scholarly journals Lateral oscillations of the center of mass of bipeds as they walk. Inverted pendulum model with two degrees of freedom

AIP Advances ◽  
2015 ◽  
Vol 5 (10) ◽  
pp. 107208
Author(s):  
Guillermo H Goldsztein
Keyword(s):  
Degrees Of Freedom ◽  
Inverted Pendulum ◽  
Center Of Mass ◽  
Two Degrees Of Freedom ◽  
Inverted Pendulum Model ◽  
Pendulum Model

scholarly journals Turning Gait Planning Method for Humanoid Robots

2018 ◽  
Vol 8 (8) ◽  
pp. 1257 ◽  
Author(s):  
Tianqi Yang ◽  
Weimin Zhang ◽  
Xuechao Chen ◽  
Zhangguo Yu ◽  
Libo Meng ◽  
...  
Keyword(s):  
Inverted Pendulum ◽  
Center Of Mass ◽  
Translational Motion ◽  
Humanoid Robots ◽  
Inverted Pendulum Model ◽  
Straight Line ◽  
Pendulum Model ◽  
The Stability ◽  
And Control ◽  
Present Simulation

The most important feature of this paper is to transform the complex motion of robot turning into a simple translational motion, thus simplifying the dynamic model. Compared with the method that generates a center of mass (COM) trajectory directly by the inverted pendulum model, this method is more precise. The non-inertial reference is introduced in the turning walk. This method can translate the turning walk into a straight-line walk when the inertial forces act on the robot. The dynamics of the robot model, called linear inverted pendulum (LIP), are changed and improved dynamics are derived to make them apply to the turning walk model. Then, we expend the new LIP model and control the zero moment point (ZMP) to guarantee the stability of the unstable parts of this model in order to generate a stable COM trajectory. We present simulation results for the improved LIP dynamics and verify the stability of the robot turning.

Stabilized Walking of Humanoid NAO using Enhanced Spring-Loaded Inverted Pendulum Model on Uneven Terrain

2022 ◽  
Vol 13 (1) ◽  
pp. 0-0
Keyword(s):  
Path Length ◽  
Inverted Pendulum ◽  
Center Of Mass ◽  
Humanoid Robots ◽  
Slip Model ◽  
Turning Angle ◽  
Uneven Terrain ◽  
Inverted Pendulum Model ◽  
Pendulum Model ◽  
Spring Loaded Inverted Pendulum

In the coming decades, humanoid robots will play a rising role in society. The present article discusses their walking control and obstacle avoidance on uneven terrain using enhanced spring-loaded inverted pendulum model (ESLIP). The SLIP model is enhanced by tuning it with an adaptive particle swarm optimization (APSO) approach. It helps the humanoid robot to reach closer to the obstacles in order to optimize the turning angle to optimize the path length. The desired trajectory, along with the sensory data, is provided to the SLIP model, which creates compatible COM (center of mass) dynamics for stable walking. This output is fed to APSO as input, which adjusts the placement of the foot during interaction with uneven surfaces and obstacles. It provides an optimum turning angle for shunning the obstacles and ensures the shortest path length. Simulation has been carried out in a 3D simulator based on the proposed controller and SLIP controller in uneven terrain.

Parameterized gait pattern generator based on linear inverted pendulum model with natural ZMP references

2016 ◽  
Vol 32 ◽  
Author(s):  
Ya-Fang Ho ◽  
Tzuu-Hseng S. Li ◽  
Ping-Huan Kuo ◽  
Yan-Ting Ye
Keyword(s):  
Inverted Pendulum ◽  
Center Of Mass ◽  
Gait Pattern ◽  
Gait Patterns ◽  
Gait Planning ◽  
Inverted Pendulum Model ◽  
Pendulum Model ◽  
Lateral Plane ◽  
Planning Algorithm ◽  
Zero Moment

AbstractThis paper presents a parameterized gait generator based on linear inverted pendulum model (LIPM) theory, which allows users to generate a natural gait pattern with desired step sizes. Five types of zero moment point (ZMP) components are proposed for formulating a natural ZMP reference, where ZMP moves continuously during single support phases instead of staying at a fixed point in the sagittal and lateral plane. The corresponding center of mass (CoM) trajectories for these components are derived by LIPM theory. To generate a parameterized gait pattern with user-defined parameters, a gait planning algorithm is proposed, which determines related coefficients and boundary conditions of the CoM trajectory for each step. The proposed parameterized gait generator also provides a concept for users to generate gait patterns with self-defined ZMP references by using different components. Finally, the feasibility of the proposed method is validated by the experimental results with a teen-sized humanoid robot, David, which won first place in the sprint event at the 20th Federation of International Robot-soccer Association (FIRA) RoboWorld Cup.

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.

