Simple Leg Placement Strategy for a One Legged Running Model

2012 ◽  
Author(s):  
Timothy Sullivan ◽  
Justin Seipel
Keyword(s):  
Stance Phase ◽  
Energy State ◽  
Center Of Mass ◽  
Mass Movement ◽  
Legged Locomotion ◽  
Energy Conserving ◽  
Lower Torque ◽  
The Stability ◽  
Time Required ◽  
Torque Values

The Spring Loaded Inverted Pendulum (SLIP) model was developed to describe center of mass movement patterns observed in animals, using only a springy leg and a point mass. However, SLIP is energy conserving and does not accurately represent any biological or robotic system. Still, this model is often used as a foundation for the investigation of improved legged locomotion models. One such model called Torque Damped SLIP (TD-SLIP) utilizes two additional parameters, a time dependent torque and dampening to drastically increase the stability. Forced Damped SLIP (FD-SLIP), a predecessor of TD-SLIP, has shown that this model can be further simplified by using a constant torque, instead of a time varying torque, while still maintaining stability. Using FD-SLIP as a base, this paper explores a leg placement strategy using a simple PI controller. The controller takes advantage of the fact that the energy state of FD-SLIP is symmetric entering and leaving the stance phase during steady state conditions. During the flight phase, the touch down leg angle is adjusted so that the energy dissipation due to dampening, during the stance phase, compensates for any imbalance of energy. This controller approximately doubles the region of stability when subjected to velocity perturbations at touchdown, enables the model to operate at considerably lower torque values, and drastically reduces the time required to recover from a perturbation, while using less energy. Finally, the leg placement strategy used effectively imitates the natural human response to velocity perturbations while running.

A Spring-Mass Model of Locomotion With Full Asymptotic Stability

2011 ◽  
Author(s):  
Zhuohua Shen ◽  
Justin Seipel
Keyword(s):  
Inverted Pendulum ◽  
Center Of Mass ◽  
Legged Locomotion ◽  
Human Locomotion ◽  
Whole Body ◽  
Slip Model ◽  
Mass Model ◽  
Energy Conserving ◽  
Spring Loaded Inverted Pendulum ◽  
Passive Model

The concept of passive dynamic walking and running [5] has demonstrated that a simple passive model can represent the dynamics of whole-body human locomotion. Since then, many passive models were developed and studied: [3,1,2,11]. The later developed Spring-Loaded Inverted Pendulum (SLIP) [1, 4, 11, 2] exhibits stable center of mass (CoM) motions just by resetting the landing angle at each touch down. Also, compared to SLIP, a SLIP-like model with simple flight leg control is better at resisting perturbations of the angle of velocity but not the magnitude [11, 2, 7]. Energy conserving models explain much about whole-body locomotion. Recently, there has been investigations of modified spring-mass models capable of greater stability, like that of animals and robots [9, 10, 8, 12]. Inspired by RHex [6], the Clock-Torqued Spring-Loaded Inverted Pendulum (CT-SLIP) model [9] was developed, and has been used to explain the robust stability of animal locomotion [12]. Here we present a model (mechanism) simpler than CT-SLIP called Forced-Damped SLIP (FD-SLIP) that can attain full asymptotically stability of the CoM during locomotion, and is capable of both walking and running motions. The FD-SLIP model, having fewer parameters, is more accessible and easier to analyze for the exploration and discovery of principles of legged locomotion.

Comparing Legged Locomotion With a Sprung-Knee and Telescoping-Spring When Hip Torque is Applied

2013 ◽  
Author(s):  
Nikhil Rao ◽  
Zhuohua Shen ◽  
Justin Seipel
Keyword(s):  
Center Of Mass ◽  
Legged Locomotion ◽  
Input Power ◽  
Whole Body ◽  
Segment Model ◽  
Distinct Structure ◽  
Body Dynamics ◽  
The Stability ◽  
Special Case

Legged locomotion has been a subject of study for many years. However, the role of the knee in whole-body dynamics of locomotion is not well understood, especially for non-conservative dynamics. Based upon a hip actuated Spring-Loaded Inverted Pendulum (Hip-actuated SLIP) model, we develop a more human-like, two-segment leg model with a pin-jointed springy knee, to see what effects a knee has in the context of an applied hip torque. Overall, we find that the governing equations for the two-segment (knee) version have a distinct structure when compared to the telescoping version of SLIP. The two-segment model with a knee spring influences forces acting on the mass center in a more complex way than a telescoping spring. While a wide variation of behavior is possible for the two-segment model, here we focus on comparing the dynamics for a special case when the knee spring resting angle is 90°. For this particular choice of resting knee angle we find that the knee version of actuated SLIP can have similar locomotion dynamics to the telescoping version of actuated SLIP. This result provides one explanation for how animals and robots with multi-segmented legs could produce overall center-of-mass dynamics that are similar to models with telescoping legs. Nonetheless, despite overall similarities for this special case, small differences in the stability of locomotion are still observed. In particular, we find that the knee version tends to be slightly more stable than the telescoping SLIP in terms of the allowable size of perturbations, while requiring higher input power.

