# Numerical Simulation and Analysis of Fish-Like Robots Swarm
## 1 Introduction  
The multi-robot control has been a topic of broad interest in recent years. A single robot with multiple capabilities cannot necessarily accomplish an intended job, whereas robots in a robot swarm in which each robot with its own functions, can be more flexible, robust, cost-effective and do complex tasks [1]. Some literature [2; 3; 4] focuses on the collaborative multi-robot studies, including the coordination and control techniques, the communication among robot groups, mapping and localization as well as the architecture of the multi-robot system. Other studies [5; 6] are concerned with certain collaborative missions, such as box-pushing, formatting and rescue. In addition, some studies [7; 8] focus on heterogeneous robots swarm which is capable of performing user-defined tasks. Based on the analysis of existing robots swarm systems [1], researchers designed the hardware architecture [9; 10] and software environment [11] of robot swarms, which enables land robots to handle various tasks in unknown or dynamic environments. Formation control is also a research direction of swarm robots [12; 13; 14; 15]. Underwater robot swarms, unlike air or land robots, can hardly maintain their formation through communication [16]. Besides, in the underwater environment, the velocity of fluids, viscosity of fluids, the complex geometry environment condition and even the interaction between robots can change the underwater robots swarm behaviors. Therefore, it is necessary to figure out a stable and efficient formation of underwater robots swarm. At present, many researchers use numerical simulation methods to study underwater robots, avoiding the limitations of experimental conditions. Furthermore, this method can provide a more intuitive hydrodynamic phenomenon, which can provide guidance for the shape design and control of the underwater robots [17; 18; 19]. There is evidence to show that fish-like underwater robots have better motion ability [20; 21; 22; 23]. The research on the formation of underwater robots is mostly based on fish-like robots. [PERSON] [24] proposes a hydrodynamic theory of schooling that a fish in a diamond school swimming between two adjacent fish wakes can save energy. [PERSON] et al. [25], through employing reinforcement learning, adjust swimming motions and relative positions to reach a stable tandem configuration, at the same time the follower swimmer can reduce energy. [PERSON] et al. [26] establish optimal undulatory propulsion for a single fish by numerical simulation and find that the follower fish saved energy at any position as it can appropriately modulate its body motions according to the oncoming vortices. [PERSON] et al. [27] show that the phalanx pattern of swimming animals can be a strategy to optimize swimming performance. [PERSON] et al. [28] discuss several kinds of coordinated swimming patterns and the results show that through deep reinforcement learning autonomous swimmers can exploit unsteady flow fields to swim efficiently. [PERSON] at al. [29] find that multiple kinds of fish school formations can keep stable by hydrodynamic interactions alone. The above studies provide many good ideas and algorithms for the control of fish-like robots swarm and propose some efficient fish-like robot formations. However, these studies adopt different geometric models, kinematic models, and hydrological environments, but do not reach a unified conclusion on the efficiency of fish-like robots swarm. Thus, it is difficult for them to provide much guidance on how to select the efficient fish-like robot formation configuration under specific conditions. Therefore, this paper studies the influence of changing swarm configuration on multiple fish-like robots based on the same geometric model, kinematic model, and hydrological environments. To be specific, the main contributions are summarized as follows:  
* Efficiency savings are simulated by changing the formation of the fish-like robots swarm and the spacing between fishes.