Stabilizing Passive Dynamic Walk Under Wide Range of Environments by Constraint Mechanism Fitted to Sole of Foot

2009 ◽  
Vol 21 (3) ◽  
pp. 403-411 ◽  
Author(s):  
Kazuyuki Hyodo ◽  
◽  
Takeshi Oshimura ◽  
Sadayoshi Mikami ◽  
Sho'ji Suzuki ◽  
...  
Keyword(s):  
Sagittal Plane ◽  
Three Dimensional ◽  
Sharp Edge ◽  
Shape Design ◽  
Geometrical Analysis ◽  
Forward Movement ◽  
Wide Range ◽  
Outdoor Environments ◽  
Lateral Plane ◽  
The Stability

This paper proposes a foot shape design to enhance the stability of passive dynamic walk by constraining fall down phenomenon in both sagittal and lateral planes. We focus on excessive side-to-side and forward leg swinging that causes a passive dynamic biped walker to fall over. Geometrical analysis showed that stability under a wide range of slope inclinations is achievable by limiting the swinging leg spatially to within a certain angle. Such a limit, or constraint, on swinging effectively prevents falling down on the lateral plane, while stable walking is maintained on the sagittal plane by constraining forward movement using a sharp edge at the head of a foot. We propose a foot prototype realizing these two constraints using a three-dimensional (3D) sole design and show that the proposed constraint is more effective for walking than an arctic foot shape. In verification experiments, the constraint stabilized the passive dynamic walker in a wide range of outdoor environments.

scholarly journals Periodic orbits relevant for the formation of inner rings in barred galaxies

1985 ◽  
Vol 106 ◽  
pp. 543-544
Author(s):  
M. Michalodimitrakis ◽  
Ch. Terzides
Keyword(s):  
Periodic Orbits ◽  
Three Dimensional ◽  
Particle Trapping ◽  
Barred Galaxies ◽  
Future Paper ◽  
Stability Of Periodic Orbits ◽  
Wide Range ◽  
The Galaxy ◽  
Stable Periodic ◽  
The Stability

The study of orbits of a test particle in the gravitational field of a model barred galaxy is a first step toward the understanding of the origin of the morphological characterstics observed in real barred galaxies. In this paper we confine our attention to the inner rings. Inner rings are a very common characteristic of barred galaxies. They are narrow, round or slightly elongated along the bar (with typical axial ratios from 0.7 to near 1.0), and of the same size as the bar. A first step to test the old hypothesis that inner rings consist of stars trapped near stable periodic orbits would be a study of particle trapping around periodic orbits encircling the bar. Such a study is contained in the work of several authors (Danby 1965, de Vaucouleurs and Freeman 1972, Michalodimitrakis 1975, Contopoulos and Papayannopoulos 1980, Athanassoula et al. 1983). In the above works the stability of periodic orbits was studied with respect to perturbations which lie on the plane of motion z = 0 (planar stability). To ensure the possibility of formation of rings, a study of stability with respect to perturbations perpendicular to the plane of motion (vertical stability) is necessary. In this paper we investigate the properties of periodic orbits which we believe to be relevant for the inner-ring problem using a sufficiently general model for the galaxy and sets of values for the parameters which cover a wide range of different possible cases. We also study the stability, planar and vertical, with respect to large perturbations in order to estimate the extent of particle trapping. A detailed numerical investigation of three-dimensional periodic orbits will be given in a future paper.

