## 2 Bio-Inspired Mechanisms Used in Locomotion
### Sperm Flagella  
Animal sperms are the motile male reproductive cells. The motile sperms have a beating tail-like flagellum to propel through fluids. A human sperm cell beats at a frequency of 10-30 Hz, which varies depending on the environmental conditions [81]. Human sperm also have a swimming velocity of around 50 \(\upmu\)m/s, a beat amplitude of around 5 \(\upmu\)m, and a beat wavelength of about 12 \(\upmu\)m [82]. The fluid regime encountered for sperm propulsion is in the low Reynolds domain. Because the low Reynolds number in their environment renders reciprocal motion inefficient, such microscale creatures require a specific approach to move to positions in fluids [83]. The swimming tactics of microorganisms are based on helical rotation with more than one degree of freedom and a time-reversal asymmetry. Thus, a complex helical motion is achieved through flagella to generate traveling waves. These waves are of two main types, helical traveling waves, and planar traveling waves [84]. With the increase of fluid viscosity, the tail of the sperm cell can switch from a planar waveform to a helical waveform [35].  
The shape and propulsive performance of the tail depend on viscous forces and bending forces. Sperm number \(Sp=L(\xi_{\perp}\omega/A)^{1/4}\) can be used to describe the relative magnitudes of these forces. Here, \(L\), \(\xi_{\perp}\), \(\omega\) and \(A\) are the length, transverse viscous drag, angular frequency of the driving action, and bending stiffness of the flexible tail respectively. Transverse viscous drag can be calculated using \(\xi_{\perp}=4\pi\mu/[\log(2L/d)\ +\ C]\), where \(\mu\) is dynamic viscosity, \(d\) is tail diameter and \(C\) is a constant (0.5 often used). The bending stiffness of the flexible tail can be calculated using \(A=EI\), where \(E\) is Young's modulus and \(I\) is the second moment of inertia of the tail [35]. When \(Sp\ll 1\), bending forces dominate and the motion of the tail is almost reciprocal, which results in negligible swimming speeds. Conversely, when \(Sp\gg 1\), viscous forces dominate and the amplitude of the motion of the tail is reduced, causing inefficient swimming [85]. In nature, sperms have a \(Sp\sim 7\)[86]. However, the propulsion of a flexible filament in a fluid has been optimized at \(Sp\sim 1\)[87].  
Sperm-shaped microrobots are fabricated to study their swimming performances. Out-of-plane wobbling of the magnetic head of a robotic sperm has been used for helical wave propagation while in-plane wobbling has been used for planar wave propagation as shown in Figure 4[88]. A flexible nanowire with a nickel head and a porous silver tail was propelled under a combination of rotating and gradient magnetic fields [89]. Similarly, a nanowire with a gold head and a nickel tail connected using a porous silver link was also controlled using a rotating magnetic field [90]. An oscillating magnetic field and a closed-loop control system with a feature tracking algorithm were also used to propel sperm-shaped microrobots [91]. In addition, a soft microrobotic sperm is used to study the effect of the concentration of the immersed particles in a viscous heterogeneous medium, on propulsion of the robot. It was experimentally proven that the speed of the microrobot increases in a small range of particle concentration [92]. The motion of sperm was mimicked by using a head created using the accumulation of iron oxide nanoparticles and a tail created by dissolving polystyrene in dimethyl formamide [84]. Apart from that, sperms were coated with magnetic nanoparticles and experimented with using an external magnetic field [93; 94].