## 1 Introduction  
The aquaculture industry plays a significant role in Japan's economy and food security. However, the fisheries industry has been facing the challenge of decreasing resources, the deterioration of the marine environment, soaring fuel prices, aging fishers, and a shortage of manpower. The total production of the fishery industry has dropped to around 33% of its peak after being faced with these challenges [1]. Various initiatives are underway to revitalize and rejuvenate the industry through the use of technology. It is expected that the demand for aquaculture produce is going to grow with the increasing population worldwide. Such a situation also necessitates stricter requirements for water quality observation. As an important technical contribution, much related research and development work has already been carried out on USVs (unmanned surface vehicles). [PERSON] et al. conducted a performance test on a USV, and it has performed well in collecting underwater vegetation data, even when disturbed by several factors such as wind speed and tidal condition [2]. Many other different types of USV have been developed for the detection of hydrological data [3, 4]. For the positioning accuracy problem, [PERSON] et al. also tested their solutions [5]. However, there are still few water quality observation ships that can adapt to such a large area such as an aquaculture farm, and can carry out long-term high-intensity observation work with good maneuverability. Therefore, [PERSON] et al. independently researched and developed an innovative maritime navigation vessel, the Quadmaran vessel, and [PERSON] et al. developed the automatic motion control system [6]. Automated monitoringvessels are a good solution to overcome the tedious task of surveying and measuring water quality parameters in the aquaculture farms. Water quality observation at aquaculture farms using this Quadmaran vessel has been conducted in earnest [7; 8]. The Quadmaran vessel has four hulls, and these hulls can rotate independently. This hull configuration makes it easier to stabilize the vessel at a fixed point and achieve Dynamic Positioning (DP). It is easier to maneuver the vessel with even a slight turn in sea areas with various obstacles, as aquaculture farms often have. The unique hull configuration also makes the DP controls much more straightforward than the traditional generalship methods [9]. The DP control system has also been successfully developed based on providing appropriate thrust to the four thrusters according to the position information [10]. From the test results conducted in recent years, it performed very well even in weather conditions with winds of around 5 m/s. The Quadmaran vessel provides reliable technical support for high-precision water quality monitoring in the aquaculture industry. The quality and reliability of the collected data depends directly on the DP system, and therefore studying the vessel motion during DP is important to improve precision. It is necessary to predict the motion of the vessel during DP. Research on DP for ships has been conducted for more than 40 years, and great effort has been put into it. A detailed survey was conducted regarding the important achievements of DP [11]. Following this, new control algorithms, such as nonlinear model predictive controls, were proposed and proven effective [12]. [PERSON] et al. also developed software to analyze the performance of a ship's DP under various environmental conditions [13]. Regarding the algorithm of thrust distribution, [PERSON] et al. proposed considerations based on fluid force interference [14]. However, most of these are targeted at large general vessels, and there are limited studies on the DP models for small multi-hull vessels such as the Quadmaran. This paper aims to better understand the motion status of a small observation ship with four hulls during DP.