RUNNING PATTERN GENERATION WITH A FIXED POINT IN A 2D PLANAR BIPED

2009 ◽  
Vol 06 (02) ◽  
pp. 241-264 ◽  
Author(s):  
BAEK-KYU CHO ◽  
JUN-HO OH
Keyword(s):  
Fixed Point ◽  
Angular Momentum ◽  
Center Of Mass ◽  
Maximum Velocity ◽  
Numerical Approach ◽  
Pattern Generation ◽  
Upper Body ◽  
Actual Environment ◽  
Virtual System ◽  
Running Pattern

This paper discusses the generation of a running pattern for a biped and verifies the validity of the proposed method of running pattern generation via experiments. When a running pattern is created with resolved momentum control, the angular momentum of the robot at the Center of Mass (COM) is set to zero, as the angular momentum causes the robot to rotate. However, this also induces unnatural motion of the upper body of the robot. To resolve this problem, the biped was set to a virtual under-actuated robot with a free joint at its support ankle, and a fixed point for a virtual system was determined. Following this, a new periodic running pattern was formulated using the fixed point. The fixed point is easily determined using a numerical approach. In an experiment, the planar biped ran forward using the proposed pattern generation method for running. Its maximum velocity was 2.88 km/h. In the future, faster running of the biped will be realized in a planar plane and the biped will run in an actual environment.

RUNNING PATTERN GENERATION OF HUMANOID BIPED WITH A FIXED POINT AND ITS REALIZATION

2009 ◽  
Vol 06 (04) ◽  
pp. 631-656 ◽  
Author(s):  
BAEK-KYU CHO ◽  
ILL-WOO PARK ◽  
JUN-HO OH
Keyword(s):  
Fixed Point ◽  
Angular Momentum ◽  
Sagittal Plane ◽  
Center Of Mass ◽  
Maximum Velocity ◽  
Frontal Plane ◽  
Numerical Approach ◽  
Pattern Generation ◽  
Upper Body ◽  
Running Pattern

This paper discusses the generation of a running pattern for a humanoid biped and verifies the validity of the proposed method of running pattern generation via experiments. Two running patterns are generated independently in the sagittal plane and in the frontal plane and the two patterns are then combined. When a running pattern is created with resolved momentum control in the sagittal plane, the angular momentum of the robot about the Center of Mass (COM) is set to zero, as the angular momentum causes the robot to rotate. However, this also induces unnatural motion of the upper body of the robot. To solve this problem, the biped was set as a virtual under-actuated robot with a free joint at its support ankle, and a fixed point for a virtual under-actuated system was determined. Following this, a periodic running pattern in the sagittal plane was formulated using the fixed point. The fixed point is easily determined in a numerical approach. In this way, a running pattern in the frontal plane was also generated. In an experiment, a humanoid biped known as KHR-2 ran forward using the proposed running pattern generation method. Its maximum velocity was 2.88 km/h.

scholarly journals ON STABILIZATION OF UNSTABLE ROTATION IN THE RESISTING MEDIUM OF THE LAGRANGE GYROSCOPE USING THE SECOND GYROSCOPE AND ELASTIC HINGES

2021 ◽  
Vol 3 (2) ◽  
pp. 103-116
Author(s):  
Ya. Sviatenko ◽  
Keyword(s):  
Fixed Point ◽  
Angular Momentum ◽  
Angular Velocity ◽  
Elastic Recovery ◽  
Center Of Mass ◽  
Uniform Rotation ◽  
Resisting Medium ◽  
The Common ◽  
Elastic Coefficients ◽  
Kinetic Moment

