Fully Actuated Approach for Safety-Critical Control of Underactuated Systems via Differential Flatness

Aiming at the challenges of infeasible safety constraints and high computational complexity in underactuated systems (UAS) caused by input coupling and model uncertainties, this paper proposes a safety-critical control method based on differential flatness theory and fully actuated systems (FAS). Firstly, the UAS is transformed into a fully actuated chained system via flat outputs, decoupling the complex nonlinear relationships between inputs and states. Secondly, control barrier function (CBF) constraints are designed in the flat space, and forward invariance of the original system's safe set is guaranteed through homeomorphic mapping, thereby avoiding optimization infeasibility issues caused by input coupling in traditional methods. Finally, the effectiveness of the proposed approach is validated through simulations on an underactuated hovercraft model. Experimental results demonstrate that the method significantly reduces computational complexity while ensuring real-time safety in trajectory tracking and dynamic obstacle avoidance, offering a novel framework for safe control of UAS.