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Goldman, Daniel I.

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Author: Goldman, Daniel I. × Author: Li, Chen ×

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A terradynamics of legged locomotion on granular media

2013-03-22 , Li, Chen , Zhang, Tingnan , Goldman, Daniel I.

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

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The Effect of limb kinematics on the speed of a legged robot on granular media

2010-04-22 , Li, Chen , Umbanhowar, Paul B. , Komsuoglu, | Haldun , Goldman, Daniel I.

Achieving effective locomotion on diverse terrestrial substrates can require subtle changes of limb kinematics. Biologically inspired legged robots (physical models of organisms) have shown impressive mobility on hard ground but suffer performance loss on unconsolidated granular materials like sand. Because comprehensive limb- ground interaction models are lacking, optimal gaits on complex yielding terrain have been determined empirically. To develop predictive models for legged devices and to provide hypotheses for biological locomotors, we systematically study the performance of SandBot, a small legged robot, on granular media as a function of gait parameters. High performance occurs only in a small region of parameter space. A previously introduced kinematic model of the robot combined with a new anisotropic granular penetration force law predicts the speed. Performance on granular media is maximized when gait parameters minimize body acceleration and limb interference, and utilize solidification features of granular media.

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Multi-functional foot use during running in the zebra-tailed lizard (Callisaurus draconoides)

2012-05 , Li, Chen , Hsieh, S. Tonia , Goldman, Daniel I.

A diversity of animals that run on solid, level, flat, non-slip surfaces appear to bounce on their legs; elastic elements in the limbs can store and return energy during each step. The mechanics and energetics of running in natural terrain, particularly on surfaces that can yield and flow under stress, is less understood. The zebra-tailed lizard (Callisaurus draconoides), a small desert generalist with a large, elongate, tendinous hind foot, runs rapidly across a variety of natural substrates. We use high-speed video to obtain detailed three-dimensional running kinematics on solid and granular surfaces to reveal how leg, foot and substrate mechanics contribute to its high locomotor performance. Running at ~10bodylengthss–1 (~1ms–1), the center of mass oscillates like a spring-mass system on both substrates, with only 15% reduction in stride length on the granular surface. On the solid surface, a strut-spring model of the hind limb reveals that the hind foot saves ~40% of the mechanical work needed per step, significant for the lizardʼs small size. On the granular surface, a penetration force model and hypothesized subsurface foot rotation indicates that the hind foot paddles through fluidized granular medium, and that the energy lost per step during irreversible deformation of the substrate does not differ from the reduction in the mechanical energy of the center of mass. The upper hind leg muscles must perform three times as much mechanical work on the granular surface as on the solid surface to compensate for the greater energy lost within the foot and to the substrate.

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Systematic study of the performance of small robots on controlled laboratory substrates

2010-04 , Li, Chen , Hoover, Aaron M. , Birkmeyer, Paul , Umbanhowar, Paul B. , Fearing, Ronald S. , Goldman, Daniel I.

The design of robots able to locomote effectively over a diversity of terrain requires detailed ground interaction models; unfortunately such models are lacking due to the complicated response of real world substrates which can yield and flow in response to loading. To advance our understanding of the relevant modeling and design issues, we conduct a comparative study of the performance of DASH and RoACH, two small, biologically inspired, six legged, lightweight (~ 10 cm, ~ 20 g) robots fabricated using the smart composite microstructure (SCM) process. We systematically examine performance of both robots on rigid and °owing substrates. Varying both ground properties and limb stride frequency, we investigate average speed, mean mechanical power and cost of transport, and stability. We find that robot performance and stability is sensitive to the physics of ground interaction: on hard ground kinetic energy must be managed to prevent yaw, pitch, and roll instability to maintain high performance, while on sand the fluidizing interaction leads to increased cost of transport and lower running speeds. We also observe that the characteristic limb morphology and kinematics of each robot result in distinct differences in their abilities to traverse different terrains. Our systematic studies are the first step toward developing models of interaction of limbs with complex terrain as well as developing improved limb morphologies and control strategies.

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Comparative studies reveal principles of movement on and within granular media

2010-06 , Ding, Yang , Gravish, Nick , Li, Chen , Maladen, Ryan D. , Mazouchova, Nicole , Sharpe, Sarah S. , Umbanhowar, Paul B. , Goldman, Daniel I.

Terrestrial locomotion can take place on complex substrates such as leaf litter, debris, and soil that flow or solidify in response to stress. While principles of movement in air and water are revealed through study of the hydrodynamic equations of fluid motion, discovery of principles of movement in complex terrestrial environments is less advanced in part because describing the physics of limb and body interaction with such environments remains challenging. We report progress our group has made in discovering principles of movement of organisms and models of organisms (robots) on and within granular materials (GM) like sand. We review current understanding of localized intrusion in GM relevant to foot and body interactions. We discuss the limb-ground interactions of a desert lizard, a hatchling sea turtle, and various robots and reveal that control of granular solidification can generate effective movement. We describe the sensitivity of movement on GM to gait parameters and discuss how changes in material state can strongly affect locomotor performance. We examine subsurface movement, common in desert animals like the sandfish lizard. High speed x-ray imaging resolves subsurface kinematics, while electromyography (EMG) allows muscle activation patterns to be studied. Our resistive force theory, numerical, and robotic models of sand-swimming reveal that subsurface swimming occurs in a “frictional fluid” whose properties differ from Newtonian fluids.

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Sensitive dependence of the motion of a legged robot on granular media

2009-03-03 , Li, Chen , Umbanhowar, Paul B. , Komsuoglu, Haldun , Koditschek, Daniel E. , Goldman, Daniel I.

Legged locomotion on flowing ground (e.g., granular media) is unlike locomotion on hard ground because feet experience both solid- and fluid-like forces during surface penetration. Recent bioinspired legged robots display speed relative to body size on hard ground comparable with high-performing organisms like cockroaches but suffer significant performance loss on flowing materials like sand. In laboratory experiments, we study the performance (speed) of a small (2.3 kg) 6-legged robot, SandBot, as it runs on a bed of granular media (1-mm poppy seeds). For an alternating tripod gait on the granular bed, standard gait control parameters achieve speeds at best 2 orders of magnitude smaller than the 2 body lengths/s (≈60 cm/s) for motion on hard ground. However, empirical adjustment of these control parameters away from the hard ground settings restores good performance, yielding top speeds of 30 cm/s. Robot speed depends sensitively on the packing fraction φ and the limb frequency ω, and a dramatic transition from rotary walking to slow swimming occurs when φ becomes small enough and/or ω large enough. We propose a kinematic model of the rotary walking mode based on generic features of penetration and slip of a curved limb in granular media. The model captures the dependence of robot speed on limb frequency and the transition between walking and swimming modes but highlights the need for a deeper understanding of the physics of granular media.

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