A Design Study of a Supersonic Air Intake Device in a Wide Range of Main Flow Parameters

2020 ◽  
pp. 44-53
Author(s):  
E.S. Studennikov ◽  
R.S. Ayupov
Keyword(s):  
Boundary Layer ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Stability Margin ◽  
Aircraft Design ◽  
Software Systems ◽  
Flow Parameters ◽  
Wide Range ◽  
Air Intake ◽  
The Stability

This paper examines operation modes of a mixed compression air intake with a rectangular cross-section at Mach number 2.0. The perfect gas model was used for the calculation. Calculations were performed for three values of Mach numbers: 1.8, 2.0 and 3.0. k–ε turbulence model was chosen for describing flows with large adverse pressure gradients. Two-dimensional and three-dimensional configurations of the air intake device were examined. Versions of geometry with and without the boundary layer drain system were considered. The influence of the boundary layer drain system on the flow in the air intake and its characteristics was established. Throttle characteristic curves were formed for all the considered modes with regard to the averaged flow parameters. A comparison of the calculation and experimental data showed a good agreement of the results. The obtained results can serve as a basis for further optimization and improvement of the efficiency of the aircraft design layout, increase in the stability margin of air intakes, as well as development of software systems for regulating supersonic input devices.

Stability and Robustness of a 3D Slip Model for Walking Using Lateral Leg Placement Control

2012 ◽  
Author(s):  
Dominik Budday ◽  
Fabian Bauer ◽  
Justin Seipel
Keyword(s):  
Humanoid Robot ◽  
Performance Test ◽  
Control Mechanism ◽  
Sagittal Plane ◽  
Control Strategies ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Slip Model ◽  
The Stability

The SLIP model has shown a way to easily represent the center of mass dynamics of human walking and running. For 2D motions in the sagittal plane, the model shows self-stabilizing effects that can be very useful when designing a humanoid robot. However, this self-stability could not be found in three-dimensional running, but simple control strategies achieved stabilization of running in three dimensions. Yet, 3D walking with SLIP has not been analyzed to the same extent. In this paper we show that three-dimensional humanoid SLIP walking is also unstable, but can be stabilized using the same strategy that has been successful for running. It is shown that this approach leads to the desired periodic solutions. Furthermore, the influence of different parameters on stability and robustness is examined. Using a performance test to simulate the transition from an upright position to periodic walking we show that the stability is robust. With a comparison of common models for humanoid walking and running it is shown that the simple control mechanism is able to achieve stable solutions for all models, providing a very general approach to this problem. The derived results point out preferable parameters to increase robustness promising the possibility of successfully realizing a humanoid walking robot based on 3D SLIP.

BORDER COLLISION BIFURCATIONS IN THREE-DIMENSIONAL PIECEWISE SMOOTH SYSTEMS

2008 ◽  
Vol 18 (02) ◽  
pp. 577-586 ◽  
Author(s):  
INDRAVA ROY ◽  
A. R. ROY
Keyword(s):  
Three Dimensional ◽  
Piecewise Smooth ◽  
Smooth Maps ◽  
Research Fields ◽  
Border Collision Bifurcations ◽  
Period 2 ◽  
Wide Range ◽  
Different Types ◽  
Piecewise Smooth Maps ◽  
The Stability

Piecewise smooth maps have been a focus of study for scientists in a wide range of research fields. These maps show qualitatively different types of bifurcations than those exhibited by generic smooth maps. We present a theoretical framework for analyzing three-dimensional piecewise smooth maps by deriving a suitable normal form and then finding the stability criteria for periodic orbits. We also show by numerical simulation different types of border collision bifurcations that can occur in such a map. We have also been able to observe a border collision bifurcation from a period-2 to a quasiperiodic orbit.

scholarly journals On the Stability of Reconstruction of Irregularly Sampled Diffraction Fields

2010 ◽  
Vol 2010 ◽  
pp. 1-12
Author(s):  
Vladislav Uzunov ◽  
Atanas Gotchev ◽  
Karen Egiazarian
Keyword(s):  
Degrees Of Freedom ◽  
Light Field ◽  
Monochromatic Light ◽  
Three Dimensional ◽  
Regularized Inversion ◽  
Volume Of Interest ◽  
Wide Range ◽  
Data Points ◽  
Data Point ◽  
The Stability

