Lateral excitation of bridges by balancing pedestrians

2008 ◽  
Vol 465 (2104) ◽  
pp. 1055-1073 ◽  
Author(s):  
John H.G Macdonald
Keyword(s):  
Effective Means ◽  
Foot Placement ◽  
Lateral Vibrations ◽  
Inverted Pendulum Model ◽  
Pendulum Model ◽  
Human Balance ◽  
Number Of Cycles ◽  
Lock In ◽  
Millennium Bridge ◽  
Lateral Excitation

On its opening day, the London Millennium Bridge (LMB) experienced unexpected large amplitude lateral vibrations due to crowd loading. This form of pedestrian–structure interaction has since been identified on several other bridges of various structural forms. The mechanism has generally been attributed to ‘pedestrian synchronous lateral excitation’ or ‘pedestrian lock-in’. However, some of the more recent site measurements have shown a lack of evidence of pedestrian synchronization, at least at the onset of the behaviour. This paper considers a simple model of human balance from the biomechanics field—the inverted pendulum model—for which the most effective means of lateral stabilization is by the control of the position, rather than the timing, of foot placement. The same balance strategy as for normal walking on a stationary surface is applied to walking on a laterally oscillating bridge. As a result, without altering their pacing frequency, averaged over a large number of cycles, the pedestrian effectively acts as a negative (or positive) damper to the bridge motion, which may be at a different frequency. This is in agreement with the empirical model developed by Arup from the measurements on the LMB, leading to divergent amplitude vibrations above a critical number of pedestrians.

Dynamic and Reactive Walking for Humanoid Robots Based on Foot Placement Control

2016 ◽  
Vol 13 (02) ◽  
pp. 1550041 ◽  
Author(s):  
Juan Alejandro Castano ◽  
Zhibin Li ◽  
Chengxu Zhou ◽  
Nikos Tsagarakis ◽  
Darwin Caldwell
Keyword(s):  
Center Of Mass ◽  
Humanoid Robots ◽  
Gait Pattern ◽  
Gait Patterns ◽  
Foot Placement ◽  
Inverted Pendulum Model ◽  
Gait Parameters ◽  
Pendulum Model ◽  
Single Mass ◽  
Walking Velocity

This paper presents a novel online walking control that replans the gait pattern based on our proposed foot placement control using the actual center of mass (COM) state feedback. The analytic solution of foot placement is formulated based on the linear inverted pendulum model (LIPM) to recover the walking velocity and to reject external disturbances. The foot placement control predicts where and when to place the foothold in order to modulate the gait given the desired gait parameters. The zero moment point (ZMP) references and foot trajectories are replanned online according to the updated foothold prediction. Hence, only desired gait parameters are required instead of predefined or fixed gait patterns. Given the new ZMP references, the extended prediction self-adaptive control (EPSAC) approach to model predictive control (MPC) is used to minimize the ZMP response errors considering the acceleration constraints. Furthermore, to ensure smooth gait transitions, the conditions for the gait initiation and termination are also presented. The effectiveness of the presented gait control is validated by extensive disturbance rejection studies ranging from single mass simulation to a full body humanoid robot COMAN in a physics based simulator. The versatility is demonstrated by the control of reactive gaits as well as reactive stepping from standing posture. We present the data of the applied disturbances, the prediction of sagittal/lateral foot placements, the replanning of the foot/ZMP trajectories, and the COM responses.

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.

DERIVATION AND VALIDATION OF A SPATIAL MULTI-LINK HUMAN POSTURAL STABILITY MODEL

2016 ◽  
Vol 40 (2) ◽  
pp. 155-167
Author(s):  
Nicholas R. Bourgeois ◽  
Robert G. Langlois
Keyword(s):  
Postural Stability ◽  
Inverted Pendulum ◽  
Dynamic Models ◽  
Alternative Methods ◽  
Ship Motions ◽  
Inverted Pendulum Model ◽  
Pendulum Model ◽  
Stability Model ◽  
Human Balance ◽  
Naval Engineering

In naval engineering and related disciplines, it is common for dynamic models of the human body to be used in conjunction with quantitative records of body and ship motions, in order to study human balance behaviour while performing various shipboard activities. Research in this area can lead to improvements in ship operations and designs that improve crew safety and efficiency. This paper presents the development of a new spatial 18 degree-of-freedom (DOF)1 ship-inverted pendulum model that incorporates 6 DOF ship motion and 3 DOF joints representing ankle, knee, hip, and neck motions. The derived model is then validated by comparing it to similar models derived using alternative methods but simulated under equivalent input conditions.

scholarly journals A controller for walking derived from how humans recover from perturbations

2019 ◽  
Vol 16 (157) ◽  
pp. 20190027 ◽  
Author(s):  
Varun Joshi ◽  
Manoj Srinivasan
Keyword(s):  
Inverted Pendulum ◽  
Upper Body ◽  
Human Walking ◽  
Control Mechanisms ◽  
Normal Walking ◽  
Foot Placement ◽  
External Perturbations ◽  
Inverted Pendulum Model ◽  
Pendulum Model ◽  
Full State

Humans can walk without falling despite some external perturbations, but the control mechanisms by which this stability is achieved have not been fully characterized. While numerous walking simulations and robots have been constructed, no full-state walking controller for even a simple model of walking has been derived from human walking data. Here, to construct such a feedback controller, we applied thousands of unforeseen perturbations to subjects walking on a treadmill and collected data describing their recovery to normal walking. Using these data, we derived a linear controller to make the classical inverted pendulum model of walking respond to perturbations like a human. The walking model consists of a point-mass with two massless legs and can be controlled only through the appropriate placement of the foot and the push-off impulse applied along the trailing leg. We derived how this foot placement and push-off impulse are modulated in response to upper-body perturbations in various directions. This feedback-controlled biped recovers from perturbations in a manner qualitatively similar to human recovery. The biped can recover from perturbations over twenty times larger than deviations experienced during normal walking and the biped’s stability is robust to uncertainties, specifically, large changes in body and feedback parameters.

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 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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