scholarly journals All common bipedal gaits emerge from a single passive model

2018 ◽  
Vol 15 (146) ◽  
pp. 20180455 ◽  
Author(s):  
Zhenyu Gan ◽  
Yevgeniy Yesilevskiy ◽  
Petr Zaytsev ◽  
C. David Remy
Keyword(s):  
Vertical Motion ◽  
Legged Robots ◽  
Nonlinear Modes ◽  
One Dimensional ◽  
Leg Motion ◽  
Mechanical Dynamics ◽  
And Control ◽  
Parameter Values ◽  
Single Set ◽  
Passive Model

In this paper, we systematically investigate passive gaits that emerge from the natural mechanical dynamics of a bipedal system. We use an energetically conservative model of a simple spring-leg biped that exhibits well-defined swing leg dynamics. Through a targeted continuation of periodic motions of this model, we systematically identify different gaits that emerge from simple bouncing in place. We show that these gaits arise along one-dimensional manifolds that bifurcate into different branches with distinctly different motions. The branching is associated with repeated breaks in symmetry of the motion. Among others, the resulting passive dynamic gaits include walking, running, hopping, skipping and galloping. Our work establishes that the most common bipedal gaits can be obtained as different oscillatory motions (or nonlinear modes) of a single mechanical system with a single set of parameter values. For each of these gaits, the timing of swing leg motion and vertical motion is matched. This work thus supports the notion that different gaits are primarily a manifestation of the underlying natural mechanical dynamics of a legged system. Our results might explain the prevalence of certain gaits in nature, and may provide a blueprint for the design and control of energetically economical legged robots.

scholarly journals Analytical solution of one-dimensional Pennes’ bioheat equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1084-1092
Author(s):  
Hongyun Wang ◽  
Wesley A. Burgei ◽  
Hong Zhou
Keyword(s):  
Analytical Solution ◽  
Radiofrequency Energy ◽  
Bioheat Equation ◽  
Surface Cooling ◽  
One Dimensional ◽  
The Fourier Transform ◽  
The One ◽  
Parameter Values ◽  
Mathematical Derivation ◽  
Effect Of Surface

Abstract Pennes’ bioheat equation is the most widely used thermal model for studying heat transfer in biological systems exposed to radiofrequency energy. In their article, “Effect of Surface Cooling and Blood Flow on the Microwave Heating of Tissue,” Foster et al. published an analytical solution to the one-dimensional (1-D) problem, obtained using the Fourier transform. However, their article did not offer any details of the derivation. In this work, we revisit the 1-D problem and provide a comprehensive mathematical derivation of an analytical solution. Our result corrects an error in Foster’s solution which might be a typo in their article. Unlike Foster et al., we integrate the partial differential equation directly. The expression of solution has several apparent singularities for certain parameter values where the physical problem is not expected to be singular. We show that all these singularities are removable, and we derive alternative non-singular formulas. Finally, we extend our analysis to write out an analytical solution of the 1-D bioheat equation for the case of multiple electromagnetic heating pulses.

Momentum exchange impact damper design methodology for object-wall-collision problems

2017 ◽  
Vol 24 (14) ◽  
pp. 3206-3218
Author(s):  
Yohei Kushida ◽  
Hiroaki Umehara ◽  
Susumu Hara ◽  
Keisuke Yamada
Keyword(s):  
Optimal Design ◽  
Design Methodology ◽  
Design Parameters ◽  
Momentum Exchange ◽  
Impact Damper ◽  
One Dimensional ◽  
Practical Design ◽  
Wall Collision ◽  
Damper Design ◽  
And Control

Momentum exchange impact dampers (MEIDs) were proposed to control the shock responses of mechanical structures. They were applied to reduce floor shock vibrations and control lunar/planetary exploration spacecraft landings. MEIDs are required to control an object’s velocity and displacement, especially for applications involving spacecraft landing. Previous studies verified numerous MEID performances through various types of simulations and experiments. However, previous studies discussing the optimal design methodology for MEIDs are limited. This study explicitly derived the optimal design parameters of MEIDs, which control the controlled object’s displacement and velocity to zero in one-dimensional motion. In addition, the study derived sub-optimal design parameters to control the controlled object’s velocity within a reasonable approximation to derive a practical design methodology for MEIDs. The derived sub-optimal design methodology could also be applied to MEIDs in two-dimensional motion. Furthermore, simulations conducted in the study verified the performances of MEIDs with optimal/sub-optimal design parameters.

