From cockroaches to tanks: The same power-mass-speed relation describes both biological and artificial ground-mobile systems.

This paper explores whether artificial ground-mobile systems exhibit a consistent regularity of relation among mass, power, and speed, similar to that which exists for biological organisms. To this end, we investigate an empirical allometric formula proposed in the 1980s for estimating the mechanical power expended by an organism of a given mass to move at a given speed, applicable over several orders of magnitude of mass, for a broad range of species, to determine if a comparable regularity applies to a range of vehicles. We show empirically that not only does a similar regularity apply to a wide variety of mobile systems; moreover, the formula is essentially the same, describing organisms and systems ranging from a roach (1 g) to a battle tank (35,000 kg). We also show that for very heavy vehicles (35,000-100,000,000 kg), the formula takes a qualitatively different form. These findings point to a fundamental similarity between biological and artificial locomotion that transcends great differences in morphology, mechanisms, materials, and behaviors. To illustrate the utility of this allometric relation, we investigate the significant extent to which ground robotic systems exhibit a higher cost of transport than either organisms or conventional vehicles, and discuss ways to overcome inefficiencies.

Legged locomotion in resistive terrains.

The utility, efficiency, and reliability of legged robots has increased dramatically in recent years. Limbed robots are now capable of locomotion across a variety of terrains, however, achieving both rapid and efficient operation when ground conditions are complex or deformable is still challenging. Resistive terrains such as streams, snow, mud, littoral regions, and tall grass are an important class or set of complex and difficult terrain which are commonly found in the desired operating environments of legged robots. This work presents a reduced-order, dynamic model designed to capture the effect of these environments on the legs of a robot while running. This model, and an experimental platform, are used to evaluate the efficacy of a pair of strategies for adapting running to the inevitable slowing that occurs in resistive terrains. Simulation and experimental results show that intelligent retraction of the foot during flight has a more beneficial effect on the maximum achievable velocity and cost of transport of the runner than a 'punting gait' for a range of fluid depths. However, this performance gap became much smaller in deep fluids suggesting that fluid depth may drive transition from a foot retraction gait to a punting gait.

Lateral Oscillation and Body Compliance Help Snakes and Snake Robots Stably Traverse Large, Smooth Obstacles.

Snakes can move through almost any terrain. Similarly, snake robots hold the promise as a versatile platform to traverse complex environments such as earthquake rubble. Unlike snake locomotion on flat surfaces which is inherently stable, when snakes traverse complex terrain by deforming their body out of plane, it becomes challenging to maintain stability. Here, we review our recent progress in understanding how snakes and snake robots traverse large, smooth obstacles such as boulders and felled trees that lack "anchor points" for gripping or bracing. First, we discovered that the generalist variable kingsnake combines lateral oscillation and cantilevering. Regardless of step height and surface friction, the overall gait is preserved. Next, to quantify static stability of the snake, we developed a method to interpolate continuous body in three dimensions (3D) (both position and orientation) between discrete tracked markers. By analyzing the base of support using the interpolated continuous body 3-D kinematics, we discovered that the snake maintained perfect stability during traversal, even on the most challenging low friction, high step. Finally, we applied this gait to a snake robot and systematically tested its performance traversing large steps with variable heights to further understand stability principles. The robot rapidly and stably traversed steps nearly as high as a third of its body length. As step height increased, the robot rolled more frequently to the extent of flipping over, reducing traversal probability. The absence of such failure in the snake with a compliant body inspired us to add body compliance to the robot. With better surface contact, the compliant body robot suffered less roll instability and traversed high steps at higher probability, without sacrificing traversal speed. Our robot traversed large step-like obstacles more rapidly than most previous snake robots, approaching that of the animal. The combination of lateral oscillation and body compliance to form a large, reliable base of support may be useful for snakes and snake robots to traverse diverse 3-D environments with large, smooth obstacles.

Snakes partition their body to traverse large steps stably.

Many snakes live in deserts, forests and river valleys and traverse challenging 3-D terrain such as rocks, felled trees and rubble, with obstacles as large as themselves and variable surface properties. By contrast, apart from branch cantilevering, burrowing, swimming and gliding, laboratory studies of snake locomotion have focused on locomotion on simple flat surfaces. Here, to begin to understand snake locomotion in complex 3-D terrain, we studied how the variable kingsnake, a terrestrial generalist, traversed a large step of variable surface friction and step height (up to 30% snout-vent length). The snake traversed by partitioning its body into three sections with distinct functions. Body sections below and above the step oscillated laterally on horizontal surfaces for propulsion, whereas the body section in between cantilevered in a vertical plane to bridge the large height increase. As the animal progressed, these three sections traveled down its body, conforming overall body shape to the step. In addition, the snake adjusted the partitioned gait in response to increase in step height and decrease in surface friction, at the cost of reduced speed. As surface friction decreased, body movement below and above the step changed from a continuous lateral undulation with little slip to an intermittent oscillatory movement with much slip, and initial head lift-off became closer to the step. Given these adjustments, body partitioning allowed the snake to be always stable, even when initially cantilevering but before reaching the surface above. Such a partitioned gait may be generally useful for diverse, complex 3-D terrain.

Body-terrain interaction affects large bump traversal of insects and legged robots.

