## 1 Introduction
In order to ensure all state variables are within constraints, studying the full-state constraint problem in NMR control is important. For example, the Ln-type barrier function is used to constrain the boundaries of the specified performance function in [20]. In [21], the authors used a tan-type barrier function to realize the collision avoidance and connectivity maintenance of the robot. In [22], the formation and collision avoidance problem of NMRs based on the artificial potential field method is proposed. To suppress the violation of tracking error constraints, a barrier Lyapunov function-based control method was proposed to realize the tracking control of incomplete mobile robots under specified performance conditions in [21]. Note that the above control schemes do not effectively control NMRs with unknown dynamics. FLSs are often used to identify unknown functions due to their strong fitting and approximation ability. In [9], a compensator and data-driven control scheme based on FLSs are designed to solve the NMRs' formation control. In [23], the formation control issue of the networked non-complete mobile robot based on the L-F framework was studied. In [24], not only the NMR's adaptive output feedback formation tracking control problem was solved but the connectivity maintenance and collision avoidance were also realized. In [25], an integrated L-F consensus formation framework using an optimized NN-based distributed model predictive control strategy was presented. Note that the formation control methods in [9; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25] cannot possibly guarantee full-state constraints and save communication resources at the same time. To the best of our knowledge, there are no results on fuzzy adaptive event-triggered formation controllers for NMRs with full-state constraints. Therefore, designing an adaptive event-triggered formation controller for NMRs under full-state constraints is a challenging and important topic. Inspired by the above analysis, this paper investigates the fuzzy adaptive formation control of NMRs with nonlinear uncertainty and full-state constraints. Our main contributions are summarized below:  
1. By utilizing FLSs to estimate the unknown nonlinear functions, and constructing the barrier Lyapunov functions, this paper develops a fuzzy adaptive formation control approach within the adaptive backstepping control design framework. Although the work in [9; 21; 22] investigated the fuzzy adaptive formation control problems of NMRSs, their methods do not consider full-state constraints. Such formation control methods do not constrain the state of the robot within a reasonable range. 2. In [24; 25; 26], authors investigated the fuzzy adaptive formation control problems of NMRs. These methods cannot decrease the unnecessary waste of resources resulting from the update of the controller signal when considering complete state constraints. Therefore, this paper designs an event-triggering mechanism to avoid unnecessary waste of resources. In Table 1, a comparison of different control algorithms is presented. The rest of this paper is structured as follows. The problem description for this work is the main content in Section 2. Section 3 describes the process of design controller and stability analysis. The proposed event-triggering protocol with numerical examples and summarizes the conclusions is verified in Section 4. Notations: \(|\bullet|\) indicates the absolute value. \(\|\bullet\|\) denotes the Euclidean norm for vectors or induced 2-norm for matrices.