BIPED HOPPING CONTROL BAzSED ON SPRING LOADED INVERTED PENDULUM MODEL

2010 ◽  
Vol 07 (02) ◽  
pp. 263-280 ◽  
Author(s):  
SEYED HOSSEIN TAMADDONI ◽  
FARID JAFARI ◽  
ALI MEGHDARI ◽  
SAEED SOHRABPOUR
Keyword(s):  
Control Strategy ◽  
Inverted Pendulum ◽  
Hybrid Control ◽  
Sagittal Plane ◽  
Center Of Mass ◽  
Slip Model ◽  
Inverted Pendulum Model ◽  
Wide Range ◽  
Spring Loaded Inverted Pendulum ◽  
Mass Spring

Human running can be stabilized in a wide range of speeds by automatically adjusting muscular properties of leg and torso. It is known that fast locomotion dynamics can be approximated by a spring loaded inverted pendulum (SLIP) system, in which leg is replaced by a single spring connecting body mass to ground. Taking advantage of the inherent stability of SLIP model, a hybrid control strategy is developed that guarantees a stable biped locomotion in sagittal plane. In the presented approach, nonlinear control methods are applied to synchronize the biped dynamics and the spring-mass dynamics. As the biped center of mass follows the mass of the mass-spring model, the whole biped performs a stable locomotion corresponding to SLIP model. Simulations are done to obtain a repeatable hopping for a three-link underactuated biped model. Results show that periodic hopping gaits can be stabilized, and the presented control strategy provides feasible gait trajectories for stance and swing phases.

Stabilized Walking of Humanoid NAO using Enhanced Spring-Loaded Inverted Pendulum Model on Uneven Terrain

2022 ◽  
Vol 13 (1) ◽  
pp. 0-0
Keyword(s):  
Path Length ◽  
Inverted Pendulum ◽  
Center Of Mass ◽  
Humanoid Robots ◽  
Slip Model ◽  
Turning Angle ◽  
Uneven Terrain ◽  
Inverted Pendulum Model ◽  
Pendulum Model ◽  
Spring Loaded Inverted Pendulum

In the coming decades, humanoid robots will play a rising role in society. The present article discusses their walking control and obstacle avoidance on uneven terrain using enhanced spring-loaded inverted pendulum model (ESLIP). The SLIP model is enhanced by tuning it with an adaptive particle swarm optimization (APSO) approach. It helps the humanoid robot to reach closer to the obstacles in order to optimize the turning angle to optimize the path length. The desired trajectory, along with the sensory data, is provided to the SLIP model, which creates compatible COM (center of mass) dynamics for stable walking. This output is fed to APSO as input, which adjusts the placement of the foot during interaction with uneven surfaces and obstacles. It provides an optimum turning angle for shunning the obstacles and ensures the shortest path length. Simulation has been carried out in a 3D simulator based on the proposed controller and SLIP controller in uneven terrain.

Towards Robustly Stable Musculo-Skeletal Simulation of Human Gait: Merging Lumped and Component-Based Modeling Approaches

2012 ◽  
Author(s):  
Justin Seipel
Keyword(s):  
Inverted Pendulum ◽  
Dynamic Models ◽  
Sagittal Plane ◽  
Center Of Mass ◽  
Human Model ◽  
Whole Body ◽  
Human Gait ◽  
Slip Model ◽  
Spring Loaded Inverted Pendulum ◽  
Low Dimensional

The objective of work presented in this paper is to increase the center-of-mass stability of human walking and running in musculo-skeletal simulation. The approach taken is to approximate the whole-body dynamics of the low-dimensional Spring-Loaded Inverted Pendulum (SLIP) model of locomotion in the OpenSim environment using existing OpenSim tools. To more directly relate low-dimensional dynamic models to human simulation, an existing OpenSim human model is first modified to more closely represent bilateral above-knee amputee locomotion with passive prostheses. To increase stability further beyond the energy-conserving SLIP model, an OpenSim model based upon the Clock-Torqued Spring-Loaded-Inverted-Pendulum (CT-SLIP) model of locomotion is also created. The result of this work is that a multi-body musculo-skeletal simulation in Open-Sim can approximate the whole-body sagittal-plane dynamics of the passive SLIP model. By adding a plugin controller to the OpenSim environment, the Clock-Torqued-SLIP dynamics can be approximated in OpenSim. To change between walking and running, only one parameter representing the preferred period of a stride is changed. The result is a robustly stable simulation of the center-of-mass locomotion for both walking and running that could serve as a first step toward increasingly anatomically accurate and robustly stable musculo-skeletal simulations.

A Spring-Mass Model of Locomotion With Full Asymptotic Stability

2011 ◽  
Author(s):  
Zhuohua Shen ◽  
Justin Seipel
Keyword(s):  
Mass Velocity ◽  
Inverted Pendulum ◽  
Center Of Mass ◽  
Legged Locomotion ◽  
Reduced Model ◽  
Asymptotically Stable ◽  
Slip Model ◽  
Mass Model ◽  
Improved Stability ◽  
Spring Loaded Inverted Pendulum

A reduced model of legged locomotion, called the Spring Loaded Inverted Pendulum (SLIP) has previously been developed to predict the dynamics of locomotion. However, due to energy conservation, the SLIP model can only be partially asymptotically stable in the center-of-mass velocity. The more recently developed Clock-Torqued Spring Loaded Inverted Pendulum (CT-SLIP) model is fully asymptotically stable, and has a significantly larger stability basin than SLIP, but requires more than twice as many parameters. To more completely explore the parameter space and understand the reason for improved stability, we develop and analyze a further reduced model called the Forced-Damped Spring Loaded Inverted Pendulum (FD-SLIP) model.

