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 ...

There was an error published in J. Exp. Biol. 218,[440][441][442][443][444][445][446][447][448][449][450] In Fig. 5 of this paper, there was a mistake in the theoretical calculation of the average slip angle, b s . The corrected calculations show that b s rises more sharply for low mean relative curvatures and approaches 90 deg. This change does not affect the conclusions set forth in the original paper, and shows better agreement with the experimental findings.The corrected figure is reproduced below:The authors apologise for any inconvenience this may have caused. b s ) with changing mean relative curvature (kl s ), average number of undulations along the body ( j), body length to width ratio (L/w) and effective friction. Force relationships were established from empirical drag data in loosely packed (LP) media. The color of the curves and experimental data correspond to different j (where dark blue is j=0, dark red is j=5). Solid curves are predictions for an undulatory swimmer with a L/w=7.1 and body-particle friction, m s , of 0.17. The dotted-dashed curves show the theoretical predictions with L/w=33.5 and m s =0.17. The dashed curves are the predictions for L/w=33.5 and half the tangential force (which occurs when there is a 50% decrease in body-particle friction, i.e. ABSTRACT Squamates classified as 'subarenaceous' possess the ability to move long distances within dry sand; body elongation among sand and soil burrowers has been hypothesized to enhance subsurface performance. Using X-ray imaging, we performed the first kinematic investigation of the subsurface locomotion of the long, slender shovel-nosed snake (Chionactis occipitalis) and compared its biomechanics with those of the shorter, limbed sandfish lizard (Scincus scincus). The sandfish was previously shown to maximize swimming speed and minimize the mechanical cost of transport during burial. Our measurements revealed that the snake also swims through sand by propagating traveling waves down the body, head to tail. Unlike the sandfish, the snake nearly followed its own tracks, thus swimming in an approximate tube of self-fluidized granular media. We measured deviations from tube movement by introducing a parameter, the local slip angle, β s , which measures the angle between the direction of movement of each segment and body orientation. The average β s was smaller for the snake than for the sandfish; granular resistive force theory (RFT) revealed that the curvature utilized by each animal optimized its performance. The snake benefits from its slender body shape (and increased vertebral number), which allows propagation of a higher number of optimal curvature body undulations. The snake's low skin friction also increases performance. The agreement between experiment and RFT combined with the relatively simple properties of the granular 'frictional fluid' make subarenaceous swimming an attractive system to study functional morphology and bauplan evolution.

There was an error published in J. Exp. Biol. 218,[440][441][442][443][444][445][446][447][448][449][450] In Fig. 5 of this paper, there was a mistake in the theoretical calculation of the average slip angle, b s . The corrected calculations show that b s rises more sharply for low mean relative curvatures and approaches 90 deg. This change does not affect the conclusions set forth in the original paper, and shows better agreement with the experimental findings.The corrected figure is reproduced below:The authors apologise for any inconvenience this may have caused. b s ) with changing mean relative curvature (kl s ), average number of undulations along the body ( j), body length to width ratio (L/w) and effective friction. Force relationships were established from empirical drag data in loosely packed (LP) media. The color of the curves and experimental data correspond to different j (where dark blue is j=0, dark red is j=5). Solid curves are predictions for an undulatory swimmer with a L/w=7.1 and body-particle friction, m s , of 0.17. The dotted-dashed curves show the theoretical predictions with L/w=33.5 and m s =0.17. The dashed curves are the predictions for L/w=33.5 and half the tangential force (which occurs when there is a 50% decrease in body-particle friction, i.e. m s of 0.085; see supplementary material Fig. S1). Experimental data are shown for sandfish (gray cross with red center) and snake (gray cross with blue center) trials in CP and LP media. Horizontal and vertical lines are centered on kl s and b s , respectively, with span representing ±1 s.d. The diagram above the main panel illustrates waves with different kl s .1111

The scales on the skin of a snake are an integral part of the snake's locomotive capabilities. It stands to reason that the integration of scales into the design of robotic snakes would open new properties to exploit. In this work, we present a robotic snake design that incorporates rigid scales in the casing of each module. To validate the impact of the scales, locomotion is tested under three conditions: with scales, covered in cloth with scales, and covered in cloth without scales. The performance of the snake robot, in each of the aforementioned scenarios, is evaluated based on its forward displacement while executing each of two pre-programmed gaits: inchworm and lateral undulation. The lateral undulation gait is tested under two additional conditions: pitched and un-pitched. Tracks of the experimental runs are presented followed by a statistical analysis demonstrating an increase in locomotive performance when incorporating scales in the chassis design.978-1-4799-6923-4/15/$31.00 ©2015 IEEE

The paper describes a computer vision method for estimating the clinical gait metrics of walking patients in unconstrained environments. The method employs background subtraction to produce a silhouette of the subject and a randomized decision forest to detect their feet. Given the feet detections, the stride and step length, cadence, and walking speed are estimated. Validation of the system is presented through an error analysis on manually annotated videos of subjects walking in different outdoor settings. This method is significant as it provides clinical therapists and non-specialists the opportunity to record from any camera and obtain high accuracy estimates of the clinical gait metrics for subjects walking at outdoor or at-home locations.