## 1 Introduction  
As technological capabilities have rapidly progressed, enabling the deeper exploration of the ocean realm, autonomous underwater vehicles (AUVs) have proven to be indispensable tools in unlocking the mysteries of the deep. These unmanned, cable-free underwater vehicles are equipped with the requisite instrumentation, including sonar, a Doppler Velocity Log (DVL), and an Inertial Measurement Unit (IMU), and rely on embedded control computers and autonomous control software to execute pre-defined navigation tasks. Due to their exceptional underwater performance, adaptability, and mission-execution capabilities, AUVs have become vital assets in various applications, including marine resource exploration and development ([PERSON] et al., 2021 [1]; [PERSON] et al., 2015 [2]), marine information monitoring ([PERSON] et al., 2011 [3]; [PERSON] et al., 2021 [4]; [PERSON] et al., 2023 [5]), marine reconnaissance ([PERSON] et al., 2023 [6]), and rescue missions ([PERSON], 2007 [7]; [PERSON] et al., 2021 [8]). These abilities have elevated AUVs to a prominent research focus in the field of ocean engineering globally ([PERSON] et al., 2005 [9]). As the demand for AUV applications expands, these vehicles are being tasked with increasingly varied and complex roles. This evolution necessitates enhanced motion control systems that allow AUVs to fulfill human demands more effectively. However, achieving the precise control of AUVs is a formidable and vital challenge, attributed to factors like strong coupling, nonlinearity, and operational constraints ([PERSON] et al., 2022 [10]; [PERSON] et al., 2022 [11]; [PERSON] et al., 2013 [12]). Model Predictive Control (MPC) is an advanced control strategy capable of addressing the input and state constraints of a system in real-time, which emanate from its inherent physical and safety limitations. These constraints arise from the physical characteristics and safety limitations of the system and are widely present in all systems ([PERSON] et al., 2019 [13]). Contrary to traditional optimal control strategies that necessitate comprehensive optimization across the entire temporal domain, MPC enhances computational efficiency by focusing on localized optimizations within a predefined future timeframe. This method not only reduces computational complexity but also endows the control system with a predictive capability, allowing it to infer future dynamics based on current and impending control inputs. Model Predictive Control (MPC) exhibits a distinct advantage in handling tasks that demand precise navigation and obstacle circumvention under various constraints, a feature that is well-evidenced in trajectory tracking and obstacle avoidance applications ([PERSON] et al., 2015 [14]; [PERSON] et al., 2017 [15]; [PERSON] et al., 2019 [16]) and obstacle avoidance ([PERSON] et al., 2019 [17]; [PERSON] et al., 2020 [18]; [PERSON] et al., 2022 [19]). Within the specialized context of AUVs, [PERSON] et al. (2022 [20]) have pioneered an integrated control approach by amalgamating optimized MPC with Nonlinear Tilted Sliding Mode Control (NTSMC) and an adaptive Radial Basis Function Neural Network (RBF NN) compensator. This innovative method is designed to enhance the accuracy of dynamic trajectory tracking. This dual-loop system effectively mitigates constraints and external disturbances, ensuring both stability and robust performance, validated through Lyapunov stability analysis and extensive simulation under varied marine conditions. Moreover, [PERSON] and [PERSON] explored the application of linear MPC in conjunction with line-of-sight (LOS) guidance for path-following control, utilizing quadratic programming to derive the control input, a method proven to be effective in simulations involving underactuated surface vessels (2010 [21]). [PERSON] et al.