# Granular Media Friction Pad for Robot Shoes--Hexagon Patterning Enhances Friction on Wet Surfaces
## 1 Introduction  
Generating large friction forces on unknown substrate geometries requires high adaptability when approaching the substrate, combined with high energy dissipation when applying transversal load. This is why we recently proposed the granular media friction pad (GMFP) as a potential universal solution for friction enhancement on a wide range of substrates [1]. The GMFP consists of a thin elastic membrane encasing granular material, such as sand, metal powder, plant seeds, etc. When applying load to the GMFP, the granular medium undergoes the jamming transition [2; 3]. The result of this is fluid-like behavior [4; 5] of the GMFP, when unloaded or approaching the substrate topography (see Figure 1a), and solid-like behavior, when pressed against the substrate (see Figure 1b). Friction forces are generated by the mechanical interlocking of the now solid-like granular material and the substrate asperities, as well as by high internal friction of the granular media [6; 7; 8; 9; 10; 11]. When taking away the normal load and pushing the GMFP onto the substrate, the granular filling becomes fluid-like again, enabling easy removal from the substrate without requiring high pull-off forces. In addition to this, the thin elastic encasing membrane holding the loosely filled granular material can create large contact areas with the substrate, contributing to the total resulting friction force by adhesion-mediated friction [12; 13; 14] and by elastic deformation of the soft membrane. In contrast to previous systems employing the jamming transition to create friction or holding forces [4; 15; 16; 17; 18; 19; 20], no active control mechanism (such as the application of a vacuum to control the jamming transition) is needed. While the GMFP can adapt to a large variety of substrate topologies and form around contaminating particles embracing them [21], this type of structure would probably fail onwet substrates due to its extremely smooth membrane [22; 23; 24] and the resulting hydrodynamic lubrication when sliding over a substrate. In nature, numerous animals live in moist or wet environments, but are still able to get a stable grip for secure attachment and locomotion [25]. For a large variety of these animals, a convergent solution appeared in the course of biological evolution to achieve this: microstructuring their attachment pad surface [26; 27] with mostly hexagonal arrays of channels, as seen, e.g., in a large diversity of frogs [25; 26; 28], in bush crickets [27; 29], stick and leaf insects [30], and salamanders [31; 32]. The microstructure not only helps in spreading secretory fluid over the whole attachment pad for adhesion enhancement, but also to remove surplus fluids and enable intimate contact with the substrate [25; 33; 34] when gripping but also while sliding. This principle has been adapted in several biomimetic studies both for similar dimensions [22; 26; 27; 32; 35] as well as for much larger structures, such as those in the tire industry [27; 36; 37; 38]. While microstructuring of a surface is highly effective for draining fluids and to enable high friction forces on smooth substrates, a second principle can be observed in nature in conforming to wet (or rough) substrates to enhance contact area for friction [39]: The microstructured attachment pads feature a complex superstructure inside, which results in extremely soft attachment pads. This can be done actively [40; 41; 42] or passively by design [25; 29; 33; 39; 43; 44]. In this study, we combine the structuring of the membrane with extreme softness and adaptability by enhancing the membrane surface with a hexagon pattern. An increase in friction on wet substrates is expected, while maintaining fluid-like behavior when approaching a rough or contaminated substrate to maximize the contact area. We investigate  
Figure 1: Granular media friction pad (GMFP).