Foot Contact Interactions of a Clock Torqued Spring-Loaded Inverted Pendulum

2012 ◽  
Author(s):  
Steven Riddle ◽  
Justin Seipel
Keyword(s):  
Disturbance Rejection ◽  
Inverted Pendulum ◽  
Center Of Mass ◽  
Legged Robots ◽  
Contact Friction ◽  
Slip Model ◽  
Specific Interest ◽  
Mass System ◽  
Friction Models ◽  
Spring Loaded Inverted Pendulum

The clock-torqued spring-loaded inverted pendulum (CT-SLIP) model describes the robust dynamic stability properties observed in most animals and some legged robots. However, the model’s behavior is sensitive to changes in liftoff conditions such as those experienced on realistic terrain. Here the incorporation of friction at the foot-ground interface is explored on the CT-SLIP model with specific interest in improving the transient center-of-mass dynamics. Multiple friction models are presented and tuned to reflect a periodic center-of-mass gait. The transient dynamics with friction are analyzed in comparison to the CT-SLIP model and improvements to the settling time and disturbance rejection were found. This addition of foot-ground contact friction may allow for better understanding of center-of-mass system dynamics on realistic terrain.

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.

scholarly journals Evolving optimal learning strategies for robust locomotion in the spring-loaded inverted pendulum model

2019 ◽  
Vol 16 (6) ◽  
pp. 172988141988570 ◽  
Author(s):  
Kathryn Walker ◽  
Helmut Hauser
Keyword(s):  
Online Learning ◽  
Learning Strategies ◽  
Inverted Pendulum ◽  
Ground Level ◽  
Step Size ◽  
Inverted Pendulum Model ◽  
Pendulum Model ◽  
Wide Range ◽  
Starting Conditions ◽  
Spring Loaded Inverted Pendulum

Robust locomotion in a wide range of environments is still beyond the capabilities of robots. In this article, we explore how exploiting the soft morphology can be used to achieve stability in the commonly used spring-loaded inverted pendulum model. We evolve adaption rules that dictate how the attack angle and stiffness of the model should be changed to achieve stability for both offline and online learning over a range of starting conditions. The best evolved rules, for both the offline and online learning, are able to find stability from a significantly wider range of starting conditions when compared to an un-adapting model. This is achieved through the interplay between adapting both the control and the soft morphological parameters. We also show how when using the optimal online rule set, the spring-loaded inverted pendulum model is able to robustly withstand changes in ground level of up to 10 m downwards step size.

Apex Height Control of a Two-Mass Robot Hopping on a Viscoelastic Foundation With Inertia

2018 ◽  
Author(s):  
Amer Allafi ◽  
Frank B. Mathis ◽  
Ranjan Mukherjee
Keyword(s):  
Control Strategy ◽  
Hybrid Control ◽  
Center Of Mass ◽  
Internal Degree ◽  
Degree Of Freedom ◽  
Integral Control ◽  
Additional Degree ◽  
Apex Height ◽  
Mass Spring ◽  
Internal Degree Of Freedom

A majority of the results in the literature on hopping robots assume the ground to be rigid. Hopping on a foundation that can be modeled as a mass-spring-damper system poses challenges due to undesired vibration of the additional degree-of-freedom and dissipation due to impact and viscous damping. A hybrid control strategy is developed to converge the maximum jumping height of the center-of-mass of a two-link prismatic-joint robot to a desired value. The hybrid control strategy uses backstepping in continuous time and integral control in discrete time to control the internal degree-of-freedom and the total energy. Simulation results are presented to demonstrate the efficacy of the controller.

Stable jump control for the wheel-legged robot based on TMS-DIP model

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Xu Li ◽  
Yixiao Fan ◽  
Haoyang Yu ◽  
Haitao Zhou ◽  
Haibo Feng ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Inverted Pendulum ◽  
Control Method ◽  
Control Strategies ◽  
Center Of Mass ◽  
Joint Space ◽  
Legged Robot ◽  
Content Type ◽  
Inverted Pendulum Model ◽  
Mass Spring

Purpose The purpose of this paper is to propose a novel jump control method based on Two Mass Spring Damp Inverted Pendulum (TMS-DIP) model, which makes the third generation of hydraulic driven wheel-legged robot prototype (WLR-3P) achieve stable jumping. Design/methodology/approach First, according to the configuration of the WLR, a TMS-DIP model is proposed to simplify the dynamic model of the robot. Then the jumping process is divided into four stages: thrust, ascent, descent and compression, and each stage is modeled and solved independently based on TMS-DIP model. Through WLR-3P kinematics, the trajectory of the upper and lower centroids of the TMS-DIP model can be mapped to the joint space of the robot. The corresponding control strategies are proposed for jumping height, landing buffer, jumping attitude and robotic balance, so as to realize the stable jump control of the WLR. Findings The TMS-DIP model proposed in this paper can simplify the WLR dynamic model and provide a simple and effective tool for the jumping trajectory planning of the robot. The proposed approach is suitable for hydraulic WLR jumping control. The performance of the proposed wheel-legged jump method was verified by experiments on WLR-3P. Originality/value This work provides an effective model (TMS-DIP) for the jump control of WLR-3P. The results showed that the number of landing shock (twice) and the pitch angle fluctuation range (0.44 rad) of center of mass of the jump control method based on TMS-DIP model are smaller than those based on spring-loaded inverted pendulum model. Therefore, the TMS-DIP model makes the jumping process of WLR more stable and gentler.

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.

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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