This paper addresses the problem of reconstruction of a monochromatic light field from data points, irregularly distributed within a volume of interest. Such setting is relevant for a wide range of three-dimensional display and beam shaping applications, which deal with physically inconsistent data. Two finite-dimensional models of monochromatic light fields are used to state the reconstruction problem as regularized matrix inversion. The Tikhonov method, implemented by the iterative algorithm of conjugate gradients, is used for regularization. Estimates of the model dimensionality are related to the number of degrees of freedom of the light field as to show how to control the data redundancy. Experiments demonstrate that various data point distributions lead to ill-poseness and that regularized inversion is able to compensate for the data point inconsistencies with good numerical performance.

scholarly journals Dynamics of three dimensional maps

2011 ◽  
Vol 24 (1) ◽  
pp. 105-117
Author(s):  
Asma Djerrai ◽  
Ilhem Djellit
Keyword(s):  
Invariant Manifolds ◽  
Three Dimensional ◽  
One Dimensional ◽  
Research Fields ◽  
Numerical Exploration ◽  
Wide Range ◽  
Planar Maps ◽  
The Stability ◽  
The One ◽  
One Dimensional Maps

Smooth 3D maps have been a focus of study in a wide range of research fields. Their Properties are investigated qualitatively and numerically. These maps show qualitatively interesting types of bifurcations than those exhibited by generic smooth planar maps. We present a theoretical framework for analyzing three-dimensional smooth coupling maps by finding the stability criteria for periodic orbits and characterizing the system behaviors with the tools of nonlinear dynamics relative to bifurcation in the parameter plane, invariant manifolds, critical manifolds, chaotic attractors. We also show by numerical simulation bifurcations that can occur in such maps. By an analytical and numerical exploration we give some properties and characteristics, since this class of three-dimensional dynamics is associated with the properties of one-dimensional maps. There is an interesting passage from the one-dimensional endomorphisms to the three-dimensional endomorphisms.

Non-isothermal flow of a liquid film on a horizontal cylinder

1992 ◽  
Vol 236 ◽  
pp. 167-196 ◽  
Author(s):  
B. Reisfeld ◽  
S. G. Bankoff
Keyword(s):  
Liquid Film ◽  
Evolution Equations ◽  
Azimuthal Angle ◽  
Three Dimensional ◽  
Thermal Conditions ◽  
Intermolecular Forces ◽  
Horizontal Cylinder ◽  
Wide Range ◽  
Viscous Liquid Film ◽  
The Stability

We consider the flow of a viscous liquid film on the surface of a cylinder that is heated or cooled. Lubrication theory is used to study a thin film under the influence of gravity, capillary, thermocapillary, and intermolecular forces. We derive evolution equations for the interface shapes as a function of the azimuthal angle about the cylinder that govern the behaviour of the film subject to the above coupled forces. We use both analytical and numerical techniques to elucidate the dynamics and steady states of the thin layer over a wide range of thermal conditions and material properties. Finally, we extend our derivation to the case of three-dimensional dynamics and explore the stability of the film to small axial disturbances.

scholarly journals An experimental study of the motion of a viscous liquid contained between two coaxial cylinders

1928 ◽  
Vol 117 (777) ◽  
pp. 388-407 ◽  
Keyword(s):  
Viscous Liquid ◽  
Three Dimensional ◽  
Critical Value ◽  
Limited Range ◽  
Axial Plane ◽  
Stream Line ◽  
Coaxial Cylinders ◽  
Wide Range ◽  
The Stability ◽  
Different Diameters