scholarly journals Spring-loaded inverted pendulum goes through two contraction-extension cycles during the single stance phase of walking

2019 ◽  
Author(s):  
Gabriel Antoniak ◽  
Tirthabir Biswas ◽  
Nelson Cortes ◽  
Siddhartha Sikdar ◽  
Chanwoo Chun ◽  
...  
Keyword(s):  
Stance Phase ◽  
Inverted Pendulum ◽  
Center Of Mass ◽  
Legged Locomotion ◽  
Quantitative Model ◽  
Active Elements ◽  
Mechanical Models ◽  
Reaction Forces ◽  
Spring Loaded Inverted Pendulum ◽  
Walking Speeds

AbstractDespite the overall complexity of legged locomotion, the motion of the center of mass (COM) itself is relatively simple, and can be qualitatively described by simple mechanical models. The spring-loaded inverted pendulum (SLIP) is one such model, and describes both the COM motion and the ground reaction forces (GRFs) during running. Similarly, walking can be modeled by two SLIP-like legs (double SLIP or DSLIP). However, DSLIP has many limitations and is unlikely to serve as a quantitative model for walking. As a first step to obtaining a quantitative model for walking, we explored the ability of SLIP to model the single stance phase of walking across the entire range of walking speeds. We show that SLIP can be employed to quantitatively model the single stance phase except for two exceptions: first, it predicts larger horizontal GRFs than empirically observed. A new model - angular and radial spring-loaded inverted pendulum (ARSLIP) can overcome this deficit. Second, even the single stance phase has active elements, and therefore a quantitative model of locomotion would require active elements. Surprisingly, the leg spring undergoes a contraction-extension-contraction-extension (CECE) during walking; this cycling is partly responsible for the M-shaped GRFs produced during walking. The CECE cycle also lengthens the stance duration allowing the COM to travel passively for a longer time, and decreases the velocity redirection between the beginning and end of a step. A combination of ARSLIP along with active mechanisms during transition from one step to the next is necessary to describe walking.

TO THE STABILITY OF TANK VEHICLES IN THE BRAKE MODE

2019 ◽  
pp. 27-32
Author(s):  
Denys Popelysh ◽  
Yurii Seluk ◽  
Sergyi Tomchuk
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Distribution Systems ◽  
Traffic Accidents ◽  
Road Traffic ◽  
Center Of Mass ◽  
Dynamic Processes ◽  
Course Stability ◽  
The Stability ◽  
Tank Vehicles

This article discusses the question of the possibility of improving the roll stability of partially filled tank vehicles while braking. We consider the dangers associated with partially filled tank vehicles. We give examples of the severe consequences of road traffic accidents that have occurred with tank vehicles carrying dangerous goods. We conducted an analysis of the dynamic processes of fluid flow in the tank and their influence on the basic parameters of the stability of vehicle. When transporting a partially filled tank due to the comparability of the mass of the empty tank with the mass of the fluid being transported, the dynamic qualities of the vehicle change so that they differ significantly from the dynamic characteristics of other vehicles. Due to large displacements of the center of mass of cargo in the tank there are additional loads that act vehicle and significantly reduce the course stability and the drivability. We consider the dynamics of liquid sloshing in moving containers, and give examples of building a mechanical model of an oscillating fluid in a tank and a mathematical model of a vehicle with a tank. We also considered the method of improving the vehicle’s stability, which is based on the prediction of the moment of action and the nature of the dynamic processes of liquid cargo and the implementation of preventive actions by executive mechanisms. Modern automated control systems (anti-lock brake system, anti-slip control systems, stabilization systems, braking forces distribution systems, floor level systems, etc.) use a certain list of elements for collecting necessary parameters and actuators for their work. This gives the ability to influence the course stability properties without interfering with the design of the vehicle only by making changes to the software of these systems. Keywords: tank vehicle, roll stability, mathematical model, vehicle control systems.

