Determinants of the center of mass trajectory in human walking and running.

1998 ◽  
Vol 201 (21) ◽  
pp. 2935-2944 ◽  
Author(s):  
C R Lee ◽  
C T Farley
Keyword(s):  
Stance Phase ◽  
Center Of Mass ◽  
Human Walking ◽  
Gait Transition ◽  
Mass System ◽  
Pendulum System ◽  
Vertical Movements ◽  
Transition Speed ◽  
Inverted Pendulum System ◽  
Limb Compression

Walking is often modeled as an inverted pendulum system in which the center of mass vaults over the rigid stance limb. Running is modeled as a simple spring-mass system in which the center of mass bounces along on the compliant stance limb. In these models, differences in stance-limb behavior lead to nearly opposite patterns of vertical movements of the center of mass in the two gaits. Our goal was to quantify the importance of stance-limb behavior and other factors in determining the trajectory of the center of mass during walking and running. We collected kinematic and force platform data during human walking and running. Virtual stance-limb compression (i.e. reduction in the distance between the point of foot-ground contact and the center of mass during the first half of the stance phase) was only 26% lower for walking (0.091 m) than for running (0.123 m) at speeds near the gait transition speed. In spite of this relatively small difference, the center of mass moved upwards by 0.031 m during the first half of the stance phase during walking and moved downwards by 0.073 m during the first half of the stance phase during running. The most important reason for this difference was that the stance limb swept through a larger angle during walking (30.4 degrees) than during running (19.2 degrees). We conclude that stance-limb touchdown angle and virtual stance-limb compression both play important roles in determining the trajectory of the center of mass and whether a gait is a walk or a run.

scholarly journals Effect of reduced gravity on the preferred walk-run transition speed.

1997 ◽  
Vol 200 (4) ◽  
pp. 821-826 ◽  
Author(s):  
R Kram ◽  
A Domingo ◽  
D P Ferris
Keyword(s):  
Froude Number ◽  
Inverted Pendulum ◽  
Center Of Mass ◽  
Reduced Gravity ◽  
Leg Length ◽  
Pendulum System ◽  
Transition Speed ◽  
Inverted Pendulum Model ◽  
Inverted Pendulum System ◽  
Pendulum Model

We investigated the effect of reduced gravity on the human walk-run gait transition speed and interpreted the results using an inverted-pendulum mechanical model. We simulated reduced gravity using an apparatus that applied a nearly constant upward force at the center of mass, and the subjects walked and ran on a motorized treadmill. In the inverted pendulum model for walking, gravity provides the centripetal force needed to keep the pendulum in contact with the ground. The ratio of the centripetal and gravitational forces (mv2/L)/(mg) reduces to the dimensionless Froude number (v2/gL). Applying this model to a walking human, m is body mass, v is forward velocity, L is leg length and g is gravity. In normal gravity, humans and other bipeds with different leg lengths all choose to switch from a walk to a run at different absolute speeds but at approximately the same Froude number (0.5). We found that, at lower levels of gravity, the walk-run transition occurred at progressively slower absolute speeds but at approximately the same Froude number. This supports the hypothesis that the walk-run transition is triggered by the dynamics of an inverted-pendulum system.

scholarly journals Estimation of leg stiffness using an approximation to the planar spring–mass system in high-speed running

2020 ◽  
Vol 17 (1) ◽  
pp. 172988141989071
Author(s):  
Wei Guo ◽  
Changrong Cai ◽  
Mantian Li ◽  
Fusheng Zha ◽  
Pengfei Wang ◽  
...  
Keyword(s):  
Analytical Solution ◽  
High Speed ◽  
Stance Phase ◽  
Center Of Mass ◽  
Critical Role ◽  
Line Center ◽  
Motion Model ◽  
Mass System ◽  
Leg Stiffness ◽  
Wide Range

Leg stiffness plays a critical role in legged robots’ speed regulation. However, the analytic solutions to the differential equations of the stance phase do not exist, of course not for the exact analytical solution of stiffness. In view of the challenge in dealing with every circumstance by numerical methods, which have been adopted to tabulate approximate answers, the “harmonic motion model” was used as approximation of the stance phase. However, the wide range leg sweep angles and small fluctuations of the “center of mass” in fast movement were overlooked. In this article, we raise a “triangle motion model” with uniform forward speed, symmetric movement, and straight-line center of mass trajectory. The characters are then shifted to a quadratic equation by Taylor expansion and obtain an approximate analytical solution. Both the numerical simulation and ADAMS-Matlab co-simulation of the control system show the accuracy of the triangle motion model method in predicting leg stiffness even in the ultra-high-speed case, and it is also adaptable to low-speed cases. The study illuminates the relationship between leg stiffness and speed, and the approximation model of the planar spring–mass system may serve as an analytical tool for leg stiffness estimation in high-speed locomotion.

