# Bioinspired Kirigami Structure for Efficient Anchoring of Soft Robots via Optimization Analysis
## 2 Design, Composer, and Experimental Setup
### Composer of the Kirigami-Skinned Crawlers for Parameters Analysis
Inspired by the morphological diversity of snake scales, five distinct patterns were tested: linear, trapezoidal, triangular, hybrid linear-triangular, and hybrid linear-trapezoidal. The primary aim was to analyze how each pattern's deformation mechanics and surface contact profile contribute to directional friction and, thus, crawling performance. Bycomparing the average crawling distance over five actuation cycles, this study aims to identify the most efficient pattern for generating propulsive force (Figure 1c). 2. PET Sheet Thickness vs. Crawling Distance: In this test, the effect of substrate flexibility and stiffness on locomotion was examined by using PET sheets of varying thicknesses: 50 \(\upmu\)m (red), 100 \(\upmu\)m, 150 \(\upmu\)m, 200 \(\upmu\)m (transparent), and 250 \(\upmu\)m (green). The experiment evaluates the average crawling distance to determine the optimal balance between mechanical compliance and anchoring effectiveness, both of which are critical for reliable propulsion (Figure 1d). 3. Kirigami Cuts Density vs. Crawling Distance: To assess the impact of surface coverage and unit repetition on locomotion performance, we analyzed five different kirigami cut densities, i.e., 2 \(\times\) 14, 3 \(\times\) 15, 4 \(\times\) 20, 5 \(\times\) 28, and 6 \(\times\) 28, implemented over a standardized contact area of 51 mm \(\times\) 140 mm. In this notation, each density value M\(\times\)N represents a grid of M cut units along the longitudinal (lengthwise) axis and N units along the transverse (widthwise) axis, covering the entire kirigami sheet. This structured arrangement modulates the number, spacing, and distribution of pop  
Figure 2: Design schematic, electronic integration, and experimental setup of the kirigami-based soft crawling robot. (**a**) Schematic of the 12 V PM linear actuator (60 N thrust, 30 mm/s speed) with labeled extension/retraction strokes and dimensions. (**b**) Mechanical layout of the crawler showing bilaterally symmetric kirigami skins oriented for directional locomotion. (**c**) Wiring diagram of the control system comprising an Arduino Uno, LN298 motor driver, and 12 V battery (See text for manufacturer details), used to actuate the crawler. (**d**) Fully assembled prototype showing the integrated crawler, power unit, and control board. (**e**) Friction measurement platform using a linear stage and digital mechanical sensor, with a smartphone for synchronized data logging. (**f**) Close-up view of triangular kirigami units interacting with a polyurethane (PU) substrate. up units, thereby influencing inter-unit mechanical interference, surface anchoring behavior, and crawling performance. * By systematically varying the cut densities, we evaluated how increasing the number of units affects deformation dynamics and effective engagement with the ground surface. This approach enabled identification of an optimal density configuration that maximizes propulsion while minimizing performance losses due to structural interference. * Stroke Length vs. Crawling Distance: This test explores how actuator stroke amplitude influences the mechanical engagement of the kirigami skin with the substrate. The following four actuation protocols were examined: 10 mm (St10), 20 mm (St20), 30 mm (St30), and 30 mm with a 1-second hold before retraction (St30h1s). By measuring the crawling distance over five actuation cycles, the experiment evaluates how increased extension--combined with dwell time--affects unit deformation, surface interaction, and net displacement. * Actuation Speed vs. Crawling Distance: This experiment evaluates how different extension/retraction speeds--10/10, 15/15, 20/20, and 30/30 mm/s--influence crawling performance. Actuation speed directly affects the contact time and engagement quality between kirigami structures and the surface. By comparing average crawling distances, the test aims to determine a speed regime that optimally balances actuation dynamics with surface interaction mechanics for efficient locomotion.