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RHex is a hexapod with compliant legs and only six actuated degrees of freedom. Its ability to traverse highly fractured and unstable terrain, as well ascend and descend a particular flight of stairs has already been documented. In this paper, we describe an open loop controller that enables our small robot (Length: 51 cm, Width: 20 cm, Height: 12.7 cm. Leg… (More)

This paper describes the implementation of a preliminary bounding gait in a small hexapod, RHex [1], with compliant legs. A four-legged bounding gait, which uses only the front and back leg pairs, achieves an average speed of 1.5 m/s and a low specific resistance. Leg touchdown angles and desired stance trajectories are fixed a priori. The only feedback… (More)

- David K Campbell
- 1995

No tribute to the legacy of Stan Ulam would be complete without a discussion of " nonlinear science, " a growing collection of interdisciplinary studies that in the past two decades has excited and challenged researchers from nearly every discipline of the natural sciences, engineering, and mathematics. Through his own research Stan played a major role in… (More)

n solid-state physics, the phenomenon of localization is usually perceived as arising from extrinsic disorder that breaks the discrete translational invariance of the perfect crystal lattice. Familiar examples include the localized vibrational phonon modes around impurities or defects (such as atomic vacancies or interstitial atoms) in crystals and Anderson… (More)

- D K Campbell, A R Bishop
- 2011

Using recent results on a model relativistic field theory, we find explicitly a new solitonlike solution, essentially the conventional strong polaron, in the continuum interacting electron-phonon model of a Peierls-dimerized chain such as polyacetylene [(CH} " ].This solution is in good agreement with recent numerical simulations in a discrete model of (CH)… (More)

We present the first controller that allows our small hexapod robot, RHex, to descend a wide variety of regular sized, " real-world " stairs. After selecting one of two sets of trajectories, depending on the slope of the stairs, our open-loop, clock-driven controllers require no further operator input nor task level feedback. Energetics for stair descent is… (More)

- D K Campbell, A R Bishop
- 2002

A continuum model of a Peierls-dimerized chain, as described generally by Brazovskii and discussed for the case of polyacetylene by Takayama, Lin-Liu and Maki (TLM), is considered. The continuum (Bogliubov-de Gennes) equations arising in this model of interacting electrons and phonons are shown to be equivalent to the static, semiclassical equations for a… (More)

- S.-W Tsai, A H Castro Neto, R Shankar, D K Campbell
- 2005

We develop an asymptotically exact renormalization-group approach that treats electron-electron and electron-phonon interactions on an equal footing. The approach allows an unbiased study of the instabilities of Fermi liquids without the assumption of a broken symmetry. We apply our method to the problem of strongly coupled superconductors and find the… (More)

We study numerically the interactions of a kink (K) and an antikink (K) in the double sine-Gordon equation with potential V(qS) =-4[-cos(q~/2) + ~ cos q~]/[1 + 14 ~1]. As a function of initial velocity in the KK collisions, we observe and analyze quantitatively a rich structure of "resonances" in most ranges of ~.

- S Mazumdar, R T Clay, D K Campbell
- 2000

We report three surprising results regarding the nature of the spatial broken symmetries in the two-dimensional ͑2D͒, quarter-filled band with strong electron-electron interactions that provides a microscopic model of the 2:1 cationic organic charge-transfer solids ͑CTS's͒. First, in direct contradiction to the predictions of one-electron theory, we find a… (More)