Damping of Self-Excited Pressure Pulsations in Petrodiesel Pipeline

2014 ◽  
Vol 630 ◽  
pp. 375-382 ◽  
Author(s):  
Daniel Himr ◽  
Vladimir Haban
Keyword(s):  
Hydraulic System ◽  
Check Valve ◽  
Control Valve ◽  
Sampling Frequency ◽  
Pressure Pulsations ◽  
One Dimensional ◽  
Fuel Storage ◽  
Excited Oscillation ◽  
Subsequent Measurement ◽  
And Control

A pumping station in a fuel storage suffered from pressure pulsations in a petrodiesel pipeline. Check valves protecting the station against back flow made a big noise when disc hit a seat. Due to employees complaints we were asked to solve the problem, which could lead to serious mechanical problems. Pressure measurement in the pipeline showed great pulsations, which were caused by self-excited oscillation of control valves at the downstream end of pipeline. The operating measurement did not catch it because of too low sampling frequency. One dimensional numerical model of the whole hydraulic system was carried out. The model consisted of check valve, pipeline and control valve, which could oscillate, so it was possible to simulate the unsteady flow. When the model was validated, a vessel with nitrogen was added to attenuate pressure pulsations. According to the results of numerical simulation, the vessel was installed on the location. Subsequent measurement proved noticeably lower pulsations and almost no noise.

scholarly journals Discovering the two faces of religious charismatic action – traditional and modern: a model

1999 ◽  
Vol 17 (1) ◽  
pp. 273-304
Author(s):  
Jane Williams-Hogan
Keyword(s):  
Structural Characteristics ◽  
Modern Society ◽  
Natural World ◽  
One Dimensional ◽  
New Religions ◽  
The World ◽  
The Gift ◽  
Rational Calculation ◽  
Traditional Societies ◽  
And Control

In this paper, the author examines the issue of charisma and prophecy in secularized societies. In traditional society the charismatic personality or the prophet brought a universalizing and rationalizing message which simultaneously expanded and penetrated the sphere of external order in the world, giving people the ability to manipulate and control the natural world. The disenchanted world is the end product of this process, when no more mysterious forces come into play, and when one can in principle master all things through rational calculation. The gift of rationality almost randomly bestowed in the ancient world becomes, for Weber, the rightful inheritance of the modern individual. Clarity brought by charisma in a dark and foreboding world loses its brilliance and its ability to beckon when the world is filled with light. In investigating charisma in only traditional societies, Weber saw charisma as one dimensional, solely as the force of rationality. So envisioned, charisma dissipates in the very act of realizing itself through the transformation of the world. Given Weber's analysis, therefore, one would not expect to find genuinely new religions emerging within our transformed and rational modern society. In the examination of the founding something that is best identified by the sociological term charisma, though obviously in modern guise, is clearly evident. This points to the possibility that charisma is not static but has the dynamic capacity to be responsive to the structural characteristics of the society in which it operates.

STABILIZATION OF CHAOTIC DYNAMICS OF ONE-DIMENSIONAL MAPS BY A CYCLIC PARAMETRIC TRANSFORMATION

1996 ◽  
Vol 06 (04) ◽  
pp. 725-735 ◽  
Author(s):  
ALEXANDER Yu. LOSKUTOV ◽  
VALERY M. TERESHKO ◽  
KONSTANTIN A. VASILIEV
Keyword(s):  
Periodic Orbits ◽  
Chaotic Dynamics ◽  
Chaotic Maps ◽  
Logistic Map ◽  
Exponential Map ◽  
One Dimensional ◽  
Stable Periodic ◽  
One Dimensional Maps ◽  
Parameter Values ◽  
Parametric Transformation

We consider one-dimensional maps, the logistic map and an exponential map, in those sets of parameter values which correspond to their chaotic dynamics. It is proven that such dynamics may be stabilized by a certain cyclic parametric transformation operating strictly within the chaotic set. The stabilization is a result of the creation of stable periodic orbits in the initially chaotic maps. The period of these stable orbits is a multiple of the period of the cyclic transformation. It is shown that stabilized behavior cannot be destroyed by a weak noise smearing of the required parameter values. The regions where the behavior stabilization takes place are numerically estimated. Periods of the created stabile periodic orbits are calculated.

scholarly journals Modeling and Control of Legged Robots

2016 ◽  
pp. 1203-1234 ◽  
Author(s):  
Pierre-Brice Wieber ◽  
Russ Tedrake ◽  
Scott Kuindersma
Keyword(s):  
Legged Robots ◽  
Modeling And Control ◽  
And Control

Intervention Time in Target-Oriented Chaos Control

2021 ◽  
Vol 31 (09) ◽  
pp. 2150134
Author(s):  
Juan Segura
Keyword(s):  
Discrete Time ◽  
Chaos Control ◽  
Control Method ◽  
Single Species ◽  
Positive Equilibrium ◽  
Population Stability ◽  
Determine Parameter ◽  
And Control ◽  
Parameter Values ◽  
Proportional Feedback

The timing of interventions plays a central role in managing and exploiting biological populations. However, few studies in the literature have addressed its effect on population stability. The Seno equation is a discrete-time equation that describes the dynamics of single-species populations harvested according to the proportional feedback method at any moment between two consecutive censuses. Here we study a discrete-time equation that generalizes the Seno equation by considering the management and exploitation of populations through the target-oriented chaos control method. We investigate the combined effect of timing, targeting, and control on population stability, focusing on global stability. We prove that high enough control values create a positive equilibrium that attracts all positive solutions. We also prove that it is possible to determine parameter values to stabilize the controlled populations at any preset population size. Finally, we investigate the parameter combinations for which the management and exploitation are optimized in different scenarios.