Functional Role of the Front and Back Legs During a Track Start with Special Reference to an Inverted Pendulum Model in College Swimmers

2016 ◽  
Vol 32 (5) ◽  
pp. 462-468 ◽  
Author(s):  
Yusuke Ikeda ◽  
Hiroshi Ichikawa ◽  
Rio Nara ◽  
Yasuhiro Baba ◽  
Yoshimitsu Shimoyama ◽  
...  
Keyword(s):  
Inverted Pendulum ◽  
Center Of Mass ◽  
Video Camera ◽  
Flight Distance ◽  
Training Methods ◽  
Vertical Force ◽  
Rotational Component ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Back Plate

This study investigated factors that determine the velocity of the center of mass (CM) and flight distance from a track start to devise effective technical and physical training methods. Nine male and 5 female competitive swimmers participated in this study. Kinematics and ground reaction forces of the front and back legs were recorded using a video camera and force plates. The track start was modeled as an inverted pendulum system including a compliant leg, connecting the CM and front edge of the starting block. The increase in the horizontal velocity of the CM immediately after the start signal was closely correlated with the rotational component of the inverted pendulum. This rotational component at hands-off was significantly correlated with the average vertical force of the back plate from the start signal to hands-off (r = .967, P < .001). The flight distance / height was significantly correlated with the average vertical force of the front plate from the back foot-off to front foot-off (r = .783, P < .01). The results indicate that the legs on the starting block in the track start play a different role in the behavior of the inverted pendulum.

scholarly journals Running springs: speed and animal size

1993 ◽  
Vol 185 (1) ◽  
pp. 71-86 ◽  
Author(s):  
C. T. Farley ◽  
J. Glasheen ◽  
T. A. McMahon
Keyword(s):  
Body Mass ◽  
Stance Phase ◽  
Center Of Mass ◽  
Vertical Vibration ◽  
Contact Phase ◽  
Mass System ◽  
Spring System ◽  
Animal Size ◽  
Resonant Period ◽  
Leg Spring

Trotting and hopping animals use muscles, tendons and ligaments to store and return elastic energy as they bounce along the ground. We examine how the musculoskeletal spring system operates at different speeds and in animals of different sizes. We model trotting and hopping as a simple spring-mass system which consists of a leg spring and a mass. We find that the stiffness of the leg spring (k(leg)) is nearly independent of speed in dogs, goats, horses and red kangaroos. As these animals trot or hop faster, the leg spring sweeps a greater angle during the stance phase, and the vertical excursion of the center of mass during the ground contact phase decreases. The combination of these changes to the spring system causes animals to bounce off the ground more quickly at higher speeds. Analysis of a wide size range of animals (0.1-140 kg) at equivalent speeds reveals that larger animals have stiffer leg springs (k(leg) [symbol: see text] M0.67, where M is body mass), but that the angle swept by the leg spring is nearly independent of body mass. As a result, the resonant period of vertical vibration of the spring-mass system is longer in larger animals. The length of time that the feet are in contact with the ground increases with body mass in nearly the same way as the resonant period of vertical vibration.

Predictor-network-based MRACS for inverted pendulum system.

1991 ◽  
Vol 111 (3) ◽  
pp. 221-229 ◽  
Author(s):  
Motomiki Uchida ◽  
Yukihiro Toyoda ◽  
Yoshikuni Akiyama ◽  
Kazushi Nakano ◽  
Hideo Nakamura
Keyword(s):  
Inverted Pendulum ◽  
Pendulum System ◽  
Inverted Pendulum System

Optimal PID Design Approaches for an Inverted Pendulum System

2016 ◽  
Vol 9 (3) ◽  
pp. 167 ◽  
Author(s):  
Muhammad Sani Gaya ◽  
Anas Abubakar Bisu ◽  
Syed Najib Syed Salim ◽  
I. S. Madugu ◽  
L. A. Yusuf ◽  
...  
Keyword(s):  
Inverted Pendulum ◽  
Pendulum System ◽  
Inverted Pendulum System

