scholarly journals Walking Stability of a Variable Length Inverted Pendulum Controlled with Virtual Constraints

2019 ◽  
Vol 16 (06) ◽  
pp. 1950040
Author(s):  
Qiuyue Luo ◽  
Christine Chevallereau ◽  
Yannick Aoustin
Keyword(s):  
Periodic Motion ◽  
Inverted Pendulum ◽  
Walking Speed ◽  
Center Of Mass ◽  
Pi Controller ◽  
Variable Length ◽  
Bipedal Walking ◽  
Human Walking ◽  
Walking Gait ◽  
Switching Condition

Bipedal walking is a complex phenomenon that is not fully understood. Simplified models make it easier to highlight the important features. Here, the variable length inverted pendulum (VLIP) model is used, which has the particularity of taking into account the vertical oscillations of the center of mass (CoM). When the desired walking gait is defined as virtual constraints, i.e., as functions of a phasing variable and not on time, for the evolution of the swing foot and the vertical oscillation of the CoM, the walk will asymptotically converge to the periodic motion under disturbance with proper choice of the virtual constraints, thus a self-stabilization is obtained. It is shown that the vertical CoM oscillation, positions of the swing foot and the choice of the switching condition play crucial roles in stability. Moreover, a PI controller of the CoM velocity along the sagittal axis is also proposed such that the walking speed of the robot can converge to another periodic motion with a different walking speed. In this way, a natural walking gait is illustrated as well as the possibility of velocity adaptation as observed in human walking.

scholarly journals Drosophila uses a tripod gait across all walking speeds, and the geometry of the tripod is important for speed control

eLife ◽  
2021 ◽  
Vol 10 ◽  
Author(s):  
Chanwoo Chun ◽  
Tirthabir Biswas ◽  
Vikas Bhandawat
Keyword(s):  
Simple Model ◽  
Spatial Resolution ◽  
Inverted Pendulum ◽  
Walking Speed ◽  
High Spatial Resolution ◽  
Center Of Mass ◽  
Mass Movement ◽  
Speed Control ◽  
Tripod Gait ◽  
Walking Speeds

Changes in walking speed are characterized by changes in both the animal’s gait and the mechanics of its interaction with the ground. Here we study these changes in walking Drosophila. We measured the fly’s center of mass movement with high spatial resolution and the position of its footprints. Flies predominantly employ a modified tripod gait that only changes marginally with speed. The mechanics of a tripod gait can be approximated with a simple model – angular and radial spring-loaded inverted pendulum (ARSLIP) – which is characterized by two springs of an effective leg that become stiffer as the speed increases. Surprisingly, the change in the stiffness of the spring is mediated by the change in tripod shape rather than a change in stiffness of individual legs. The effect of tripod shape on mechanics can also explain the large variation in kinematics among insects, and ARSLIP can model these variations.

Mechanics of locomotion in lizards.

1997 ◽  
Vol 200 (16) ◽  
pp. 2177-2188 ◽  
Author(s):  
C T Farley ◽  
T C Ko
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Inverted Pendulum ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Gravitational Potential Energy ◽  
Lateral Bending ◽  
Walking Gait ◽  
Bending Force

Lizards bend their trunks laterally with each step of locomotion and, as a result, their locomotion appears to be fundamentally different from mammalian locomotion. The goal of the present study was to determine whether lizards use the same two basic gaits as other legged animals or whether they use a mechanically unique gait due to lateral trunk bending. Force platform and kinematic measurements revealed that two species of lizards, Coleonyx variegatus and Eumeces skiltonianus, used two basic gaits similar to mammalian walking and trotting gaits. In both gaits, the kinetic energy fluctuations due to lateral movements of the center of mass were less than 5% of the total external mechanical energy fluctuations. In the walking gait, both species vaulted over their stance limbs like inverted pendulums. The fluctuations in kinetic energy and gravitational potential energy of the center of mass were approximately 180 degrees out of phase. The lizards conserved as much as 51% of the external mechanical energy required for locomotion by the inverted pendulum mechanism. Both species also used a bouncing gait, similar to mammalian trotting, in which the fluctuations in kinetic energy and gravitational potential energy of the center of mass were nearly exactly in phase. The mass-specific external mechanical work required to travel 1 m (1.5 J kg-1) was similar to that for other legged animals. Thus, in spite of marked lateral bending of the trunk, the mechanics of lizard locomotion is similar to the mechanics of locomotion in other legged animals.

Genetic algorithm-based optimal bipedal walking gait synthesis considering tradeoff between stability margin and speed

Robotica ◽  
2009 ◽  
Vol 27 (3) ◽  
pp. 355-365 ◽  
Author(s):  
Goswami Dip ◽  
Vadakkepat Prahlad ◽  
Phung Duc Kien
Keyword(s):  
Genetic Algorithm ◽  
Degrees Of Freedom ◽  
Walking Speed ◽  
Stability Margin ◽  
Biped Robot ◽  
Bipedal Walking ◽  
Step Size ◽  
Walking Gait ◽  
Gait Synthesis ◽  
The Stability

SUMMARYThe inverse kinematics of a 12 degrees-of-freedom (DOFs) biped robot is formulated in terms of certain parameters. The biped walking gaits are developed using the parameters. The walking gaits are optimized using genetic algorithm (GA). The optimization is carried out considering relative importance of stability margin and walking speed. The stability margin depends on the position of zero-moment-point (ZMP) while walking speed varies with step-size. The ZMP is computed by an approximation-based method which does not require system dynamics. The optimal walking gaits are experimentally realized on a biped robot.

