states. At the same time, corresponding resolution rule and strategy are proposed to decompose conflicts and resolve them in groups consists of several UAVs. A conflict resolution algorithm is also designed to calculate control variables for each UAV and to ensure no subsequent conflicts will be generated, which leads to a consistent unique decision for conflicting UAVs.