# Bioinspired Kirigami Structure for Efficient Anchoring of Soft Robots via Optimization Analysis
## 3 Results and Analysis
### Kirigami Cuts Density vs. Craving Distance
#### 3.3.2 Performance Analysis  
Figure 6a illustrates the relationship between kirigami cut density and crawling distance for both triangular and trapezoidal patterns. The experimental results reveal a nonlinear trend, indicating that increasing cut density initially enhances crawling performance up to an optimal point, after which further increases lead to degradation. Among the tested samples, the 4 \(\times\) 20 triangular kirigami configuration achieved the highest crawling distance of 74 mm, followed by 65 mm for the trapezoidal counterpart. This performance peak is attributed to an optimal balance between unit spacing and surface interaction. At this density, individual kirigami units have sufficient room to buckle vertically, achieving a favorable pop-up height while maintaining effective contact with the surface. This combination enhances anisotropic friction and enables forward propulsion. In contrast, both lower and higher densities resulted in reduced crawling performance. For instance, the 2 \(\times\) 14 configuration exhibited limited surface interaction due to fewer anchoring units and limited deformation engagement with the surface, achieving only 55 mm (triangular) and 48 mm (trapezoidal) of crawling distance. Although the 3 \(\times\) 15 configuration showed modest improvement (61 mm and 54 mm), the performance dropped notably in the 5 \(\times\) 28 and 6 \(\times\) 28 configurations, with crawling distances decreasing to 42-44 mm and further to 34-36 mm, respectively. The primary cause of reduced crawling performance at higher cut densities can be attributed to two interrelated factors. First, although individual kirigami units do deform across all tested configurations, the buckling height notably decreases in samples with smaller and more densely packed cuts. This lower vertical deformation limits the  
Figure 5: Average crawling distance of the robot for PET sheets with triangular and trapezoidal patterns of varying thickness. capacity of each unit to generate the anisotropic friction necessary for effective surface anchoring. As a result, despite undergoing buckling, these compact units fail to produce enough vertical engagement with the substrate, weakening their contribution to forward propulsion. Secondly, overcrowding from excessive unit density reduces the effective interaction area between the kirigami skin and the surface. With less spacing between adjacent units, the deformation of kirigami units may interfere with its nearby units, diminishing the structure's ability to conform and grip the surface effectively. This leads to less consistent contact and reduced anchoring force per unit during the actuation cycle. Collectively, these two effects--lower pop-up height and compromised surface engagement--cause diminished frictional force and, consequently, reduced locomotion efficiency at high cut densities. To further validate these findings, we conducted frictional force analysis using a friction measuring setup (Section 2.2). As shown in Figure 7, the 4 \(\times\) 20 configuration exhibited the highest stick-slip friction peaks (\(\sim\)3 N). In contrast, 5 \(\times\) 28 and 6 \(\times\) 28 configurations demonstrated lower peak values, confirming that excessive density reduces frictional effectiveness. Figure 6b includes side-by-side deformation images of  
Figure 6: Influence of kirigami unit density on crawling performance and deformation characteristics. (**a**) Crawling distance comparison for triangular and trapezoidal kirigami skins across five different unit densities. The lower part is schematic illustrations of triangular kirigami patterns for each density, and at corresponding bars are experimental results for triangular and trapezoidal skins. (**b**) Experimental images of actuated triangular kirigami skins corresponding to the densities showing the pop-up deformation behavior. kirigami samples at each density, clearly demonstrating the decreasing buckling amplitude and effective contact area.