## 4 Motion Planning Algorithm Based on Co-Optimization of Communication and Sensing
### Cooperative Target Tracking Algorithm Based on Co-Optimization of Communication and Sensing  
The block diagram in Figure 5 summarizes the cooperative target tracking algorithm based on the co-optimization of communication and sensing. At each time \(k\), first, according the positions of UAVs and the base station, the weighted minimum spanning tree strategy is used to optimize the communication network topology. Based on the MST communication topology, the Dijkstra algorithm  
Figure 4: Example of a communication topology and its corresponding minimum weighted spanning tree.  
is used to find the route with the highest successful transmission probability between each UAV \(A_{i}\) and the base station. Next, all the UAVs are sorted in the ascending order of the total number of hops to the base station as described in the previous section. The UAVs successively perform the local optimization calculation according to the sorted results. Next, each UAV \(A_{i}\) uses an EIF to obtain the local estimation results \(\hat{\mathbf{x}}_{i,k|k}\) of the target state. The local information terms \(\mathbf{i}_{i,k}\) and \(\mathbf{I}_{i,k}\), which are generated based on the measurement \(z_{i,k}\) of the target, are summed at the base station to produce a global estimation. \(A_{i}\) then computes its own trajectory based on the planned results of \(A_{j}\), which is the relay of \(A_{i}\) in the current MST communication topology. In distributed fashion, each UAV \(A_{i}\) solves the local optimization problem in Equation (42) to obtain the optimal control sequence \(\mathbf{u}^{*}_{i,k}\) during a planning time horizon \(T_{\text{P}}\). Finally, the control input in the sequence is implemented, \(A_{i}\) changes its flight state \(\mathbf{x}_{i,k}\), and obtains a new measurement \(z_{i,k}\) of the target restarting the cycle.  
**Remark 2**.: _Our algorithm uses the concept of the MST to optimize the communication network topology according to the positions of the UAVs and the base station. The MST communication topology determines the planning hierarchy, which determines the order of the optimization calculation in the distributed framework. In this way, our algorithm can effectively adapt to a dynamic environment such as moving targets and the non-static spatial distribution of the UAVs. Thus, in the dynamic scenario of tracking a moving target, our algorithm can produce a more efficient target state estimate than the algorithm in Reference [18]. However, there is a limitation in our algorithm, which also exists in Reference [18]; the scalability of the planning approach. As trajectory optimization is performed sequentially, each UAV plans its own trajectory based on the planned results of other UAVs. For large networks, exchanging the planned trajectories between the UAVs requires many communications. However, due to the bandwidth limitation of realistic wireless communication links, it is hard to receive all the required information within one sampling time. In addition, as the number of UAVs increases, solving the optimization problem in Equation (42) becomes difficult in real time. In future work, we will design a planning algorithm with low computational complexity._