# Magnetically Deployable Robots Using Layered Lamina Emergent Mechanism
## 1 Introduction
### Biomimetic Locomotion  
Biomimetic locomotion patterns are often inspired by worms and annelids, which rely on friction to generate directed motion. These biomimetic locomotion patterns include peristaltic, inchworm and stick-slip. Peristaltic motions are the more commonly incorporated worm-like locomotion patterns. By incorporating various actuation methods and designs, research teams have mimicked and adapted certain movement features by studying earthworms. For example, [PERSON] [7], [PERSON] [11], and [PERSON] [19] have attempted to create radial contraction and expansion mechanisms that underlie peristaltic motions by using shape memory alloys (SMA) or dielectric elastomers, which can be designed to respond in a specific manner in terms of shape or length upon applying voltage. The biomimetic crawler created by [PERSON] [11] achieved peristaltic motion using an SMA spring that contracts under heat. The mechanism has a silicone shell with microhooks embedded in the shell to mimic setae by providing anchor points. [PERSON] [7] reports a meshworm that incorporates a braided mesh-tube structure, wrapped around by nickel-titanium (NiTi) coil SMA actuators, which act as contracting \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Acuation** & \multicolumn{2}{c}{**Characteristics**} & **Advantages** & **Disadvantages** \\ \hline Smart memory alloys & \(\bullet\) & Activated by heating (e.g., electric current) & Light [6], flexible [7], simple control [8], large energy density per cycle, and high mass-specific force [1] & Slow cycle frequency due to cooling [9], small force/stroke generated per cell [10], low controllability [11] \\ \hline Dielectric elastomer (DEA) & \(\bullet\) & Activated by electric current. Operation range: 40\% strain/stroke & Large strain capability with high energy density, simple control [5], good stiffening capability and scalability [12] & Lower output force, high driving voltage, reliant on compliant electrodes [13], short lifetime \\ \hline Pneumatic & \(\bullet\) & Actuated by pressureed air & \(\bullet\) & Great speed and power density, resilient to adverse external conditions with silicone body, scalable, less complex to produce & Challenge in containing high actuating pressure, short lifespan [14], hard to control due to non-linear system dynamic [15], complex supply system \\ \hline Motors & \(\bullet\) & Traditional motor designs use stiff joints and components & \(\bullet\) & High actuation speed [9], efficient, easy to control & Bulky and complicated mechanism, difficult for miniaturization, structural stiffness \\ \hline Magnetic & \(\bullet\) & Operation range: 15-25\% strain/stroke [16] & \(\bullet\) & Can achieve high power density when printed on soft materials. Untethered, EM actuators have high response speed and simple control [17] & Low-energy conversion [14], magnetic interference, magnetic actuators with permanent magnets have low controllability [18] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of actuators used in literature for compliant mechanisms. muscles. The use of SMA coils as contracting muscles is also found in the designs of other soft mechanisms reported in [10; 19; 20]. [PERSON] [21], [PERSON] [22], and [PERSON] [23] relied primarily on the axial expansion of the designed structures, with additional frictional features to achieve peristaltic-inspired forward movement. [PERSON] [21], in particular, designed a pneumatically actuated earthworm-inspired mechanism with a kirigami skin to provide traction that anchors the mechanism's head and tail during movement. The pneumatically actuated earthworm-inspired mechanism by [PERSON] [22] is modeled as a double-mass-spring damper that can vary frictional forcers at its extreme ends. [PERSON] [24] and [PERSON] [25] also employ designs and mechanisms inspired by earthworms using motors and motion transferring mechanisms to recreate the peristalsis motion for colonoscopy applications.