Input to State Stability of Bipedal Walking Robots: Application to DURUS

Bipedal robots are a prime example of systems which exhibit highly nonlinear dynamics, underactuation, and undergo complex dissipative impacts. This paper discusses methods used to overcome a wide variety of uncertainties, with the end result being stable bipedal walking. The principal contribution of this paper is to establish sufficiency conditions for yielding input to state stable (ISS) hybrid periodic orbits, i.e., stable walking gaits under model-based and phase-based uncertainties. In particular, it will be shown formally that exponential input to state stabilization (e-ISS) of the continuous dynamics, and hybrid invariance conditions are enough to realize stable walking in the 23-DOF bipedal robot DURUS. This main result will be supported through successful and sustained walking of the bipedal robot DURUS in a laboratory environment.Comment: 16 pages, 10 figure

Dynamic Walking: Toward Agile and Efficient Bipedal Robots

Dynamic walking on bipedal robots has evolved from an idea in science fiction to a practical reality. This is due to continued progress in three key areas: a mathematical understanding of locomotion, the computational ability to encode this mathematics through optimization, and the hardware capable of realizing this understanding in practice. In this context, this review article outlines the end-to-end process of methods which have proven effective in the literature for achieving dynamic walking on bipedal robots. We begin by introducing mathematical models of locomotion, from reduced order models that capture essential walking behaviors to hybrid dynamical systems that encode the full order continuous dynamics along with discrete footstrike dynamics. These models form the basis for gait generation via (nonlinear) optimization problems. Finally, models and their generated gaits merge in the context of real-time control, wherein walking behaviors are translated to hardware. The concepts presented are illustrated throughout in simulation, and experimental instantiation on multiple walking platforms are highlighted to demonstrate the ability to realize dynamic walking on bipedal robots that is agile and efficient

Control of Separable Subsystems with Application to Prostheses

Nonlinear control methodologies have successfully realized stable human-like walking on powered prostheses. However, these methods are typically restricted to model independent controllers due to the unknown human dynamics acting on the prosthesis. This paper overcomes this restriction by introducing the notion of a separable subsystem control law, independent of the full system dynamics. By constructing an equivalent subsystem, we calculate the control law with local information. We build a subsystem model of a general open-chain manipulator to demonstrate the control method's applicability. Employing these methods for an amputee-prosthesis model, we develop a model dependent prosthesis controller that relies solely on measurable states and inputs but is equivalent to a controller developed with knowledge of the human dynamics and states.Comment: 8 pages, 6 figure

Measurement of the Associated γ+μ±\gamma + \mu^\pm Production Cross Section in ppˉp \bar p Collisions at s=1.8\sqrt{s} = 1.8 TeV

We present the first measurement of associated direct photon + muon production in hadronic collisions, from a sample of 1.8 TeV $p \bar p$ collisions recorded with the Collider Detector at Fermilab. Quantum chromodynamics (QCD) predicts that these events are primarily from the Compton scattering process $cg \to c\gamma$, with the final state charm quark producing a muon. Hence this measurement is sensitive to the charm quark content of the proton. The measured cross section of $29\pm 9 pb^{-1}$ is compared to a leading-order QCD parton shower model as well as a next-to-leading-order QCD calculation.Comment: 12 pages, 4 figures Added more detailed description of muon background estimat

Control of Separable Subsystems with Application to Prostheses

Nonlinear control methodologies have successfully realized stable human-like walking on powered prostheses. However, these methods are typically restricted to model independent controllers due to the unknown human dynamics acting on the prosthesis. This paper overcomes this restriction by introducing the notion of a separable subsystem control law, independent of the full system dynamics. By constructing an equivalent subsystem, we calculate the control law with local information. We build a subsystem model of a general open-chain manipulator to demonstrate the control method's applicability. Employing these methods for an amputee-prosthesis model, we develop a model dependent prosthesis controller that relies solely on measurable states and inputs but is equivalent to a controller developed with knowledge of the human dynamics and states

Search for the Supersymmetric Partner of the Top-Quark in ppˉp \bar{p} Collisions at s=1.8TeV\sqrt{s} = 1.8 {\rm TeV}

We report on a search for the supersymmetric partner of the top quark (stop) produced in $t \bar{t}$ events using $110 {\rm pb}^{-1}$ of $p \bar{p}$ collisions at $\sqrt{s} = 1.8 {\rm TeV}$ recorded with the Collider Detector at Fermilab. In the case of a light stop squark, the decay of the top quark into stop plus the lightest supersymmetric particle (LSP) could have a significant branching ratio. The observed events are consistent with Standard Model $t \bar{t}$ production and decay. Hence, we set limits on the branching ratio of the top quark decaying into stop plus LSP, excluding branching ratios above 45% for a LSP mass up to 40 {\rm GeV/c}$^{2}$.Comment: 11 pages, 4 figure