Reverse torque values of abutment screws after dynamic loading: The effects of sealant agents and the taper of conical connections

2020 ◽  
Author(s):  
Arda Ozdiler ◽  
suleyman dayan ◽  
Burc Gencel ◽  
Gulbahar Isık-Ozkol
Keyword(s):  
Dynamic Loading ◽  
Antibacterial Agent ◽  
In Vitro Study ◽  
Control Group ◽  
Silicone Sealant ◽  
Reverse Torque ◽  
The Stability ◽  
Torque Values ◽  
Chlorhexidine Gel

This in vitro study evaluated the influence of taper angles on the internal conical connections of implant systems and of the application of chlorhexidine gel as an antibacterial agent or a polyvinyl siloxane (PVS) sealant on the reverse torque values of abutment screws after dynamic loading. The current study tested four implant systems with different taper angles (5.4°, 12°, 45°, and 60°). Specimens were divided into three groups: control (neither chlorhexidine gel filled nor silicone sealed), 2% chlorhexidine gel-filled or silicone-sealed group, and group subjected to a dynamic load of 50 N at 1 Hz for 500,000 cycles prior to reverse torque measurements. Quantitative positive correlation was observed between the taper angle degree and the percentage of tightening torque loss. However, this correlation was significant only for the 60° connection groups except in the group in which a sealant was applied ( p = 0.013 for the control group, p = 0.007 for the chlorhexidine group). Percentages of decrease in the torque values of the specimens with silicone sealant application were significantly higher compared with both the control and chlorhexidine groups ( p = 0.001, p = 0.002, p = 0.001, and p = 0.002, respectively, according to the increasing taper angles); the percentage of decrease in torque values due to chlorhexidine application was statistically insignificant when compared with the control group. The application of gel-form chlorhexidine as an antibacterial agent does not significantly affect the stability of the implant–abutment connection under dynamic loads. PVS sealants may cause screw loosening under functional loads.

scholarly journals A Bio-Inspired Compliance Planning and Implementation Method for Hydraulically Actuated Quadruped Robots with Consideration of Ground Stiffness

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2838
Author(s):  
Xiaoxing Zhang ◽  
Haoyuan Yi ◽  
Junjun Liu ◽  
Qi Li ◽  
Xin Luo
Keyword(s):  
Harmonic Oscillation ◽  
Ground Surface ◽  
Legged Locomotion ◽  
Soft Ground ◽  
Quadruped Robots ◽  
In Series ◽  
Reaction Forces ◽  
Implementation Method ◽  
The Stability ◽  
Natural Dynamics

There has been a rising interest in compliant legged locomotion to improve the adaptability and energy efficiency of robots. However, few approaches can be generalized to soft ground due to the lack of consideration of the ground surface. When a robot locomotes on soft ground, the elastic robot legs and compressible ground surface are connected in series. The combined compliance of the leg and surface determines the natural dynamics of the whole system and affects the stability and efficiency of the robot. This paper proposes a bio-inspired leg compliance planning and implementation method with consideration of the ground surface. The ground stiffness is estimated based on analysis of ground reaction forces in the frequency domain, and the leg compliance is actively regulated during locomotion, adapting them to achieve harmonic oscillation. The leg compliance is planned on the condition of resonant movement which agrees with natural dynamics and facilitates rhythmicity and efficiency. The proposed method has been implemented on a hydraulic quadruped robot. The simulations and experimental results verified the effectiveness of our method.

scholarly journals Vertical Jumping for Legged Robot Based on Quadratic Programming

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3679
Author(s):  
Dingkui Tian ◽  
Junyao Gao ◽  
Xuanyang Shi ◽  
Yizhou Lu ◽  
Chuzhao Liu
Keyword(s):  
Quadratic Programming ◽  
Stance Phase ◽  
Center Of Mass ◽  
Maximum Error ◽  
Legged Robot ◽  
Flight Phase ◽  
Programming Framework ◽  
Vertical Jumping ◽  
Control Schemes ◽  
And Control

The highly dynamic legged jumping motion is a challenging research topic because of the lack of established control schemes that handle over-constrained control objectives well in the stance phase, which are coupled and affect each other, and control robot’s posture in the flight phase, in which the robot is underactuated owing to the foot leaving the ground. This paper introduces an approach of realizing the cyclic vertical jumping motion of a planar simplified legged robot that formulates the jump problem within a quadratic-programming (QP)-based framework. Unlike prior works, which have added different weights in front of control tasks to express the relative hierarchy of tasks, in our framework, the hierarchical quadratic programming (HQP) control strategy is used to guarantee the strict prioritization of the center of mass (CoM) in the stance phase while split dynamic equations are incorporated into the unified quadratic-programming framework to restrict the robot’s posture to be near a desired constant value in the flight phase. The controller is tested in two simulation environments with and without the flight phase controller, the results validate the flight phase controller, with the HQP controller having a maximum error of the CoM in the x direction and y direction of 0.47 and 0.82 cm and thus enabling the strict prioritization of the CoM.

