Predefined-time distributed Nash equilibrium searching in cross-dimensional formation reconfiguration control for AAV–AGV system

This article investigates the formation reconfiguration problem of autonomous aerial vehicle–autonomous ground vehicle (AAV–AGV) system and constructs the real-time desired configuration of the formation system in the moving stereo domain. Firstly, since AAVs and AGVs move in different dimensions, in order to solve the problem of cooperative control of heterogeneous formation, the cross-dimension formation protocol method is employed, which enables the agents in the same cluster to form the desired time-varying formation in their respective dimensions, while different clusters move in different dimensions. Secondly, each agent in the heterogeneous formation is positioned to achieve the target configuration. At the same time, the sum of the squares of the Euclidean distances between it and its corresponding agents are minimized to ensure the optimal energy consumption during the formation reconfiguration process. According to the theories and methods above, the problem is reformulated as a time-varying noncooperative game. Subsequently, a distributed time-varying Nash equilibrium search algorithm based on time transformation technique and gradient descent technique is developed. This algorithm enables the heterogeneous system to complete the formation reconfiguration within the predefined time. The convergence of the algorithm is proved by Lyapunov stability theorem and a iterative method. Finally, a simulation example is provided to prove the effectiveness of the algorithm.