Limbless organisms like snakes can navigate nearly all terrain. In particular, desert-dwelling sidewinder rattlesnakes (C. cerastes) operate effectively on inclined granular media (like sand dunes) that induce failure in field-tested limbless robots through slipping and pitching. Our laboratory experiments reveal that as granular incline angle increases, sidewinder rattlesnakes increase the length of their body in contact with the sand. Implementing this strategy in a physical robot model of the snake enables the device to ascend sandy slopes close to the angle of maximum slope stability. Plate drag experiments demonstrate that granular yield stresses decrease with increasing incline angle. Together these three approaches demonstrate how sidewinding 1 arXiv:1410.2945v1 [physics.bio-ph] 11 Oct 2014 with contact-length control mitigates failure on granular media.The majority of terrestrial mobile robots are restricted to laboratory environments, in part because such robots are designed to roll on hard flat surfaces. It is difficult to systematically improve such terrestrial robots because we lack understanding of the physics of interaction with complex natural substrates like sand, dirt and tree bark. We are thus limited in our ability to computationally explore designs for potential all-terrain vehicles; in contrast, many of the recent developments in aerial and aquatic vehicles have been enabled by sophisticated computationaldynamics tools that allow such systems to be designed in silico (1).Compared with human-made devices, organisms such as snakes, lizards, and insects move effectively in nearly all natural environments. In recent years, scientists and engineers have sought to systematically discover biological principles of movement and implement these in robots (2). This "bioinspired robotics" approach (3) has proved fruitful to design laboratory robots with new capabilities (new gaits, morphologies, control schemes) including rapid running (2, 4), slithering (5), flying (6), and swimming in sand (7). Fewer studies have transferred biological principles into robust field-ready devices (4, 8) capable of operating in, and interacting with, natural terrain.Limbless locomotors like snakes are excellent systems to study to advance real-world allterrain mobility. Snakes are masters of most terrains: they can move rapidly on land (9, 10) and through water (11), burrow and swim through sand and soil (12), slither through tiny spaces (13), climb complex surfaces (14), and even glide through the air (15). Relative to legged locomotion, limbless locomotion is less studied, and thus broad principles which govern multi-environment movement are lacking. Recently developed limbless robotic platforms (5), based generally on the snake body plan, are appealing for multi-functional robotics study because they are also capable of a variety of modes of locomotion. These robots can traverse confined spaces, climb trees and pipes, and potentially dive through loose material. However, 2 the gaits that carry these robots across fir...

Anuran jumping is one of the most powerful accelerations in vertebrate locomotion. Several species are hypothesized to use a catapult-like mechanism to store and rapidly release elastic energy, producing power outputs far beyond the capability of muscle. Most evidence for this mechanism comes from measurements of whole-body power output; the decoupling of joint motion and muscle shortening expected in a catapult-like mechanism has not been demonstrated. We used high-speed marker-based biplanar X-ray cinefluoroscopy to quantify plantaris muscle fascicle strain and ankle joint motion in frogs in order to test for two hallmarks of a catapult mechanism: (i) shortening of fascicles prior to joint movement (during tendon stretch), and (ii) rapid joint movement during the jump without rapid muscle-shortening (during tendon recoil). During all jumps, muscle fascicles shortened by an average of 7.8 per cent (54% of total strain) prior to joint movement, stretching the tendon. The subsequent period of initial joint movement and high joint angular acceleration occurred with minimal muscle fascicle length change, consistent with the recoil of the elastic tendon. These data support the plantaris longus tendon as a site of elastic energy storage during frog jumping, and demonstrate that catapult mechanisms may be employed even in sub-maximal jumps.

SUMMARY Animals moving through arboreal habitats face several functional challenges, including fitting onto and moving on cylindrical branches with variable diameters and inclines. In contrast to lizards and primates, the arboreal locomotion of snakes is poorly understood, despite numerous snake species being arboreal. We quantified the kinematics and performance of corn snakes (Elaphe guttata) moving on seven cylinders (diameters 1.6–21 cm) with five inclines (horizontal, ±45° and±90°) and through horizontal tunnels of corresponding widths. When perches were inclined at either 45° or 90°, snakes were unable to move uphill or downhill on the larger diameters. None of the locomotion on perches conformed to any previously described mode of limbless locomotion. On horizontal and uphill perches snakes performed a variant of concertina locomotion with periodic stopping and gripping. When moving downhill, snakes often slid continuously while grasping the perch to reduce their speed. Mean forward velocity decreased both with increased incline and with increased perch diameter, contrary to the beneficial effect of increased diameter on the speeds of lizards. Both tunnel width and perch diameter had widespread and similar effects on kinematics. When perches and tunnels were narrower, the snakes had more lateral bends at shallower angles. The numerous effects of perch diameter on kinematics and the similarity to tunnel concertina locomotion emphasize the importance of fit as a limitation in arboreal locomotion of snakes. However, the slower speeds on horizontal perches compared to tunnels also suggest that balance and grip may further limit locomotor performance.

Many organisms move using traveling waves of body undulation, and most work has focused on single-plane undulations in fluids. Less attention has been paid to multiplane undulations, which are particularly important in terrestrial environments where vertical undulations can regulate substrate contact. A seemingly complex mode of snake locomotion, sidewinding, can be described by the superposition of two waves: horizontal and vertical body waves with a phase difference of ±90°. We demonstrate that the high maneuverability displayed by sidewinder rattlesnakes (Crotalus cerastes) emerges from the animal's ability to independently modulate these waves. Sidewinder rattlesnakes used two distinct turning methods, which we term differential turning (26°change in orientation per wave cycle) and reversal turning (89°). Observations of the snakes suggested that during differential turning the animals imposed an amplitude modulation in the horizontal wave whereas in reversal turning they shifted the phase of the vertical wave by 180°. We tested these mechanisms using a multimodule snake robot as a physical model, successfully generating differential and reversal turning with performance comparable to that of the organisms. Further manipulations of the two-wave system revealed a third turning mode, frequency turning, not observed in biological snakes, which produced large (127°) in-place turns. The two-wave system thus functions as a template (a targeted motor pattern) that enables complex behaviors in a high-degree-offreedom system to emerge from relatively simple modulations to a basic pattern. Our study reveals the utility of templates in understanding the control of biological movement as well as in developing control schemes for limbless robots.sidewinder | biomechanics | robotics | template | control P ropagating waves of flexion along the axis of a long, slender body (henceforth "axial waves") to produce propulsion is common in biological locomotion in aquatic and terrestrial environments. The majority of biological studies of axial wave propulsion at different scales have occurred in aquatic environments (1, 2). Understanding the efficacy of given wave patternswhich are often assumed to act in a single plane (e.g., mediolateral axial bending)-can be gained through full solution of the equations of hydrodynamics (3) or approximations (4). Terrestrial environments such as sand, mud, and cluttered heterogeneous substrates encountered by limbless axial undulators such as snakes can display similar (if not greater) complexity, yet far less attention has been paid to such locomotion (5, 6).Snake axial propulsion in terrestrial environments differs from fluid locomotion in two key ways. First, most substrates are not yet described at the level of fluids (7), making it a challenge to understand how substrate-body interactions affect locomotor performance, and therefore requiring robotic physical models. Second, the body may be both laterally and/or dorsoventrally flexed (5) to allow different elements of the body to contact ...