scholarly journals Entrapment of the Fastest Known Carbonic Anhydrase with Biomimetic Silica and Its Application for CO2 Sequestration

Polymers ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2452
Author(s):  
Chia-Jung Hsieh ◽  
Ju-Chuan Cheng ◽  
Chia-Jung Hu ◽  
Chi-Yang Yu
Keyword(s):  
Carbonic Anhydrase ◽  
High Activity ◽  
Co2 Sequestration ◽  
Residual Activity ◽  
Entrapment Efficiency ◽  
Free Form ◽  
Uncatalyzed Reaction ◽  
The Stability ◽  
Time Required

Capturing and storing CO2 is of prime importance. The rate of CO2 sequestration is often limited by the hydration of CO2, which can be greatly accelerated by using carbonic anhydrase (CA, EC 4.2.1.1) as a catalyst. In order to improve the stability and reusability of CA, a silica-condensing peptide (R5) was fused with the fastest known CA from Sulfurihydrogenibium azorense (SazCA) to form R5-SazCA; the fusion protein successfully performed in vitro silicification. The entrapment efficiency reached 100% and the silicified form (R5-SazCA-SP) showed a high activity recovery of 91%. The residual activity of R5-SazCA-SP was two-fold higher than that of the free form when stored at 25 °C for 35 days; R5-SazCA-SP still retained 86% of its activity after 10 cycles of reuse. Comparing with an uncatalyzed reaction, the time required for the onset of CaCO3 formation was shortened by 43% and 33% with the addition of R5-SazCA and R5-SazCA-SP, respectively. R5-SazCA-SP shows great potential as a robust and efficient biocatalyst for CO2 sequestration because of its high activity, high stability, and reusability.

scholarly journals The Application of an Impedance-Passivity Controller in Haptic Stability Analysis

2021 ◽  
Vol 11 (4) ◽  
pp. 1618
Author(s):  
Ping-Nan Chen ◽  
Yung-Te Chen ◽  
Hsin Hsiu ◽  
Ruei-Jia Chen
Keyword(s):  
Control Systems ◽  
Force Feedback ◽  
Training System ◽  
Considerable Time ◽  
Virtual Training ◽  
Control Gain ◽  
Negative Damping ◽  
The Stability ◽  
Time Required ◽  
Stable Control

This paper proposes a passivity theorem on the basis of energy concepts to study the stability of force feedback in a virtual haptic system. An impedance-passivity controller (IPC) was designed from the two-port network perspective to improve the chief drawback of haptic systems, namely the considerable time required to reach stability if the equipment consumes energy slowly. The proposed IPC can be used to achieve stability through model parameter selection and to obtain control gain. In particular, haptic performance can be improved for extreme cases of high stiffness and negative damping. Furthermore, a virtual training system for one-degree-of-freedom sticking was developed to validate the experimental platform of our IPC. To ensure consistency in the experiment, we designed a specialized mechanical robot to replace human operation. Finally, compared with basic passivity control systems, our IPC could achieve stable control rapidly.

A Simple Analytical Tool for Legged Robot Design

2012 ◽  
Author(s):  
Zhuohua Shen ◽  
Justin Seipel
Keyword(s):  
Analytical Solutions ◽  
Inverted Pendulum ◽  
Legged Locomotion ◽  
Robot Design ◽  
Slip Model ◽  
Legged Robot ◽  
Biologically Relevant ◽  
Analytical Approximations ◽  
Energy Conserving ◽  
Spring Loaded Inverted Pendulum

Although legged locomotion is better at tackling complicated terrains compared with wheeled locomotion, legged robots are rare, in part, because of the lack of simple design tools. The dynamics governing legged locomotion are generally nonlinear and hybrid (piecewise-continuous) and so require numerical simulation for analysis and are not easily applied to robot designs. During the past decade, a few approximated analytical solutions of Spring-Loaded Inverted Pendulum (SLIP), a canonical model in legged locomotion, have been developed. However, SLIP is energy conserving and cannot predict the dynamical stability of real-world legged locomotion. To develop new analytical tools for legged robot designs, we first analytically solved SLIP in a new way. Then based on SLIP solution, we developed an analytical solution of a hip-actuated Spring-Loaded Inverted Pendulum (hip-actuated-SLIP) model, which is more biologically relevant and stable than the canonical energy conserving SLIP model. The analytical approximations offered here for SLIP and the hip actuated-SLIP solutions compare well with the numerical simulations of each. The analytical solutions presented here are simpler in form than those resulting from existing analytical approximations. The analytical solutions of SLIP and the hip actuated-SLIP can be used as tools for robot design or for generating biological hypotheses.

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