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Goldman, Daniel I.

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Author: Umbanhowar, Paul B. × End date: 2009 × Start date: 2008 ×

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    Sensitive dependence of the motion of a legged robot on granular media
    (Georgia Institute of Technology, 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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    Integrating a Hierarchy of Simulation Tools for Legged Robot Locomotion
    (Georgia Institute of Technology, 2008-09) Slatton, Andrew ; Cohen, Daniel ; Ding, Yang ; Umbanhowar, Paul B. ; Goldman, Daniel I. ; Haynes, G. Clark ; Komsuoglu, Haldun ; Koditschek, Daniel E.
    We are interested in the development of a variety of legged robot platforms intended for operation in unstructured outdoor terrain. In such settings, the traditions of rational engineering design, driven by analytically informed and computationally assisted studies of robot-environment models, remain ineffective due to the complexity of both the robot designs and the terrain in which they must operate. Instead, empirical trial and error often drives the necessary incremental and iterative design process, hence the development of such robots remains expensive both in time and cost, and is often closely dependent upon the substrate properties of the locomotion terrain. This paper describes a series of concurrent but increasingly coordinated software development efforts that aim to diminish the gap between easily interfaced and physically sound computational models of a real robot’s operation in a complex natural environment. We describe a robot simulation environment in which simple robot modifications can be easily prototyped along and “played” into phenomenological models of contact mechanics. We particularly focus on the daunting but practically compelling example of robot feet interacting granular media, such as gravel or sand, offering a brief report of our progress in deriving and importing physically accurate but computationally tractable phenomenological substrate models into the robot execution simulation environment. With a goal of integration for future robot prototyping simulations, we review the prospects for diminishing the gap between the integrated computational models and the needs of physical platform development.
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    Scaling and Dynamics of Sphere and Disk Impact into Granular Media
    (Georgia Institute of Technology, 2008-02-29) Goldman, Daniel I. ; Umbanhowar, Paul B.
    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. Examination of the measured forces on the sphere in the vicinity of these features leads to an 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.