The stability of a viscous liquid contained between two coaxial cylinders which are capable of independent rotation has been investigated by G. I. Taylor. At low speeds of rotation the motion of the liquid is two-dimensional, each particle of liquid rotating in a circle concentric with the cylinders. This type of motion is possible whether the cylinders rotate in the same or in opposite directions, and is stable for velocities of the inner cylinder not exceeding a certain critical value. At the critical speed the laminar motion is succeeded by a three-dimensional motion, such that the circulation of the liquid is confined to a scries of annular compartments, one above the other. When both cylinders rotate in the same direction, the height of each compartment equals the distance between the cylinders, and the motion in an axial plane appears to consist of a series of vortices in square compartments, adjacent vortices rotating in opposite directions. For cylinders rotating in opposite directions there are, at a given horizontal level, two annular compartments side by side and concentric with the cylinders. In this case, the circulation in an axial plane appears to consist of two series of vortices, adjacent vortices both vertically and horizontally rotating in opposite directions. By using coloured liquid filaments to follow the motion, Taylor verified experimentally, within a limited range, the expression for the critical velocity at which the stream-line motion becomes unstable and certain other points. The apparatus used was large and robust, the length of the cylinders being 90 cm., and it was unsuitable for investigating the motion under varying conditions, such as with inner cylinders of different diameters and with liquids giving a wide range in viscosity.

scholarly journals Stability boundaries of roll and square convection in binary fluid mixtures with positive separation ratio

2000 ◽  
Vol 408 ◽  
pp. 121-147 ◽  
Author(s):  
B. HUKE ◽  
M. LÜCKE ◽  
P. BÜCHEL ◽  
CH. JUNG
Keyword(s):  
Three Dimensional ◽  
Stationary Solutions ◽  
Stability Boundaries ◽  
Binary Fluid ◽  
Fluid Mixtures ◽  
Separation Ratio ◽  
Wide Range ◽  
The Stability ◽  
Binary Fluid Mixtures ◽  
Rayleigh Benard

Rayleigh–Bénard convection in horizontal layers of binary fluid mixtures heated from below with realistic horizontal boundary conditions is studied theoretically using multi-mode Galerkin expansions. For positive separation ratios the main difference between the mixtures and pure fluids lies in the existence of stable three-dimensional patterns near onset in a wide range of the parameter space. We evaluated the stationary solutions of roll, crossroll, and square convection and we determined the location of the stability boundaries for many parameter combinations thereby obtaining the Busse balloon for roll and square patterns.

scholarly journals Planet formation and stability in polar circumbinary discs

2019 ◽  
Vol 628 ◽  
pp. A119 ◽  
Author(s):  
Nicolás Cuello ◽  
Cristian A. Giuppone
Keyword(s):  
Three Dimensional ◽  
Orbital Plane ◽  
Equal Mass ◽  
Wide Range ◽  
Rotation Vectors ◽  
Hydrodynamical Simulations ◽  
Binary Orbit ◽  
The Stability ◽  
P Type

Context. Dynamical studies suggest that most circumbinary discs (CBDs) should be coplanar (i.e. the rotation vectors of the binary and the disc should be aligned). However, some theoretical works show that under certain conditions a CBD can become polar, which means that its rotation vector is orthogonal with respect to the binary orbital plane. Interestingly, very recent observations show that polar CBDs exist in nature (e.g. HD 98800). Aims. We test the predictions of CBD alignment around eccentric binaries based on linear theory. In particular, we compare prograde and retrograde CBD configurations. Then, assuming planets form in these systems, we thoroughly characterise the orbital behaviour and stability of misaligned (P-type) particles. This is done for massless and massive particles. Methods. The evolution of the CBD alignment for various configurations was modelled through three-dimensional hydrodynamical simulations. For the orbital characterisation and the analysis stability, we relied on long-term N-body integrations and structure and chaos indicators, such as Δe and MEGNO. Results. We confirm previous analytical predictions on CBD alignment, but find an unexpected symmetry breaking between prograde and retrograde configurations. More specifically, we observe polar alignment for a retrograde misaligned CBD that was expected to become coplanar with respect to the binary disc plane. Therefore, the likelihood of becoming polar for a highly misaligned CBD is higher than previously thought. Regarding the stability of circumbinary P-type planets (also know as Tatooines), polar orbits are stable over a wide range of binary parameters. In particular, for binary eccentricities below 0.4 the orbits are stable for any value of the binary mass ratio. In the absence of gas, planets with masses below 10−5 M⊙ have negligible effects on the binary orbit. Finally, we suggest that mildly eccentric equal-mass binaries should be searched for polar Tatooines.

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