Small animals and robots must often rapidly traverse large bump-like obstacles when moving through complex 3D terrains, during which, in addition to leg-ground contact, their body inevitably comes into physical contact with the obstacles. However, we know little about the performance limits of large bump traversal and how body-terrain interaction affects traversal. To address these, we challenged the discoid cockroach and an open-loop six-legged robot to dynamically run into a large bump of varying height to discover the maximal traversal performance, and studied how locomotor modes and traversal performance are affected by body-terrain interaction. Remarkably, during rapid running, both the animal and the robot were capable of dynamically traversing a bump much higher than its hip height (up to 4 times the hip height for the animal and 3 times for the robot, respectively) at traversal speeds typical of running, with decreasing traversal probability with increasing bump height. A stability analysis using a novel locomotion energy landscape model explained why traversal was more likely when the animal or robot approached the bump with a low initial body yaw and a high initial body pitch, and why deflection was more likely otherwise. Inspired by these principles, we demonstrated a novel control strategy of active body pitching that increased the robot's maximal traversable bump height by 75%. Our study is a major step in establishing the framework of locomotion energy landscapes to understand locomotion in complex 3D terrains.

Dynamic traversal of large gaps by insects and legged robots reveals a template.

It is well known that animals can use neural and sensory feedback via vision, tactile sensing, and echolocation to negotiate obstacles. Similarly, most robots use deliberate or reactive planning to avoid obstacles, which relies on prior knowledge or high-fidelity sensing of the environment. However, during dynamic locomotion in complex, novel, 3D terrains, such as a forest floor and building rubble, sensing and planning suffer bandwidth limitation and large noise and are sometimes even impossible. Here, we study rapid locomotion over a large gap-a simple, ubiquitous obstacle-to begin to discover the general principles of the dynamic traversal of large 3D obstacles. We challenged the discoid cockroach and an open-loop six-legged robot to traverse a large gap of varying length. Both the animal and the robot could dynamically traverse a gap as large as one body length by bridging the gap with its head, but traversal probability decreased with gap length. Based on these observations, we developed a template that accurately captured body dynamics and quantitatively predicted traversal performance. Our template revealed that a high approach speed, initial body pitch, and initial body pitch angular velocity facilitated dynamic traversal, and successfully predicted a new strategy for using body pitch control that increased the robot's maximal traversal gap length by 50%. Our study established the first template of dynamic locomotion beyond planar surfaces, and is an important step in expanding terradynamics into complex 3D terrains.

How seabirds plunge-dive without injuries.

In nature, several seabirds (e.g., gannets and boobies) dive into water at up to 24 m/s as a hunting mechanism; furthermore, gannets and boobies have a slender neck, which is potentially the weakest part of the body under compression during high-speed impact. In this work, we investigate the stability of the bird's neck during plunge-diving by understanding the interaction between the fluid forces acting on the head and the flexibility of the neck. First, we use a salvaged bird to identify plunge-diving phases. Anatomical features of the skull and neck were acquired to quantify the effect of beak geometry and neck musculature on the stability during a plunge-dive. Second, physical experiments using an elastic beam as a model for the neck attached to a skull-like cone revealed the limits for the stability of the neck during the bird's dive as a function of impact velocity and geometric factors. We find that the neck length, neck muscles, and diving speed of the bird predominantly reduce the likelihood of injury during the plunge-dive. Finally, we use our results to discuss maximum diving speeds for humans to avoid injury.

Dogs lap using acceleration-driven open pumping.

Dogs lap because they have incomplete cheeks and cannot suck. When lapping, a dog's tongue pulls a liquid column from the bath, suggesting that the hydrodynamics of column formation are critical to understanding how dogs drink. We measured lapping in 19 dogs and used the results to generate a physical model of the tongue's interaction with the air-fluid interface. These experiments help to explain how dogs exploit the fluid dynamics of the generated column. The results demonstrate that effects of acceleration govern lapping frequency, which suggests that dogs curl the tongue to create a larger liquid column. Comparing lapping in dogs and cats reveals that, despite similar morphology, these carnivores lap in different physical regimes: an unsteady inertial regime for dogs and steady inertial regime for cats.

Particle motion induced by bubble cavitation.

Cavitation bubbles induce impulsive forces on surrounding substrates, particles, or surfaces. Even though cavitation is a traditional topic in fluid mechanics, current understanding and studies do not capture the effect of cavitation on suspended objects in fluids. In the present work, the dynamics of a spherical particle due to a cavitation bubble is experimentally characterized and compared with an analytical model. Three phases are observed: the growth of the bubble where the particle is pushed away, its collapse where the particle approaches the bubble, and a longer time scale postcollapse where the particle continues to move toward the collapsed bubble. The particle motion in the longer time scale presumably results from the asymmetric cavitation evolution at an earlier time. Our theory considering the asymmetric bubble dynamics shows that the particle velocity strongly depends on the distance from the bubble as an inverse-fourth-power law, which is in good agreement with our experimentation. This study sheds light on how small free particles respond to cavitation bubbles in fluids.

Dynamics of squeezing fluids: clapping wet hands.

Droplets splash around when a fluid volume is quickly compressed. This phenomenon has been observed during common activities such as kids clapping with wet hands. The underlying mechanism involves a fluid volume being compressed vertically between two objects. This compression causes the fluid volume to be ejected radially and thereby generate fluid threads and droplets at a high speed. In this study, we designed and performed laboratory experiments to observe the process of thread and drop formation after a fluid is squeezed. A thicker rim at the outer edge forms and moves after the squeezing, and then becomes unstable and breaks into smaller drops. This process differs from previous well-known examples (i.e., transient crown splashes and continuous water bells) in aspects of transient fluid feeding, expanding rim dynamics, or sparsely distributed drops. We compared experimental measurements with theoretical models over three different stages; early squeezing, intermediate sheet-expansion, and later break-up of the liquid thread. In the earlier stage, the fluid is squeezed and its initial velocity is governed by the lubrication force. The outer rim of the liquid sheet forms curved trajectories due to gravity, inertia, drag, and surface tension. At the late stage, drop spacing set by the initial capillary instability does not change in the course of rim expansion, consequently final ejected droplets are very sparse compared to the size of the rim.