Increase the feasible step region of biped robots through active vertical flexion and extension motions

Robotica ◽  
2016 ◽  
Vol 35 (7) ◽  
pp. 1541-1561 ◽  
Author(s):  
Wei Gao ◽  
Zhenzhong Jia ◽  
Chenglong Fu
Keyword(s):  
Vertical Motion ◽  
Vertical Movement ◽  
Point Mass ◽  
Simple Point ◽  
Mass Model ◽  
Biped Robots ◽  
Inverted Pendulum Model ◽  
Pendulum Model ◽  
Flexion And Extension ◽  
New Strategies

SUMMARYThis paper investigates the active vertical motion of biped systems and its significance to the balance of biped robots, which have been commonly neglected by the use of a well-known model called the Linear Inverted Pendulum Model. The feasible step location is theoretically estimated by considering the active vertical movement on a simple point mass model. Based on the estimation, we present two new strategies, namely the flexion strategy and the extension strategy, to enable biped robots to restore balance through active upward and downward motions. The analytical results demonstrate that the robot is able to recover from much larger disturbances using our proposed methods. Simulations of the simple point mass model validate our analysis. Besides, prototype controllers that incorporate our proposed strategies have also been implemented on a simulated humanoid robot. Numerical simulations on both the simple point mass model and the realistic humanoid model prove the effectiveness of proposed strategies.

Energy-Efficient Bipedal Walking: From Single-Mass Model to Three-Mass Model

Robotica ◽  
2021 ◽  
pp. 1-23
Author(s):  
Jiatao Ding ◽  
Jiangchen Zhou ◽  
Zhao Guo ◽  
Xiaohui Xiao
Keyword(s):  
Energy Efficient ◽  
Inverted Pendulum ◽  
Energy Performance ◽  
Cost Evaluation ◽  
Bipedal Walking ◽  
Energetic Cost ◽  
Optimization Approach ◽  
Mass Model ◽  
Inverted Pendulum Model ◽  
Pendulum Model

SUMMARY The work aims to realize energy-efficient bipedal walking by employing the three-mass inverted pendulum model (3MIPM) and compare its energy performance with linear inverted pendulum model (LIPM). To do this, a general optimal index on center of mass (CoM) acceleration is first derived for energetic cost evaluation. After defining the equivalent zero moment point (ZMP) motion, an unconstrained optimization approach for CoM generation is extended for 3MIPM, which can track different ZMP references and address the height variation as well. To make use of the allowable ZMP movement, a constrained optimization method is also employed, contributing to lower energetic cost. Simulation and hardware experiments on a humanoid robot demonstrate that the 3MIPM could achieve higher energy efficiency.

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.

A point-mass model of gibbon locomotion

1999 ◽  
Vol 202 (19) ◽  
pp. 2609-2617 ◽  
Author(s):  
J.E. Bertram ◽  
A. Ruina ◽  
C.E. Cannon ◽  
Y.H. Chang ◽  
M.J. Coleman
Keyword(s):  
Energy Exchange ◽  
Forest Canopy ◽  
Mechanical Energy ◽  
Single Point ◽  
Metabolic Cost ◽  
Point Mass ◽  
Mass Model ◽  
Natural Behavior ◽  
Continuous Contact ◽  
Mechanical Factors

In brachiation, an animal uses alternating bimanual support to move beneath an overhead support. Past brachiation models have been based on the oscillations of a simple pendulum over half of a full cycle of oscillation. These models have been unsatisfying because the natural behavior of gibbons and siamangs appears to be far less restricted than so predicted. Cursorial mammals use an inverted pendulum-like energy exchange in walking, but switch to a spring-based energy exchange in running as velocity increases. Brachiating apes do not possess the anatomical springs characteristic of the limbs of terrestrial runners and do not appear to be using a spring-based gait. How do these animals move so easily within the branches of the forest canopy? Are there fundamental mechanical factors responsible for the transition from a continuous-contact gait where at least one hand is on a hand hold at a time, to a ricochetal gait where the animal vaults between hand holds? We present a simple model of ricochetal locomotion based on a combination of parabolic free flight and simple circular pendulum motion of a single point mass on a massless arm. In this simple brachiation model, energy losses due to inelastic collisions of the animal with the support are avoided, either because the collisions occur at zero velocity (continuous-contact brachiation) or by a smooth matching of the circular and parabolic trajectories at the point of contact (ricochetal brachiation). This model predicts that brachiation is possible over a large range of speeds, handhold spacings and gait frequencies with (theoretically) no mechanical energy cost. We then add the further assumption that a brachiator minimizes either its total energy or, equivalently, its peak arm tension, or a peak tension-related measure of muscle contraction metabolic cost. However, near the optimum the model is still rather unrestrictive. We present some comparisons with gibbon brachiation showing that the simple dynamic model presented has predictive value. However, natural gibbon motion is even smoother than the smoothest motions predicted by this primitive model.

Point mass impulse-momentum model of the equine rotational fall

2019 ◽  
Vol 15 (3) ◽  
pp. 157-165
Author(s):  
M.H. Foreman ◽  
J.R. Engsberg ◽  
J.H. Foreman
Keyword(s):  
Point Mass ◽  
Future Research ◽  
Collision Time ◽  
Mass Model ◽  
Impact Forces ◽  
Force Transfer ◽  
Reference Curves ◽  
Key Variables ◽  
Cross Country ◽  
Input Variables

Rotational falls are a serious cause of injury and death to horse and rider, particularly in the cross-country phase of eventing. The forces involved when horses galloping cross-country strike an immovable fence are unknown. The objective of this study was to mathematically model those forces using existing kinematic data measured from jumping horses. Data were obtained from published research using motion capture to measure mechanics about the center of gravity of the jumping horse at take-off. A convenience method from video evidence of rotational falls was used to estimate time of collision (Δt). A point mass model using equations of impulse-momentum and incorporating key variables was systematically implemented in Matlab (r2016a). The mean collision time (Δt=0.79s) produced horizontal, vertical, and resultant impact forces of 8,580, 8,245, and 12,158 N, respectively. Reference curves of impact forces were created for ranges of relevant input variables including collision time. Proportional relationships showed that shorter impact duration led to higher magnitude of force transfer between horse and obstacle. This study presents a preliminary range of collision forces based on a simplified model and numerous assumptions related to input variables. Future research should work to build upon these estimates through more complex modelling and data collection to enhance applicability for the design of cross-country safety devices.

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