Dynamics of a Pedestrian’s Walking Motion Based on the Inverted Pendulum Model

2018 ◽  
Vol 18 (11) ◽  
pp. 1850145 ◽  
Author(s):  
Lijun Ouyang ◽  
TingTing Li ◽  
Bin Zhen ◽  
Lei Wei
Keyword(s):  
Inverted Pendulum ◽  
Vertical Direction ◽  
Lateral Force ◽  
Vertical Vibration ◽  
Step Frequency ◽  
Inverted Pendulum Model ◽  
Pendulum Model ◽  
Walking Motion ◽  
Vertical Step ◽  
The Stability

In this paper, the inverted pendulum model is proposed to describe a pedestrian’s walking motion by considering that the pivot point vibrates periodically up and down. The stability, periodic solutions and oscillations of the inverted pendulum are theoretically investigated, the correctness of which is illustrated by numerical simulations. According to frequency spectrum analysis, the inverted pendulum can exhibit periodically or quasi-periodically stable oscillations. However, we demonstrate that the inverted pendulum will maintain the ratio between the lateral and vertical vibration frequencies near [Formula: see text] as an optimizing selection of stability. The theoretical result agrees with the measurement result for a normal pedestrian such that the lateral step frequency is always half the vertical step frequency, which means that it is feasible and reasonable to describe a pedestrian’s walking motion using the inverted pendulum with the pivot vibrating harmonically in the vertical direction. The inverted pendulum model suggested in this paper could contribute to the study of pedestrian–footbridge interaction, which overcomes the difficulty of directly determining the expression of the lateral force induced by pedestrians.

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.

scholarly journals An Inverted Pendulum Model Describing the Lateral Pedestrian-Footbridge Interaction

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Bin Zhen ◽  
Liang Chang ◽  
Zigen Song
Keyword(s):  
Inverted Pendulum ◽  
Measurement Data ◽  
Lateral Force ◽  
Frequency Locking ◽  
Whole Process ◽  
Lateral Vibrations ◽  
Inverted Pendulum Model ◽  
Semiempirical Approach ◽  
Pendulum Model ◽  
Key Factor

In this paper, the lateral pedestrian-footbridge interaction is investigated by using the model of an inverted pendulum on a cart. The inverted pendulum and the cart separately represent the synchronous pedestrians and the footbridge. The pivot point of the inverted pendulum is considered to vibrate harmonically to model the walking motion of the pedestrians. The proposed inverted pendulum model avoids the difficulty of the determination of the lateral force induced by the pedestrians applying to the footbridge, which was usually treated based on a semiempirical approach in previous works. Moreover, the model can describe the whole process: how the lateral amplitude of the bridge increases from small to large. Measurement data showed that a normal pedestrian always keeps the ratio of 1/2 between the lateral and vertical step frequencies. The theoretical analysis for the inverted pendulum model indicates that such walking habit of pedestrians is the root of the frequency-locking phenomenon, which eventually results in excessive lateral vibrations of the bridge. Furthermore, such walking habit also is a key factor in the occurrence of the “jump phenomenon” in the London Millennium Bridge.

A Control Method of Four-Legged Robot Stable Walking with Diagonal Gait

2011 ◽  
Vol 148-149 ◽  
pp. 82-87
Author(s):  
Chang Hua Fan ◽  
Zhen Jiang ◽  
Bai Yu He
Keyword(s):  
Dynamic Equation ◽  
Stability Problem ◽  
Inverted Pendulum ◽  
Control Method ◽  
Flip Angle ◽  
Legged Robot ◽  
Motion Stability ◽  
Inverted Pendulum Model ◽  
Pendulum Model ◽  
The Stability

This paper proposes a kind of control method used to solve the stability problem of the trotted robot. Propose the concept of inside flip design four-footed robot and build a double inverted pendulum model. Establish dynamic equation to analyze the factors of affecting the motion stability. During walking, the center of gravity can maintain a proper vibration and have a maximum safety region of flip angle. Finally, use Adams to verify the control method.

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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