Modeling and Simulation of Lower Extremity Exoskeleton

2014 ◽  
Vol 487 ◽  
pp. 504-508 ◽  
Author(s):  
Yu Zhang ◽  
Xiao Bo Wu ◽  
Hui Fang Liu
Keyword(s):  
Lower Extremity ◽  
Degrees Of Freedom ◽  
Inverted Pendulum ◽  
Three Dimensional ◽  
Human Walking ◽  
Auxiliary Equipment ◽  
Walking Gait ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
Physical Prototype

In order to make the paralyzed live on their own and return to the society to the most degree, mechanical exoskeleton technology is tried to applied in the field of auxiliary equipment. First, degrees of freedom and mechanical structure at the each joint of lower extremity exoskeleton was ascertained.Then a three dimensional modeling design for the lower extremity exoskeleton was carried out with SIEMENS NX8.0 and a walking gait on a flat for it was planned on MATLAB basing on inverted pendulum model.Finally the legs model was simulated on ADAMS.The result of the simulation was basically the same as planned gait which can better satisfy the requirement of human walking and can be used as reference for developping the physical prototype of lower extremity exoskeleton.

Optimum Design of a Bipedal Walking Robot

1991 ◽  
Author(s):  
Karen Martin ◽  
Mark Reuber
Keyword(s):  
Walking Speed ◽  
Design For Manufacturing ◽  
Bipedal Walking ◽  
Human Walking ◽  
Walking Robot ◽  
Walking Machine ◽  
Start Up ◽  
Final Weight ◽  
Computer Controlled ◽  
Structural Parts

Abstract This paper describes the design, fabrication, and testing of “Bigfoot,” a bipedal walking machine designed to optimize speed, cost, and ease of assembly. Bigfoot walks at near-human walking speed (0.24 m/s), can be assembled/disassembled in two hours, and has a programmable, computer-controlled start-up procedure. Design for manufacturing and assembly techniques (DFMA) were used to reduce the final weight of the robot to 12 kg, the number of structural parts to 39 individual pieces held together with 50 fasteners, and the final robot cost to $300.

scholarly journals Feedforward control for underactuated bipedal walking on varying compliant slopes

2018 ◽  
Vol 42 (2) ◽  
pp. 90-104 ◽  
Author(s):  
Daojin Yao ◽  
Siyu He ◽  
Yao Wu ◽  
Xiaohui Xiao ◽  
Yang Wang
Keyword(s):  
Control Strategy ◽  
Walking Speed ◽  
Feedforward Control ◽  
Center Of Mass ◽  
Kinematic Chain ◽  
Bipedal Walking ◽  
Natural Environments ◽  
Gait Characteristics ◽  
Motion State ◽  
Definition Of

In this paper, a feedforward control strategy is proposed to enable stable underactuated bipedal walking on varying compliant slopes with a known inclination angle, to handle the variation in natural environments. First, spring–damper units were employed in the horizontal and vertical directions to model the compliant ground, which is described as a rigid kinematic chain coupled with a spring–damper system. Second, a new definition of stable underactuated bipedal walking, based on walking speed, was proposed. Stable walking is achieved by adjusting the velocity of the biped’s center of mass (CoM) within limits that have been proven to allow at least one walking cycle. The proposed feedforward control strategy was based on the motion state of a robot’s CoM, using the new definition of stability and inspired by the gait characteristics of human walking on varying slopes. Speed control is realized by adjusting the displacement of the CoM with the change of slope to achieve stable walking. Finally, simulations were conducted to validate the proposed controller. The simulation results demonstrate that stable walking is achieved on varying compliant slopes by implementing the proposed control strategy.

scholarly journals Walking in simulated reduced gravity: mechanical energy fluctuations and exchange

1999 ◽  
Vol 86 (1) ◽  
pp. 383-390 ◽  
Author(s):  
Timothy M. Griffin ◽  
Neil A. Tolani ◽  
Rodger Kram
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Inverted Pendulum ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Metabolic Cost ◽  
Metabolic Energy ◽  
Gravitational Potential Energy ◽  
Reduced Gravity

Walking humans conserve mechanical and, presumably, metabolic energy with an inverted pendulum-like exchange of gravitational potential energy and horizontal kinetic energy. Walking in simulated reduced gravity involves a relatively high metabolic cost, suggesting that the inverted-pendulum mechanism is disrupted because of a mismatch of potential and kinetic energy. We tested this hypothesis by measuring the fluctuations and exchange of mechanical energy of the center of mass at different combinations of velocity and simulated reduced gravity. Subjects walked with smaller fluctuations in horizontal velocity in lower gravity, such that the ratio of horizontal kinetic to gravitational potential energy fluctuations remained constant over a fourfold change in gravity. The amount of exchange, or percent recovery, at 1.00 m/s was not significantly different at 1.00, 0.75, and 0.50 G (average 64.4%), although it decreased to 48% at 0.25 G. As a result, the amount of work performed on the center of mass does not explain the relatively high metabolic cost of walking in simulated reduced gravity.

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.

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