Adaptive Formation Control of Nonlinear High-Order Fully Actuated Multiagent Systems With Full-State Constraints and Its Application

This adaptive formation tracking control is investigated for high-order fully actuated (HOFA) multiagent systems (MASs) with unknown nonlinear dynamics and full-state constraints. To tackle the dynamic uncertainty while maintaining safety constraints on system state, a novel hierarchical formation control framework is presented. First, a nonlinear mapping function (NMF) is introduced, which, by integrating HOFA theory, effectively transforms the original constrained system into an unconstrained HOFA tracking error model, thus removing the feasibility conditions typically required in traditional barrier Lyapunov function methods. Subsequently, distributed observers are designed in the upper layer for followers to estimate the leader's information, while an adaptive formation controller is directly constructed for each follower in the lower layer using the fully actuated theory. Particularly, the neural network approximators are used to learn unknown nonlinear dynamics. By employing Lyapunov stability theory, the designed formation controller guarantees that the entire state stays within the specified constraint set while also ensuring the desired formation performance. Finally, the developed formation control algorithm is proven effective by applying it to a network of multiple robotic arm systems.