Biped Walking Using Multiple-Link Virtual Inverted Pendulum Models

1999 ◽  
Vol 11 (4) ◽  
pp. 304-309 ◽  
Author(s):  
Takayuki Furuta ◽  
◽  
Hideaki Yamato ◽  
Ken Tomiyama
Keyword(s):  
Degrees Of Freedom ◽  
Humanoid Robot ◽  
Inverted Pendulum ◽  
Model Reference ◽  
Biped Walking ◽  
Experimental Platform ◽  
Walking Control ◽  
Inverted Pendulum Model ◽  
Pendulum Model

The purpose of this study is to realize 3D biped walking in a humanoid robot. A robot that has 12 degrees of freedom with 2 legs was designed and constructed as an experimental platform. Model reference walking control with a virtual inverted pendulum model is proposed, implemented on the robot to realize stable walking.

scholarly journals Capture Steps: Robust Walking for Humanoid Robots

2019 ◽  
Vol 16 (06) ◽  
pp. 1950032 ◽  
Author(s):  
Marcell Missura ◽  
Maren Bennewitz ◽  
Sven Behnke
Keyword(s):  
Degrees Of Freedom ◽  
Center Of Mass ◽  
Humanoid Robots ◽  
Open Loop ◽  
Bipedal Walking ◽  
Foot Placement ◽  
Inverted Pendulum Model ◽  
Push Recovery ◽  
Pendulum Model ◽  
Walking Velocity

Stable bipedal walking is a key prerequisite for humanoid robots to reach their potential of being versatile helpers in our everyday environments. Bipedal walking is, however, a complex motion that requires the coordination of many degrees of freedom while it is also inherently unstable and sensitive to disturbances. The balance of a walking biped has to be constantly maintained. The most effective ways of controlling balance are well timed and placed recovery steps — capture steps — that absorb the expense momentum gained from a push or a stumble. We present a bipedal gait generation framework that utilizes step timing and foot placement techniques in order to recover the balance of a biped even after strong disturbances. Our framework modifies the next footstep location instantly when responding to a disturbance and generates controllable omnidirectional walking using only very little sensing and computational power. We exploit the open-loop stability of a central pattern generated gait to fit a linear inverted pendulum model (LIPM) to the observed center of mass (CoM) trajectory. Then, we use the fitted model to predict suitable footstep locations and timings in order to maintain balance while following a target walking velocity. Our experiments show qualitative and statistical evidence of one of the strongest push-recovery capabilities among humanoid robots to date.

scholarly journals Trajectory Planning of Flexible Walking for Biped Robots Using Linear Inverted Pendulum Model and Linear Pendulum Model

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1082
Author(s):  
Long Li ◽  
Zhongqu Xie ◽  
Xiang Luo ◽  
Juanjuan Li
Keyword(s):  
Trajectory Planning ◽  
Inverted Pendulum ◽  
Negative Impact ◽  
Center Of Mass ◽  
Biped Robot ◽  
Biped Robots ◽  
Double Support ◽  
Inverted Pendulum Model ◽  
Pendulum Model ◽  
Support Phase

Linear inverted pendulum model (LIPM) is an effective and widely used simplified model for biped robots. However, LIPM includes only the single support phase (SSP) and ignores the double support phase (DSP). In this situation, the acceleration of the center of mass (CoM) is discontinuous at the moment of leg exchange, leading to a negative impact on walking stability. If the DSP is added to the walking cycle, the acceleration of the CoM will be smoother and the walking stability of the biped will be improved. In this paper, a linear pendulum model (LPM) for the DSP is proposed, which is similar to LIPM for the SSP. LPM has similar characteristics to LIPM. The dynamic equation of LPM is also linear, and its analytical solution can be obtained. This study also proposes different trajectory-planning methods for different situations, such as periodic walking, adjusting walking speed, disturbed state recovery, and walking terrain-blind. These methods have less computation and can plan trajectory in real time. Simulation results verify the effectiveness of proposed methods and that the biped robot can walk stably and flexibly when combining LIPM and LPM.

scholarly journals Balancing on a narrow ridge: biomechanics and control

1999 ◽  
Vol 354 (1385) ◽  
pp. 869-875 ◽  
Author(s):  
E. Otten
Keyword(s):  
Hip Joint ◽  
Ground Reaction Force ◽  
Inverted Pendulum ◽  
Reaction Force ◽  
Angular Acceleration ◽  
Centre Of Mass ◽  
Inverted Pendulum Model ◽  
Pendulum Model ◽  
Narrow Ridge ◽  
Standing Humans

The balance of standing humans is usually explained by the inverted pendulum model. The subject invokes a horizontal ground–reaction force in this model and controls it by changing the location of the centre of pressure under the foot or feet. In experiments I showed that humans are able to stand on a ridge of only a few millimetres wide on one foot for a few minutes. In the present paper I investigate whether the inverted pendulum model is able to explain this achievement. I found that the centre of mass of the subjects sways beyond the surface of support, rendering the inverted pendulum model inadequate. Using inverse simulations of the dynamics of the human body, I found that hip–joint moments of the stance leg are used to vary the horizontal component of the ground–reaction force. This force brings the centre of mass back over the surface of support. The subjects generate moments of force at the hip–joint of the swing leg, at the shoulder–joints and at the neck. These moments work in conjunction with a hip strategy of the stance leg to limit the angular acceleration of the head–arm–trunk complex. The synchrony of the variation in moments suggests that subjects use a motor programme rather than long latency reflexes.

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