## 2 Related Work  
[PERSON] et al. [25] proposed the use of an air-ground cooperative model to address the shortcomings of a single platform, e.g., the low accuracy of UAVs when locating ground targets and the narrow view of UGVs when observing distant obstacles. They designed a cooperative control framework and algorithm to search for and locate targets in a specified area, providing ideas for cooperative air-ground platforms to search for targets. [PERSON] et al. [26] considered the problem of communication constraints between two UAVs that cooperate to complete a mission. To address this issue, they proposed using UAVs to collect information and developed a branch-and-cut algorithm to solve the path-planning problem of UGVs and UAVs, offering a new idea for the cooperative path planning of UGVs and UAVs under communication constraints. In addition, they presented a cooperative reconnaissance and data-collection method for UGVs and UAVs. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Type of UAV** & **Advantages** & **Disadvantages** \\ \hline \multirow{4}{*}{UAV} & \multirow{4}{*}{Small fixed-wing UAV} & Fast velocity & Low load capacity \\  & & Wide field-of-view & Low observation accuracy \\  & & Excellent communication & \\ \cline{2-4}  & \multirow{2}{*}{Small rotary-wing UAV} & Vertical takeoff landing & \\  & & Good reconnaissance & \\ \hline \multirow{4}{*}{UGV} & \multirow{4}{*}{High load capacity} & Small field-of-view & \\  & & Precise observation of ground targets & Low velocity \\ \cline{1-1}  & & & Weak communication \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Advantages and disadvantages of UAVs and UGVs. To address the problem that the line of sight of a ground vehicle's sensors is limited by the geometry of the environment, [PERSON] et al. [27] presented a method to capture aerial images of the mission area using multi-rotors, construct a terrain map, and then navigate the ground robot to the destination. This method provides a theoretical and practical basis for the application of air-ground cooperative systems for cooperative navigation in outdoor environments. However, the aforementioned studies on air-ground cooperation focus mostly on image transmission, map construction, and target localization, and do not consider the impact of UAV-UGV formation on the overall quality of cooperative operations. In fact, when UGVs and UAVs perform cooperative combat missions, formation adjustments are required, including initial formation generation, formation maintenance, contraction, expansion, and reconfiguration. Therefore, research on the formation control of UGVs and UAVs is of great significance, and can even affect whether a combat mission can be successfully completed. UAVs and UGVs have completely different physical structures, and their established kinematic and dynamic models are entirely different. Moreover, UAVs perform three-dimensional movements in air, whereas UGVs perform two-dimensional movements on the ground. As a result, studying the time-varying formation-tracking control of heterogeneous cluster systems is a key problem to solve in cross-media heterogeneous collaboration, including air-ground collaboration, which has great theoretical research value and engineering significance. Currently, common formation-control strategies include behavior-, virtual structure-, and consistency-based methods [28; 29; 30]. However, behavior-based formation methods rely on qualitative behavior rules, making it difficult to establish a quantitative model of the entire system. Consequently, such a method cannot guarantee the stability of the formation movement of an entire system. Virtual structure-based methods require centralized control by a central node, and cannot be implemented in a distributed manner.