# Bioinspired Kirigami Structure for Efficient Anchoring of Soft Robots via Optimization Analysis
## 1 Introduction  
The field of soft robotics has emerged as a transformative domain in automation, offering compliance, adaptability, and resilience to navigate unstructured and constrained environments--capabilities that rigid robotic systems often lack [1, 2, 3]. Among nature's most efficient movers, snakes exhibit remarkable terrain adaptability, navigating tight crevices or uneven surfaces using a repertoire of locomotion strategies such as rectilinear progression and lateral undulation [4, 5, 6]. Central to their locomotion efficiency is the anisotropic friction generated by ventral scales, which provide directional anchoring and propulsion with minimal energy expenditure [4, 7]. These scales interlock with ground asperities and generate higher resistance to backward or lateral motion than forward, as experimentally shown by [PERSON] et al. [4], who quantitatively modeled how belly scale anisotropy enables effective slithering on flat terrain. Drawing inspiration from biomechanical principles, researchers have sought to emulate this anchoring capability in soft robotic platforms, targeting applications such as confined space navigation, biomedical systems, and terrain-adaptive exploration where traditional robots are not an appropriate option [8; 9; 10; 11]. One promising approach involves the use of kirigami, the ancient art of patterned cuts in thin sheets--reimagined as a tool to engineer deformable surfaces with tunable mechanical and frictional properties to engage the surface in a scale-like fashion [12; 13; 14]. The morphological diversity found in reptilian scales offers a bioinspired template for the design of kirigami skins capable of controlled deformation and surface interaction. In this study, five distinct kirigami patterns are explored to optimize anchoring behavior: linear cuts that provide minimal frictional interaction but maintain structural stability; triangular cuts inspired by the sharp-edged ventral scales of Purff Adders, enhancing anisotropic friction and grip; trapezoidal patterns derived from the whiptail lizard, offering a balance between flexibility and mechanical support; and two hybrid variants, linear-triangular and linear-trapezoidal, that combine stability with directional anchoring features [6; 15; 16; 17; 18]. These structures enable tunable anisotropic friction under compression, echoing the engagement-release anchoring mechanics observed in snakes during slithering and concertina locomotion [19]. Prior implementations of kirigami-based soft robotic systems have commonly relied on pneumatic actuation to induce the necessary buckling deformation for locomotion. However, these systems often suffer from bulk, noise, and the need for sealed chambers and external pumps, limiting their compactness and autonomy [20; 21]. This study utilizes a permanent magnet (PM) linear actuator as the actuation source. This actuator provides a silent, energy-efficient, and compact solution, enabling controlled axial compression and repeatable deformation cycles of the kirigami skin [22; 23]. Overall, this work is to optimize the anchoring performance of a kirigami-based soft robotic crawler through systematic variation of both structural and actuation parameters. Anchoring efficiency is assessed via crawling distance, stride efficiency, and net propulsive force under varying conditions of cut geometry, PET sheet thickness, cut density, actuator stroke, and actuation speed. The combination of experimental testing with analytical modeling allows for a comprehensive investigation of how geometric and mechanical factors contribute to effective directional anchoring. To support the design process, a theoretical model is developed that integrates classical buckling mechanics with a friction-based analytical framework, enabling prediction of pop-up height and anisotropic friction forces. This dual perspective offers not only validation of observed results but also a foundation for further optimization of kirigami-based anchoring systems.