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Abstract When terrestrial organisms locomote in natural settings, they must navigate complex surfaces that vary in incline angles and substrate roughness. Variable surface structures are common in arboreal environments and can be challenging to traverse. This study examines the walking gait of katydids (Tettigoniidae) as they traverse a custom-built platform with varying incline angles (30○, 45○, 60○, 75○, 90○) and substrate roughness (40, 120, and 320 grit sandpaper). Our results show that katydids walk more slowly as the incline angle increases and as katydid mass increases, with a decrease of around 0.3 body lengths per second for every 1○ increase in incline. At steeper inclines and larger sizes, katydids are also less likely to use an alternating tripod gait, opting instead to maintain more limbs in contact with the substrate during walking. Katydids also increased average duty factor when climbing steeper inclines and with increasing body mass. However, substrate roughness did not affect walking speed or gait preference in our trials. These findings provide insights into how environmental factors influence locomotor strategies in katydids and enhance our understanding of effective locomotor strategies in hexapods. 

Self-propelling organisms locomote via generation of patterns of self-deformation. Despite the diversity of body plans, internal actuation schemes and environments in limbless vertebrates and invertebrates, such organisms often use similar traveling waves of axial body bending for movement. Delineating how self-deformation parameters lead to locomotor performance (e.g. speed, energy, turning capabilities) remains challenging. We show that a geometric framework, replacing laborious calculation with a diagrammatic scheme, is well-suited to discovery and comparison of effective patterns of wave dynamics in diverse living systems. We focus on a regime of undulatory locomotion, that of highly damped environments, which is applicable not only to small organisms in viscous fluids, but also larger animals in frictional fluids (sand) and on frictional ground. We find that the traveling wave dynamics used by mm-scale nematode worms and cm-scale desert dwelling snakes and lizards can be described by time series of weights associated with two principal modes. The approximately circular closed path trajectories of mode weights in a self-deformation space enclose near-maximal surface integral (geometric phase) for organisms spanning two decades in body length. We hypothesize that such trajectories are targets of control (which we refer to as “serpenoid templates”). Further, the geometric approach reveals how seemingly complex behaviors such as turning in worms and sidewinding snakes can be described as modulations of templates. Thus, the use of differential geometry in the locomotion of living systems generates a common description of locomotion across taxa and provides hypotheses for neuromechanical control schemes at lower levels of organization. 

The small structures that decorate biological surfaces can significantly affect behavior, yet the diversity of animal–environment interactions essential for survival makes ascribing functions to structures challenging. Microscopic skin textures may be particularly important for snakes and other limbless locomotors, where substrate interactions are mediated solely through body contact. While previous studies have characterized ventral surface features of some snake species, the functional consequences of these textures are not fully understood. Here, we perform a comparative study, combining atomic force microscopy measurements with mathematical modeling to generate predictions that link microscopic textures to locomotor performance. We discover an evolutionary convergence in the ventral skin structures of a few sidewinding specialist vipers that inhabit sandy deserts—an isotropic texture that is distinct from the head-to-tail-oriented, micrometer-sized spikes observed on a phylogenetically broad sampling of nonsidewinding vipers and other snakes from diverse habitats and wide geographic range. A mathematical model that relates structural directionality to frictional anisotropy reveals that isotropy enhances movement during sidewinding, whereas anisotropy improves movement during slithering via lateral undulation of the body. Our results highlight how an integrated approach can provide quantitative predictions for structure–function relationships and insights into behavioral and evolutionary adaptations in biological systems. 

While terrestrial locomotors often contend with permanently deformable substrates like sand, soil, and mud, principles of motion on such materials are lacking. We study the desert-specialist shovel-nosed snake traversing a model sand and find body inertia is negligible despite rapid transit and speed dependent granular reaction forces. New surface resistive force theory (RFT) calculation reveals how wave shape in these snakes minimizes material memory effects and optimizes escape performance given physiological power limitations. RFT explains the morphology and waveform-dependent performance of a diversity of non-sand-specialist snakes but overestimates the capability of those snakes which suffer high lateral slipping of the body. Robophysical experiments recapitulate aspects of these failure-prone snakes and elucidate how re-encountering previously deformed material hinders performance. This study reveals how memory effects stymied the locomotion of a diversity of snakes in our previous studies (Marvi et al., 2014) and indicates avenues to improve all-terrain robots. 

Limbless animals like snakes inhabit most terrestrial environments, generating thrust to overcome drag on the elongate body via contacts with heterogeneities. The complex body postures of some snakes and the unknown physics of most terrestrial materials frustrates understanding of strategies for effective locomotion. As a result, little is known about how limbless animals contend with unplanned obstacle contacts. We studied a desert snake,Chionactis occipitalis, which uses a stereotyped head-to-tail traveling wave to move quickly on homogeneous sand. In laboratory experiments, we challenged snakes to move across a uniform substrate and through a regular array of force-sensitive posts. The snakes were reoriented by the array in a manner reminiscent of the matter-wave diffraction of subatomic particles. Force patterns indicated the animals did not change their self-deformation pattern to avoid or grab the posts. A model using open-loop control incorporating previously described snake muscle activation patterns and body-buckling dynamics reproduced the observed patterns, suggesting a similar control strategy may be used by the animals. Our results reveal how passive dynamics can benefit limbless locomotors by allowing robust transit in heterogeneous environments with minimal sensing.