Delay-Adaptive Linear Control

2020 ◽  
Author(s):  
Yang Zhu ◽  
Miroslav Krstic
Keyword(s):  
Nonlinear Differential Equations ◽  
Stability Study ◽  
Delay Systems ◽  
Engineering Practice ◽  
Delay Compensation ◽  
Infinite Dimensional ◽  
Controlled Systems ◽  
Finite Dimensional ◽  
And Control ◽  
Parameter Values

Actuator and sensor delays are among the most common dynamic phenomena in engineering practice, and when disregarded, they render controlled systems unstable. Over the past sixty years, predictor feedback has been a key tool for compensating such delays, but conventional predictor feedback algorithms assume that the delays and other parameters of a given system are known. When incorrect parameter values are used in the predictor, the resulting controller may be as destabilizing as without the delay compensation. This book develops adaptive predictor feedback algorithms equipped with online estimators of unknown delays and other parameters. Such estimators are designed as nonlinear differential equations, which dynamically adjust the parameters of the predictor. The design and analysis of the adaptive predictors involves a Lyapunov stability study of systems whose dimension is infinite, because of the delays, and nonlinear, because of the parameter estimators. This book solves adaptive delay compensation problems for systems with single and multiple inputs/outputs, unknown and distinct delays in different input channels, unknown delay kernels, unknown plant parameters, unmeasurable finite-dimensional plant states, and unmeasurable infinite-dimensional actuator states. Presenting breakthroughs in adaptive control and control of delay systems, the book offers powerful new tools for the control engineer and the mathematician.

scholarly journals Novel Solution for Leg Motion with 5-Link Belt Mechanism

2014 ◽  
Vol 19 (4) ◽  
pp. 699-708 ◽  
Author(s):  
Lovasz E.Ch. ◽  
Pop C. ◽  
Pop F. ◽  
Dolga V.
Keyword(s):  
Mathematical Model ◽  
Step Height ◽  
Crossing Over ◽  
The Novel ◽  
Leg Motion ◽  
Walking Mechanism ◽  
And Control

Abstract From the analysis of Theo Jansen walking mechanism and of the path curve that it describes the reduced capability for crossing over obstacles of the Jansen leg (1 DOF) is pointed out. By using a 5 link belt mechanism with 2 DOF can be adapted for generating similar Jansen mechanism path curve, where the step height of this path can be increased. For this purpose a mathematical model is conceived in order to analyse and determine the parameters for driving and control of the operation of the novel walking leg solution.

scholarly journals Escherichia coli O157 infection on Scottish cattle farms: dynamics and control

2010 ◽  
Vol 8 (60) ◽  
pp. 1051-1058 ◽  
Author(s):  
Xu-Sheng Zhang ◽  
Mark E. J. Woolhouse
Keyword(s):  
Escherichia Coli ◽  
Herd Size ◽  
Parameter Estimates ◽  
Control Effort ◽  
Considerable Uncertainty ◽  
Targeted Interventions ◽  
Dynamics And Control ◽  
And Control ◽  
Parameter Values ◽  
Cattle Farms

In this study, we parametrize a stochastic individual-based model of the transmission dynamics of Escherichia coli O157 infection among Scottish cattle farms and use the model to predict the impacts of both targeted and non-targeted interventions. We first generate distributions of model parameter estimates using Markov chain Monte Carlo methods. Despite considerable uncertainty in parameter values, each set of parameter values within the 95th percentile range implies a fairly similar impact of interventions. Interventions that reduce the transmission coefficient and/or increase the recovery rate of infected farms (e.g. via vaccination and biosecurity) are much more effective in reducing the level of infection than reducing cattle movement rates, which improves effectiveness only when the overall control effort is small. Targeted interventions based on farm-level risk factors are more efficient than non-targeted interventions. Herd size is a major determinant of risk of infection, and our simulations confirmed that targeting interventions at farms with the largest herds is almost as effective as targeting based on overall risk. However, because of the striking characteristic that the infection force depends weakly on the number of infected farms, no interventions that are less than 100 per cent effective can eradicate E. coli O157 infection from Scottish cattle farms, implying that eliminating the disease is impractical.

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