Incorporating Energy Variations Into Controlled Sagittal Plane Locomotion Dynamics

The spring loaded inverted pendulum template has been shown to accurately model the steady locomotion dynamics of a variety of running animals. While the template models the leg dynamics by an energy-conserving spring, insects and animals have structures that dissipate, store and produce energy during a stance phase. Recent investigations into the spring-like properties of limbs, as well as animal response to drop step perturbations, suggest that animals use their legs to manage energy storage and dissipation, and that this management is important for gait stability. In this paper, we extend our previous analysis of control of the spring loaded inverted pendulum template via changes in the leg touch-down angle to include energy variations during the stance phase. We incorporate energy variations through leg actuation that varies the force-free leg length during the stance phase, yet maintains qualitatively correct force and velocity profiles. In contrast to the partially asymptotically stable gaits identified in previous analyses, we find that incorporating energy and leg angle variations in this manner enables the system to recover from perturbations similar to those that might be encountered during locomotion over rough terrain.

A Simple Analytical Tool for Legged Robot Design

Volume 4: 36th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2012-71452 ◽

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 ◽

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.

Comparison of Hip Torque and Radial Forcing Effects on Locomotion Stability and Energetics

Volume 6B: 37th Mechanisms and Robotics Conference ◽

10.1115/detc2013-13516 ◽

2013 ◽

Cited By ~ 1

Author(s):

Zhuohua Shen ◽

Peter Larson ◽

Justin Seipel

Keyword(s):

Inverted Pendulum ◽

Legged Robots ◽

Asymptotically Stable ◽

Alternative Strategies ◽

Advantages And Disadvantages ◽

Potential Alternative ◽

Hip torque and radial forcing along the leg are two common actuation methods for legged robots. However, hip torque and radial forcing have not been compared as potential alternative strategies of actuation. The respective advantages and disadvantages of hip torque and radial forcing are not well known. In this paper, we compare hip torque and radial forcing actuation through the simulation of two models: a Rotary-forced Spring-Loaded Inverted Pendulum and a Radially Forced Spring-Loaded Inverted Pendulum. Both actuation methods can produce fully asymptotically stable locomotion. Interestingly, it is found that they improve locomotion stability in different ways: hip torque first destabilizes locomotion when initially introduced but greatly stabilizes locomotion when it keeps increasing; radial forcing always stabilizes locomotion, but in a moderate way.

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

Volume 3: 38th Design Automation Conference, Parts A and B ◽

10.1115/detc2012-71473 ◽

2012 ◽

Author(s):

Justin Seipel

Keyword(s):

Inverted Pendulum ◽

Dynamic Models ◽

Sagittal Plane ◽

Center Of Mass ◽

Human Model ◽

Whole Body ◽

Human Gait ◽

Slip Model ◽

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.

Volume 7: Dynamic Systems and Control; Mechatronics and Intelligent Machines, Parts A and B ◽

A Spring-Mass Model of Locomotion With Full Asymptotic Stability

10.1115/imece2011-65652 ◽

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 ◽

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.

BIPED HOPPING CONTROL BAzSED ON SPRING LOADED INVERTED PENDULUM MODEL

International Journal of Humanoid Robotics ◽

10.1142/s0219843610002106 ◽

2010 ◽

Vol 07 (02) ◽

pp. 263-280 ◽

Cited By ~ 13

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 ◽

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.

A Spring-Mass Model of Locomotion With Full Asymptotic Stability

ASME 2011 Summer Bioengineering Conference, Parts A and B ◽

10.1115/sbc2011-53973 ◽

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 ◽

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.

Enforced symmetry of the stance phase for the Spring-Loaded Inverted Pendulum

2012 IEEE International Conference on Robotics and Automation ◽

10.1109/icra.2012.6224656 ◽

2012 ◽

Cited By ~ 14

Author(s):

Giulia Piovan ◽

Katie Byl

Keyword(s):

Stance Phase ◽

Inverted Pendulum ◽

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

10.1101/509687 ◽

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 ◽

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.

The Spring Loaded Inverted Pendulum as the Hybrid Zero Dynamics of an Asymmetric Hopper

IEEE Transactions on Automatic Control ◽

10.1109/tac.2009.2024565 ◽

2009 ◽

Vol 54 (8) ◽

pp. 1779-1793 ◽

Cited By ~ 144

Author(s):

I. Poulakakis ◽

J.W. Grizzle

Keyword(s):

Inverted Pendulum ◽

Zero Dynamics ◽

Hybrid Zero Dynamics ◽

IMU-Based Effects Assessment of the Use of Foot Orthoses in the Stance Phase during Running and Asymmetry between Extremities

Sensors ◽

10.3390/s21093277 ◽

2021 ◽

Vol 21 (9) ◽

pp. 3277

Author(s):

Juan Luis Florenciano Restoy ◽

Jordi Solé-Casals ◽

Xantal Borràs-Boix

Keyword(s):

Contact Time ◽

Stance Phase ◽

Inertial Sensors ◽

Sagittal Plane ◽

Plantar Flexion ◽

Foot Orthoses ◽

Foot Kinematics ◽

Running Injuries ◽

The Right ◽

Movement Differences

The objectives of this study were to determine the amplitude of movement differences and asymmetries between feet during the stance phase and to evaluate the effects of foot orthoses (FOs) on foot kinematics in the stance phase during running. In total, 40 males were recruited (age: 43.0 ± 13.8 years, weight: 72.0 ± 5.5 kg, height: 175.5 ± 7.0 cm). Participants ran on a running treadmill at 2.5 m/s using their own footwear, with and without the FOs. Two inertial sensors fixed on the instep of each of the participant’s footwear were used. Amplitude of movement along each axis, contact time and number of steps were considered in the analysis. The results indicate that the movement in the sagittal plane is symmetric, but that it is not in the frontal and transverse planes. The right foot displayed more degrees of movement amplitude than the left foot although these differences are only significant in the abduction case. When FOs are used, a decrease in amplitude of movement in the three axes is observed, except for the dorsi-plantar flexion in the left foot and both feet combined. The contact time and the total step time show a significant increase when FOs are used, but the number of steps is not altered, suggesting that FOs do not interfere in running technique. The reduction in the amplitude of movement would indicate that FOs could be used as a preventive tool. The FOs do not influence the asymmetry of the amplitude of movement observed between feet, and this risk factor is maintained. IMU devices are useful tools to detect risk factors related to running injuries. With its use, even more personalized FOs could be manufactured.