The possibility of stabilizing an unstable uniform rotation in a resisting medium of a "sleeping" Lagrange gyroscope using a rotating second gyroscope and elastic spherical hinges is considered. The "sleeping" gyroscope rotates around a fixed point with an elastic recovery spherical hinge, and the second gyroscope is located above it. The gyroscopes are also connected by an elastic spherical restorative hinge and their rotation is supported by constant moments directed along their axes of rotation. It is shown that stabilization will be impossible in the absence of elasticity in the common joint and the coincidence of the center of mass of the second gyroscope with its center. With the help of the kinetic moment of the second gyroscope and the elasticity coefficients of the hinges, on the basis of an alternative approach, the stabilization conditions obtained in the form of a system of three inequalities and the conditions found on the elasticity coefficients at which the leading coefficients of these inequalities are positive. It is shown that stabilization will always be possible at a sufficiently large angular velocity of rotation of the second gyroscope under the assumption that the center of mass of the second gyroscope and the mechanical system are below the fixed point. The possibility of stabilizing the unstable uniform rotation of the "sleeping" Lagrange gyroscope using the second gyroscope and elastic spherical joints in the absence of dissipation is also considered. The "sleeping" gyroscope rotates at an angular velocity that does not meet the Mayevsky criterion. It is shown that stabilization will be impossible in the absence of elasticity in the common joint and the coincidence of the center of mass of the second gyroscope with its center. On the basis of the innovation approach, stabilization conditions were obtained in the form of a system of three irregularities using the kinetic moment of the second gyroscope and the elastic coefficients of the hinges. The condition for the angular momentum of the first gyroscope and the elastic coefficients at which the leading coefficients of these inequalities are positive are found. It is shown that if the condition for the angular momentum of the first gyroscope is fulfilled, stabilization will always be possible at a sufficiently large angular velocity of rotation of the second gyroscope, and in this case the center of mass of the second gyroscope can be located above the fixed point.

scholarly journals Angular momentum regulation may dictate the slip severity in young adults

2019 ◽  
Author(s):  
Mohammad Moein Nazifi ◽  
Kurt Beschorner ◽  
Pilwon Hur
Keyword(s):  
Young Adults ◽  
Angular Momentum ◽  
Center Of Mass ◽  
Upper Body ◽  
Group Differences ◽  
Normal Gait ◽  
Double Phase ◽  
Single Support Phase ◽  
Time Lead ◽  
Support Phase

AbstractFalls vastly affect the economy and the society with their high cost, injuries, and mortalities. Slipping is the main trigger for falling. Yet, individuals differ in their ability to recover from slips. Mild slippers can accommodate slips without falling, whereas severe slippers indicate inadequate or slow pre-or post-slip control that make them more prone to fall after a slip. Knowing the discrepancies in different kinematic and kinetic variables in mild and severe slippers helps pinpoint the adverse control responsible for severe slipping and falling. This study examined Center of Mass (COM) height, sagittal angular momentum (H), upper body kinematics, and the duration of single/double phase in mild and severe slippers for both normal walking and slipping to identify their differences and possible relationships. Possible causality of such relationships were also studied by observing the time-lead of the deviations. Twenty healthy young adults walked in a long walkway for several trials and were slipped unexpectedly. They were classified into mild and severe slippers based on their slip severity. No inter-group differences were observed in the upper extremity kinematics. It was found that mild and severe slippers do not differ in the studied variables during normal gait; however, they do show significant differences through slipping. Compared to mild slippers, sever slippers lowered their COM height following a slip, presented higher H, and shortened their single support phase (p-value<0.05 for all). Based on the time-lead observed in H over all other variables suggests that angular momentum may be the key variable in controlling slips.

scholarly journals Infrared effects in the late stages of black hole evaporation

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Éanna É. Flanagan
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Center Of Mass ◽  
Planck Scale ◽  
Black Hole Mass ◽  
Order Unity ◽  
Intrinsic Angular Momentum ◽  
Hole Position ◽  
Late Stages ◽  
Shear Tensor

