## 2 State-of-the-Art
### Evolution of Projects Developed and Actuation Systems  
One of the first jellyfish prototypes, developed by the University of Kagawa (Figure 1a), used the conductive ionic polymer film (ICPF) as an actuation system [18]. It generates contractions using an articulated mechanism. The next representative development was realized by the Virginia Center of Investigation that created a jellyfish using SMA named \"Robojelly\" (2011). It has a polyethylene coverage, inspired in the Aurita Aurelia species. When the SMA is activated, it produces a reaction with the water that generates hydrogen that helps the displacement [19]. Along the same line, a jellyfish robot based on a mechanism of spring retraction was implemented (Figure 1b) [20]. It was controlled by servomotors and had a silicone body, capable of generating a unilateral contraction. Another prototype based on the same operation principle, but actuated by elastomers producing an expansion to expel the water, is presented in [21]. Within the most recent developments in 2018, the University of Atlantic Florida implemented a jellyfish operated by air microvalves, which is capable of generating a lateral movement limiting airflow to four of the eight tentacles (Figure 1c) [22]. In 2019, a jellyfish operated by SMA capable of moving vertically, thanks to a central SMA, was developed (Figure 1d) [23]. One of the last works developed is a soft jellyfish with a diameter of 3 mm actuated through an external oscillating magnetic field, capable of generating movements with a degree of vertical inclination of the body. Table 1 shows complementary information on additional related projects carried out under this same line of research [24; 25].  
Despite various developments focused on jellyfish with different performance, no great progress was made in obtaining lateral movements especially in the control algorithms. Furthermore, the implementation of control systems to generate coordinated movements through defined trajectories,  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Work** & **Acuation** & **Body Material** & **Movement** & **CFD Analysis** \\ \hline Micro robot-jellyfish (2007) [33] & ICPF & Late-polymer & Vertical & NO \\ \hline Jellyfish biomimetic & & & & \\ behavior-Simulation (2010) [34] & Lineal Actuators & HDPE & Vertical & NO \\ \hline Biomimetic jellyfish (2011) [35] & Electrical & IPMC & Vertical & NO \\ \hline Robojelly (2011) [36] & SMA &
\begin{tabular}{c} Flexible Silicon \\ and polystyrene \\ \end{tabular} & Vertical & NO \\ \hline Bioinspired jellyfish (2011) [21] & Biosynthetic & Surgical tissue & Vertical & NO \\ \hline Jellyfish-like Robot for & & & \\ mimicking propulsion (2012) [37] & Servomotors & Silicone & Vertical & NO \\ \hline Robotic jellyfish (2015) [19] & Electrical & IPMC & Vertical & NO \\ \hline Pneumatic jellyfish (2016) [20] & Pneumatic & Elastomer & Vertical & NO \\ \hline Robo-jellyfish (2018) [38] & Pneumatic & Silicone RTV & Vertical and Lateral & NO \\ \hline Jellyfish acted by & & & & \\ springs(2019) [39] & SMA & Silicone & Vertical & NO \\ \hline Biomimetic Soft Jellyfish (2019) [40] & Electro-active & & & \\ \hline Multi-functional & & & & \\ soft-bodied jellyfish-like & & & & \\ swimming (2019) [22] & & & & \\ \hline JellyRobcib & SMA & Silicone & Vertical-Lateral & YES \\ \hline \hline \end{tabular}
\end{table}
Table 1: Previous designs of jellyfishes, their actuation, materials and type of movements.  
Figure 1: (**a**) Bell-shaped mechanism that generates a contraction. (**b**) Jellyfish actuated by spring retraction. (**c**) Jellyfish act pneumatically. (**d**) Jellyfish capable of performing only vertical movements using a shape-memory alloy (SMA).  
especially using SMA, has not been emphasized enough. Additionally, previous works have not focused on specific applications for this kind of robots. These are relevant aspects that this research addresses.