## 3 Task Assignment Algorithm Based on Extended CNP
### Distributed Multi-Constraint Dynamic Task Assignment Algorithm
Combining the value function and the penalty function, the individual bidding function \(B_{ij}\) of UAV \(V_{i}\) for \(Task_{j}\) is denoted by

Figure 4:6

where a greater value of \(B_{ij}\) indicates the reward of performing the task. \(B_{ij}\) monotonically increases with \(h_{i,est}\) and decreases with \(L_{ij}\) and \(t_{task_{j}}\), which agrees with the actual scenario, which suggests that \(B_{ij}\) has practical significance. #### 3.2.2 Bidding Function of Each Subset

The bidding function of subsets is based on the individual function. For target \(T_{j}\), supposing that the bidding value set is \(\{B_{1},B_{2}\}\) after the subtask assignment in subset \(G_{i}\), \(B_{1}\), \(B_{2}\) respectively express the bidding value of subset \(G_{i}\) performing the reconnaissance subtask and the attack one. The bidding function of subsets is defined as the sum of elements in \(\{B_{1},B_{2}\}\), which is

Figure 4:7

## 4 Dynamic Assignment Strategy Based on Event Triggering

### Event Trigger Conditions for Dynamic Tasks

Due to the incomplete perception of the situation at the beginning and the occurrence of emergencies during the task execution, the initial assignment scheme needs to be adjusted. Therefore, the event trigger conditions are introduced to judge whether or not to carry out the dynamic task assignment. Event trigger conditions are the key to realizing dynamic task assignments, which need to be selected in combination with different scenarios. The dynamic task assignment process based on event triggering can be expressed as:

Figure 4:8

where \(g(\mathbf{s}(t),\mathbf{s}_{t,j}(t))\geq 0\) is the triggering condition, \(\mathbf{s}(t)\) is the state of UAV (such as the position), \(\mathbf{s}_{t,j}(t)\) is the status of target \(T_{j}\). \(Target_{j}\gets TargetInfo^{*}_{j}\) expresses the update of the set of targets, and \(\ Task_{j,k}\gets TaskInfo^{*}_{j,k}\) expresses the update of the set of subtasks. (1) The unknown targets appear

The initial target assignment is based on the initial situation awareness information, which can only cover the known targets but is not guaranteed to cover all the targets in the mission area. After the reconnaissance UAV or reconnaissance-attack UAV \(V_{i}\) flies near the unknown target \(T_{j}\) during task execution, it will detect the target and obtains the target information \(TargetInfo_{new,j}\) and then updates the target set and the subtask set. Event trigger conditions can be described as

Figure 4:9

where \(DA(\mathbf{r}_{i},\mathbf{r}_{nt,j},R_{detect,i})\) is defined as the reconnaissance payload constraint, which is the constraint on the relative position and angle relations between UAV \(V_{i}\) and target \(T_{j}\). The details are in reference [34]. When target \(T_{j}\) is located in the detect area of the reconnaissance-attack UAV or reconnaissance UAV, \(DA(\mathbf{r}_{i},\mathbf{r}_{nt,j},R_{detect,i})\geq 0\); \(\mathbf{r}_{i}\) is the position vector of UAV \(V_{i}\); \(\mathbf{r}_{nt,j}\) is the position vector of target \(T_{j}\); \(R_{detect,i}\) is the detection range of UAV \(V_{i}\). The event-triggering process can be expressed as

\[Winner_{k}=Index(B_{(1),k},\ B_{(2),k},\ \ldots,\ B_{(Np,k),k}) \tag{14}\]0

\[Winner_{k}=Index(B_{(1),k},\ B_{(2),k},\ \ldots,\ B_{(Np,k),k}) \tag{14}\]1

where \(\ Target_{N_{target}+j}\gets TargetInfo_{new,j}\) indicates the update of target set, \(N_{target}\) is the number of targets; \(\ Task_{N_{target}+j,k}\gets TaskInfo_{New,j,k}\) indicates the update of subtask set, \(N_{neutask,j}\) is the number of subtasks of \(T_{j}\). (2) The UAV encounters faults and cannot perform tasks

During task execution, UAVs may encounter non-cooperative behaviors such as collision and attack and lose mission capability. Its tasks that have not been executed will be reassigned.