## 3 Adhesion Performance
### Peeling Test  
A peeling strength analysis is performed according to the [PERSON]'s peeling model [28]:  
\[{(\frac{F}{b})}^{2}\frac{1}{2 Ed}+(\frac{F}{b})(1-\cos\theta)-R=0 \tag{1}\]  
where \(F\) is the peeling force, \(d\) is the thickness of the adhesive, \(b\) is the width of the adhesive, \(E\) is the Young's modulus of the adhesive, \(\theta\) is the peeling angle, and \(R\) is the energy required to fracture a unit area of interface.  
[PERSON]'s peeling model demonstrates that peel strength increases with increasing Young's modulus of the backing layer. When the PVS is peeled off from a substrate, fibrills are stretched and deformed until the tension stress surpasses the pull-off stress. Under this condition, detachment  
Figure 3: **(a)** Image of the setup used to measure the pull-off force; **(b)** The pull-off force measured between mushroom-shaped adhesive microstructure (MSAMS) and glass as a function of load at different load velocities.  
is started. For the fibrillar surface, the stretching velocity of the fibril influences the resulting peel force [29]. Previous studies have shown that the relationship between the peel force and the peel velocity at the same peel angle can be described by [30; 31; 32]  
\[\frac{F}{b}=kV^{n} \tag{2}\]  
where \(k\) is a function of the peel angle and is related to the thickness of the adhesive, \(V\) is peel velocity, and \(n\) is a constant related to the intrinsic properties of the adhesive: this parameter is often called adhesive energy.  
Our testing platform was set up to estimate the effect of peel velocity and the thickness of the adhesive on the peel strength (Figure 4). Pieces of the MSAMS dry adhesive (20 mm \(\times\) 100 mm) with different thickness of backing layer (Polyvinyl chloride plastic) were attached to a smooth glass surface (average roughness \(Ra\) = 3.2 \(\pm\) 1.9 nm) and preloaded with different weights. The peel angle was adjusted by fixing the glass surface at various tilted angles. Different peel velocities are obtained by changing the loading weights.  
A linear relationship is found between the peel strength and the peel velocity in the log-log plot. Peel strength keeps increasing while thickness of the backing layer increases. The slopes of the four curves are almost the same, indicating that the physical properties of the adhesive are identical, while the differences between the intercepts indicate the different stiffness of the backing layer. The results agree with the experimental results obtained by [PERSON] et al. [31] and [PERSON] et al. [33]. When the thickness of the backing layer is varied, the stiffness of the backing layer is changed, resulting in the increasing of the peel strength as stiffness increasing up until a saturation point (Figure 5). For the robot's footpad, the backing layer is indispensable, because of the stronger peeling strength. Thin backing layer effects not only in low peeling strength, which might be advantageous for contact breakage, but also in strong toe deformation during contact formation, which might prevent proper contact formation.  
Figure 4: Results of the peeling test. (**a**) Schematic diagram of the peeling experiment; (**b**) The relationship between peel strength and peel velocity at a peeling angle of 30\({}^{\circ}\) with different thicknesses of backing layer in log-log coordinates.