## 1 Introduction  
Over the past few decades, ROVs have played a crucial role in deep-sea resource exploitation, underwater rescue, and ocean mapping [1; 2]. During ROV operations, accurate position keeping and trajectory tracking are important for completing missions efficiently and safely. However, precise control is a difficult and challenging task for ROVs due to the fact that ROVs' control systems are affected by coupling nonlinearities, hydrodynamic parameter uncertainties, mathematical model parameter uncertainties, and unknown environment disturbances, such as wave, tide, and currents [3]. Therefore, overcoming these difficulties in order to improve the position and orientation holding performance and trajectory tracking performance of ROVs has become the focus of long-term research in this field. Scholars in various countries have proposed a large number of control methods to solve these problems. The proportional-integral-derivative (PID) control scheme, as a classical linear control method, has become one of the most widely used position and attitude control techniques for underwater robots due to its simple structure, easy adjustment of control parameters, high reliability, and strong robustness [4; 5; 6]. This can be attributed to their simple design and easy-to-adjust parameters. Other methods include sliding mode control (SMC) [7; 8], adaptive control [9], neural network control [10], and the combination of several control methods [11]. In particular, sliding mode control is popular because of its high tolerance to model uncertainties and high robustness, and it is increasingly used to control ROV motion in complex underwater conditions. However, sliding mode control suffers from chattering, which tends to cause high-frequency oscillations in the actuator. The SMC control law has a switch term that is a component of discontinuous feedback, which is used to compensate for dynamic errors. It is a source of robustness in SMC, but also leads the system to chatter violently on the sliding mode surface. In the case of ROVs, chattering can lead to high-frequency switching between the forward and reverse rotations of the thrusters, resulting in an increased energy consumption and a reduced thruster lifespan. In fact, ROVs equipped with underwater thrusters cannot perform high-frequency forward and reverse switching due to their own performance limitations. As a result, conventional sliding mode control (CSMC) is not as effective as it could be. Scholars have proposed many methods to tackle the chatter problem in CSMC. To effectively mitigate the chatter effect, [PERSON] et al. [12] developed a fractional sliding mode robust controller. [PERSON] et al. [13] presented a second-order sliding mode control scheme based on a double-loop structure, which incorporates the dynamic characteristics of the rudder actuators to adjust the boundary layer thickness of the sliding mode using dynamically boundary layer to achieve an anti-chatter effect. The composite sliding mode speed control (CSMCC) proposed by [PERSON] et al. [14] consists of a novel fast law-based sliding mode control (FRL-SMC) scheme combined with an expansion state observer (ESO). In particular, the FRL-SMC scheme can resolve the contradiction between response speed and chatter amplitude in sliding mode control effectively. [PERSON] et al. [15] investigated an event-triggered fixed-time integral sliding mode control scheme to design an adaptive fixed-time sliding mode control scheme for AUVs, which ensures good anti-disturbance and trajectory tracking capabilities of the system. Although SMC has been improved by several methods, the state of the ROV control system still suffers from a conflict between chatter amplitude and convergence time on the sliding mode surface. The external disturbances of an ROVs are time-varying and difficult to characterize using specific mathematical methods.