Abstract As a black hole evaporates, each outgoing Hawking quantum carries away some of the black holes asymptotic charges associated with the extended Bondi-Metzner-Sachs group. These include the Poincaré charges of energy, linear momentum, intrinsic angular momentum, and orbital angular momentum or center-of-mass charge, as well as extensions of these quantities associated with supertranslations and super-Lorentz transformations, namely supermomentum, superspin and super center-of-mass charges (also known as soft hair). Since each emitted quantum has fluctuations that are of order unity, fluctuations in the black hole’s charges grow over the course of the evaporation. We estimate the scale of these fluctuations using a simple model. The results are, in Planck units: (i) The black hole position has a uncertainty of $$ \sim {M}_i^2 $$ ∼ M i 2 at late times, where Mi is the initial mass (previously found by Page). (ii) The black hole mass M has an uncertainty of order the mass M itself at the epoch when M ∼ $$ {M}_i^{2/3} $$ M i 2 / 3 , well before the Planck scale is reached. Correspondingly, the time at which the evaporation ends has an uncertainty of order $$ \sim {M}_i^2 $$ ∼ M i 2 . (iii) The supermomentum and superspin charges are not independent but are determined from the Poincaré charges and the super center-of-mass charges. (iv) The supertranslation that characterizes the super center-of-mass charges has fluctuations at multipole orders l of order unity that are of order unity in Planck units. At large l, there is a power law spectrum of fluctuations that extends up to l ∼ $$ {M}_i^2/M $$ M i 2 / M , beyond which the fluctuations fall off exponentially, with corresponding total rms shear tensor fluctuations ∼ MiM−3/2.

THE STEREODYNAMICS STUDY OF THE C(3P) + OH (X2 Π) → CO(X1Σ+) + H(2S) REACTION

2010 ◽  
Vol 09 (05) ◽  
pp. 935-943 ◽  
Author(s):  
PENG SONG ◽  
YONG-HUA ZHU ◽  
JIAN-YONG LIU ◽  
FENG-CAI MA
Keyword(s):  
Angular Momentum ◽  
Cross Sections ◽  
Collision Energy ◽  
Energy Surface ◽  
Center Of Mass ◽  
Title Reaction ◽  
High Collision Energy ◽  
Dependency Relationship ◽  
Energy Dependency ◽  
Mass Frame

The stereodynamics of the title reaction on the ground electronic state X2A' potential energy surface (PES)1 has been studied using the quasiclassical trajectory (QCT) method. The commonly used polarization-dependent differential cross-sections (PDDCSs) of the product and the angular momentum alignment distribution, P(θr) and P(Φr), are generated in the center-of-mass frame using QCT method to gain insight of the alignment and orientation of the product molecules. Influence of collision energy on the stereodynamics is shown and discussed. The results reveal that the distribution of P(θr) and P(Φr) is sensitive to collision energy. The PDDCSs exhibit different collision energy dependency relationship at low and high collision energy ranges.

scholarly journals The Use of Integrals in Numerical Integrations of theN-Body Problem

1971 ◽  
Vol 10 ◽  
pp. 40-51
Author(s):  
Paul E. Nacozy
Keyword(s):  
Angular Momentum ◽  
Numerical Integration ◽  
Degrees Of Freedom ◽  
Body Problem ◽  
Center Of Mass ◽  
Integration Step ◽  
Gravitational System ◽  
Systems Of Differential Equations ◽  
Numerical Integrations ◽  
Original Number

AbstractThe numerical integration of systems of differential equations that possess integrals is often approached by using the integrals to reduce the number of degrees of freedom or by using the integrals as a partial check on the resulting solution, retaining the original number of degrees of freedom.Another use of the integrals is presented here. If the integrals have not been used to reduce the system, the solution of a numerical integration may be constrained to remain on the integral surfaces by a method that applies corrections to the solution at each integration step. The corrections are determined by using linearized forms of the integrals in a least-squares procedure.The results of an application of the method to numerical integrations of a gravitational system of 25-bodies are given. It is shown that by using the method to satisfy exactly the integrals of energy, angular momentum, and center of mass, a solution is obtained that is more accurate while using less time of calculation than if the integrals are not satisfied exactly. The relative accuracy is ascertained by forward and backward integrations of both the corrected and uncorrected solutions and by comparison with more accurate integrations using reduced step-sizes.

scholarly journals Numerical evolution of the center of mass and angular momentum for binary black holes

2021 ◽  
Vol 104 (8) ◽  
Author(s):  
Emmanuel A. Tassone ◽  
Paula A. Mandrilli ◽  
Carlos N. Kozameh ◽  
Gonzalo D. Quiroga ◽  
José I. Nieva
Keyword(s):  
Black Holes ◽  
Angular Momentum ◽  
Center Of Mass ◽  
Binary Black Holes
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