Robust full-link trajectory tracking control for underwater snake robots with actuator faults under time-varying uncertainties

This paper presents a trajectory tracking control approach for an underwater snake robot (USR) under conditions of internal modeling discrepancies, external time-varying disturbances, and actuator malfunctions, utilizing a fast fixed-time disturbance observer. Initially, a stabilized control system with fast fixed-time convergence is developed, offering superior performance over existing methods. Leveraging the USR's unique kinematic properties, a decoupled control strategy for full-link trajectory tracking is introduced, alongside a cascade controller design based on the mathematical model of an orthogonally-connected USR with a head-mounted propeller. Furthermore, a disturbance observer is designed to estimate both internal uncertainties and external significant disturbance terms, grounded in the dynamics of the USR and the properties of the fast fixed-time stabilization system. By integrating the disturbance estimation and fast fixed-time system with a non-singular terminal sliding mode surface, a fast fixed-time non-singular terminal sliding-mode controller with strong robustness is devised to track the desired link angles, with its fast fixed-time convergence rigorously demonstrated through Lyapunov stability theory. Eventually, extensive simulation results demonstrate the efficacy of the proposed control framework, confirming its robustness and performance in challenging underwater environments.