The desert-dwelling sandfish (Scincus scincus) moves within dry sand, a material that displays solid and fluidlike behavior. High-speed x-ray imaging shows that below the surface, the lizard no longer uses limbs for propulsion but generates thrust to overcome drag by propagating an undulatory traveling wave down the body. Although viscous hydrodynamics can predict swimming speed in fluids such as water, an equivalent theory for granular drag is not available. To predict sandfish swimming speed, we developed an empirical model by measuring granular drag force on a small cylinder oriented at different angles relative to the displacement direction and summing these forces over the animal movement profile. The agreement between model and experiment implies that the noninertial swimming occurs in a frictional fluid.

The theories of aero- and hydrodynamics predict animal movement and device design in air and water through the computation of lift, drag, and thrust forces. Although models of terrestrial legged locomotion have focused on interactions with solid ground, many animals move on substrates that flow in response to intrusion. However, locomotor-ground interaction models on such flowable ground are often unavailable. We developed a force model for arbitrarily-shaped legs and bodies moving freely in granular media, and used this "terradynamics" to predict a small legged robot's locomotion on granular media using various leg shapes and stride frequencies. Our study reveals a complex but generic dependence of stresses in granular media on intruder depth, orientation, and movement direction and gives insight into the effects of leg morphology and kinematics on movement.

Direct measurements of the acceleration of spheres and disks impacting granular media reveal simple power law scalings along with complex dynamics which bear the signatures of both fluid and solid behavior. The penetration depth scales linearly with impact velocity while the collision duration is constant for sufficiently large impact velocity. Both quantities exhibit power law dependence on sphere diameter and density, and gravitational acceleration. The acceleration during impact is characterized by two jumps: a rapid, velocity dependent increase upon initial contact and a similarly sharp, depth dependent decrease as the impacting object comes to rest. Examining the measured forces on the sphere in the vicinity of these features leads to a new experimentally based granular force model for collision. We discuss our findings in the context of recently proposed phenomenological models that capture qualitative dynamical features of impact but fail both quantitatively and in their inability to capture significant acceleration fluctuations that occur during penetration and which depend on the impacted material.

A statistical description of static granular material requires ergodic sampling of the phase space spanned by the different configurations of the particles. We periodically fluidize a column of glass beads and find that the sequence of volume fractions φ of post-fluidized states is history independent and Gaussian distributed about a stationary state. The standard deviation of φ exhibits, as a function of φ, a minimum corresponding to a maximum in the number of statistically independent regions. Measurements of the fluctuations enable us to determine the compactivity X, a temperature-like state variable introduced in the statistical theory of Edwards and Oakeshott [Physica A 157, 1080[Physica A 157, (1989].PACS numbers: 64.30.+t, 47.55.Kf Granular materials consist of a large number N (typically more than 10 6 ) dissipative particles that are massive enough so that their potential energy is orders of magnitude larger than their thermal energy. The large number suggests that a statistical description might be feasible. Edwards and coworkers [1] developed such a description with the volume V of the system, rather than the energy, as the key extensive quantity in a static granular system. The corresponding configuration space contains all possible mechanically stable arrangements of grains.Brownian motion is insufficient for a granular system to explore its configuration space, so energy must be supplied by external forcing such as tapping [2], shearing [3] or both [4]. The theory of Edwards requires that the forcing assures ergodicity: all mechanically stable configurations must be equally probable and accessible. A necessary condition for ergodicity is history independence: the physical properties of the system must not depend on the way a specific state was reached. History independence has previously been demonstrated only by Nowak et al.[2] for tapped glass beads at volume fractions φ > 0.625.In this paper we explore the configuration space using a periodic train of flow pulses in a fluidized bed. A stationary column of glass beads in water is expanded by an upward stream of water until it reaches a homogeneously fluidized state [5], and then the flow is switched off. The fluidized bed collapses [6] and forms a sediment of volume fraction φ, which we find depends in a reproducible way on the flow rate Q of the flow pulse. This forcing results in a history independent steady state where the volume exhibits Gaussian fluctuations around its average value.A central postulate of the Edwards theory is the existence of a temperature-like state variable called compactivity X = ∂V /∂S. The entropy S is defined in analogy to classical statistical mechanics as S(V, N ) = λ ln Ω, where Ω is the number of mechanically stable configurations of N particles in V , and λ is an unknown analog to the Boltzmann constant. The assumption that X is a relevant control parameter in granular systems has found support in simulations of segregation in binary mixtures [7], compaction under vertical tapping [8], and shearing [9]. How...

. Single-leg force patterns differed significantly from level running. During vertical climbing, all legs generated forces to pull the animal up the plate. Front and middle legs pulled laterally toward the midline. Front legs pulled the head toward the wall, while hind legs pushed the abdomen away. These singleleg force patterns summed to generate dynamics of the whole animal in the frontal plane such that the center of mass cyclically accelerated up the wall in synchrony with cyclical side-to-side motion that resulted from alternating net lateral pulling forces. The general force patterns used by cockroaches and geckos have provided biological inspiration for the design of a climbing robot named RiSE (Robots in Scansorial Environments).

Geckos are nature's elite climbers. Their remarkable climbing feats have been attributed to specialized feet with hairy toes that uncurl and peel in milliseconds. Here, we report that the secret to the gecko's arboreal acrobatics includes an active tail. We examine the tail's role during rapid climbing, aerial descent, and gliding. We show that a gecko's tail functions as an emergency fifth leg to prevent falling during rapid climbing. A response initiated by slipping causes the tail tip to push against the vertical surface, thereby preventing pitch-back of the head and upper body. When pitch-back cannot be prevented, geckos avoid falling by placing their tail in a posture similar to a bicycle's kickstand. Should a gecko fall with its back to the ground, a swing of its tail induces the most rapid, zero-angular momentum air-righting response yet measured. Once righted to a sprawled gliding posture, circular tail movements control yaw and pitch as the gecko descends. Our results suggest that large, active tails can function as effective control appendages. These results have provided biological inspiration for the design of an active tail on a climbing robot, and we anticipate their use in small, unmanned gliding vehicles and multisegment spacecraft.

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...

Step length as a function of derived from 2s ϭ 2v / reveals the condition for the onset of swimming for տ 0.6 as s/R Ϸ 1. The solid lines and symbols are for values of 0. 580, 0.590, 0.600, 0.611, 0.616, 0.622, and 0.633.