A quantitative measure of the degree of output controllability for output regulation control systems: Concept, approach, and applications

2021 ◽  
pp. 107754632110201
Author(s):  
Yaping Xia ◽  
Ruiyu Li ◽  
Minghui Yin ◽  
Yun Zou
Keyword(s):  
Structural Parameters ◽  
Quantitative Measure ◽  
Output Regulation ◽  
State Regulation ◽  
Control Effect ◽  
Pendulum System ◽  
Design And Optimization ◽  
Inverted Pendulum System ◽  
State Regulator ◽  
Output Controllability

Currently, many research studies reveal that for state regulator problems, the higher the degree of controllability is, the better the control effect likely is. Note that for the output regulator problems, the control performance is often evaluated by outputs. This article hence generalizes the concept and applications of degree of controllability to the case of output regulator. To this end, a kind of degree of output controllability is presented. Furthermore, simulations on wind turbines and the inverted pendulum system demonstrate that better control effect may be achieved by increasing the degree of output controllability measure. These results imply that similar to the case of degree of controllability for state regulation control, the degree of output controllability measure is likely a feasible candidate index for the design and optimization of the structural parameters of controlled plants in the case of output regulation control.

scholarly journals An Optimized Triggering Algorithm for Event-Triggered Control of Networked Control Systems

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1262
Author(s):  
Sunil Kumar Mishra ◽  
Amitkumar V. Jha ◽  
Vijay Kumar Verma ◽  
Bhargav Appasani ◽  
Almoataz Y. Abdelaziz ◽  
...  
Keyword(s):  
Control Systems ◽  
Networked Control Systems ◽  
Networked Control ◽  
Pendulum System ◽  
Uniform Sampling ◽  
Inverted Pendulum System ◽  
Event Triggering ◽  
Non Uniform Sampling ◽  
System States ◽  
Event Triggered

This paper presents an optimized algorithm for event-triggered control (ETC) of networked control systems (NCS). Initially, the traditional backstepping controller is designed for a generalized nonlinear plant in strict-feedback form that is subsequently extended to the ETC. In the NCS, the controller and the plant communicate with each other using a communication network. In order to minimize the bandwidth required, the number of samples to be sent over the communication channel should be reduced. This can be achieved using the non-uniform sampling of data. However, the implementation of non-uniform sampling without a proper event triggering rule might lead the closed-loop system towards instability. Therefore, an optimized event triggering algorithm has been designed such that the system states are always forced to remain in stable trajectory. Additionally, the effect of ETC on the stability of backstepping control has been analyzed using the Lyapunov stability theory. Two case studies on an inverted pendulum system and single-link robot system have been carried out to demonstrate the effectiveness of the proposed ETC in terms of system states, control effort and inter-event execution time.

scholarly journals Vertical Jumping for Legged Robot Based on Quadratic Programming

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3679
Author(s):  
Dingkui Tian ◽  
Junyao Gao ◽  
Xuanyang Shi ◽  
Yizhou Lu ◽  
Chuzhao Liu
Keyword(s):  
Quadratic Programming ◽  
Stance Phase ◽  
Center Of Mass ◽  
Maximum Error ◽  
Legged Robot ◽  
Flight Phase ◽  
Programming Framework ◽  
Vertical Jumping ◽  
Control Schemes ◽  
And Control

The highly dynamic legged jumping motion is a challenging research topic because of the lack of established control schemes that handle over-constrained control objectives well in the stance phase, which are coupled and affect each other, and control robot’s posture in the flight phase, in which the robot is underactuated owing to the foot leaving the ground. This paper introduces an approach of realizing the cyclic vertical jumping motion of a planar simplified legged robot that formulates the jump problem within a quadratic-programming (QP)-based framework. Unlike prior works, which have added different weights in front of control tasks to express the relative hierarchy of tasks, in our framework, the hierarchical quadratic programming (HQP) control strategy is used to guarantee the strict prioritization of the center of mass (CoM) in the stance phase while split dynamic equations are incorporated into the unified quadratic-programming framework to restrict the robot’s posture to be near a desired constant value in the flight phase. The controller is tested in two simulation environments with and without the flight phase controller, the results validate the flight phase controller, with the HQP controller having a maximum error of the CoM in the x direction and y direction of 0.47 and 0.82 cm and thus enabling the strict prioritization of the CoM.

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