Adaptive fixed-time fuzzy formation control for multiple AUV systems considering time-varying tracking error constraints and asymmetric actuator saturation

Safe Robust Adaptive Motion Control for Underactuated Marine Robots

“…Referring to (1), the boundedness of ṗi , along with the Assumptions 1 and 3, and considering the upper-boundedness of external disturbances in Kinematics, leads to the conclusion that the internal velocity signals u r and r are also bounded. Referring to (2), the boundedness of ur and ṙ can be deduced under the assumption of upper-bounded external disturbances in Dynamics and lateral velocity, as well as other upper-bounded signals in (2).…”

“…The resulting advancements have led to significant progress, providing valuable insights into the field. These insights could find numerous applications, such as marine research, subsea pipeline monitoring, lifesaving operations, oil and gas exploration, and many other missions [ 1 , 2 , 3 ]. However, despite the considerable strides made, the complexities surrounding underwater robotics persist.…”

“…There are different ways to ensure the stability and safety of the system. One strong way to ensure formal stability is to use the Control Lyapunov functions [ 1 , 2 , 3 ]. These functions can provide a rigorous mathematical foundation for stability analysis.…”

“…To address different uncertainties a strong approximation may be used. Among different approaches, Fuzzy Systems due to their special mathematical structure can be flexible enough to attract great attention to providing a strategy that could generally work for nonlinear systems and handling complex systems while being computationally efficient [ 2 , 8 , 9 , 10 ]. To overcome unmodelled dynamics, parametric uncertainties, and external disturbances, Sliding Mode Control (SMC) [ 1 , 11 ] proved to be effective enough to address these difficulties.…”

“…Additionally, unlike the methods discussed in [ 1 , 12 ], our proposed boundary layer does not incorporate a sign function within its structure, ensuring the robot’s signals remain within the safe set. In terms of feasibility and robustness, our proposed scheme surpasses much of the above research by considering a broader range of uncertainties through the utilization of a more straightforward fuzzy estimator compared to [ 2 , 8 ]. Moreover, the developed method does not use the direct feedback of the lateral velocity, eliminating the need for a costly lateral velocity sensor and thereby enhancing its economic viability.…”