# Study on Oscillatory and Undulatory Motion of Robotic Fish
## 1 Introduction  
The ocean is a vital source of resources for society, with the demand for seawater, minerals, and biological resources surpassing that of land. The scientific community aims to explore and utilize the ocean safely and effectively [1]. Modern multipurpose submernsibles can operate at various depths, from shallow to oceanic. New development goals focus on optimizing performance, addressing complex hydrodynamic effects like swimming and noise control, drawing inspiration from underwater animals [2]. In contrast to traditional submarines, fish have evolved to use oscillatory motions, providing high thrust, excellent maneuverability, and low noise levels in the flow field. The study also illustrates the ability of aquatic animals to sense complex underwater environments. Research in fish biology, inspired by nature and the design of fish robots, plays a crucial role in developing the next generation of submarines [3, 4].  
While extensive research has been conducted in related fields, numerous scientific and technological challenges persist. Computational fluid dynamics (CFDs) serve as a key tool to bolster experimental research but face notable issues, particularly the demand for substantial computational resources [5]. The fish's propulsion ability arises from the coordinated action of muscle groups, facilitating even weight distribution across the body and an efficient movement structure that conserves space. These fluid recognition systems empower aluminum foils to discern turbulence information within the flow field, effectively harnessing energy to enhance efficiency. In conventional simulation studies, the observation of vortex shedding in fluid flow often involves a simplified representation of stationary objects due to the intricate nature of fluid dynamics [6]. However, in thisparticular investigation, a novel approach is taken, where the fluid flow is simulated through a dynamically moving object. This unique methodology aims to provide insights into and support the design of the streamlined shape for robotic fish.  
Swimming, a phenomenon deeply ingrained in the evolutionary tapestry of nature, continues to captivate the scientific and engineering communities [7,8]. Fish swimming, in particular, has been a subject of keen interest, offering profound insights into the optimization of underwater vehicles and biomimetic robots. The kinematic equation of motion is a key focus area, where advanced equations of motion control, particularly in oscillation and undulation, are leveraged to conduct fluid dynamics calculations. This approach aims to unravel the underlying physics governing fish movements [9,10]. This interdisciplinary exploration promises to provide valuable insights into the fluid dynamics and kinematics of fish-inspired swimming. The knowledge gained has the potential to impact the optimization of underwater vehicles and inspire advancements in biomimetic robotic systems. This research embarks on a computational journey to explore the intricacies of fish-inspired swimming, focusing on two fundamental forms of motion: undulatory and oscillatory. The aims of this study are as follows:  
* Utilize the equations of motion control (oscillation and undulation) for fluid dynamic calculations.
* Develop the model's shape and control the movement approach to aid in reaching the desired fish swimming at high speed.  
The rest of this paper is organized as follows: mathematical modeling of the oscillatory and undulatory motion is presented in Section 2; computer simulation of the drag force of the fish model is presented in Section 3; and conclusions are presented in Section 4.