A Fuzzy-Theoretic Cooperative Game Framework for Adaptive Robust Control of Air–Ground Vehicle Systems

To enhance the efficiency and safety of transportation, low-altitude economy has garnered increasing attention. In this study, we consider air–ground systems composed of both uncrewed ground vehicles and uncrewed aerial vehicles. A novel integrated framework for modeling, control, and optimization is proposed, which creatively unifies kinematics, dynamics, and control into a structured setting for approximate constraint following. The framework consists of three key phases. First, in the modeling phase, desired system behaviors, such as collision avoidance, compact formation, and trajectory tracking, are formulated into a unified performance metric. This metric is then treated as a constraint, and the system's dynamics for approximate constraint following are derived using the Udwadia–Kalaba approach. Second, in the control phase, an adaptive robust control scheme is developed to compensate for system uncertainties. Notably, the method does not require prior knowledge of the uncertainty bounds, while still guaranteeing consistent system performance in uncertain environments. Third, in the optimization phase, the fuzzy nature of the uncertainty bounds is considered. The uncertainty bound is modeled as a fuzzy set characterized by a membership function, which is incorporated into a fuzzy-theoretic performance index. The Pareto-optimal game theory is then employed to determine the optimal control parameters. The proposed framework enables the air–ground logistics system to follow constraints with reduced error, as validated through simulation results.