A Detailed Look at the SLIP Model Dynamics: Bifurcations, Chaotic Behavior, and Fractal Basins of Attraction

Zaytsev, Petr; Cnops, Tom; Remy, C. David

doi:10.1115/1.4043453

Cited by 7 publications

(2 citation statements)

References 34 publications

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“…An equilibrium point (limit-cycle) is stable if nearby points (orbits) eventually converge towards it, and unstable if they diverge. Locomotion is often thought of as a limit-cycle, which allows a wealth of mathematical tools to be used for analysis [15][16][17][18][19]. However, Birn-Jeffery et al [9] suggest that convergence may not be a task-level priority for running birds.…”

Section: Introductionmentioning

confidence: 99%

A little damping goes a long way: a simulation study of how damping influences task-level stability in running

et al. 2020

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It is currently unclear if damping plays a functional role in legged locomotion, and simple models often do not include damping terms. We present a new model with a damping term that is isolated from other parameters: that is, the damping term can be adjusted without retuning other model parameters for nominal motion. We systematically compare how increased damping affects stability in the face of unexpected ground-height perturbations. Unlike most studies, we focus on task-level stability: instead of observing whether trajectories converge towards a nominal limit-cycle, we quantify the ability to avoid falls using a recently developed mathematical measure. This measure allows trajectories to be compared quantitatively instead of only being separated into a binary classification of ‘stable' or ‘unstable'. Our simulation study shows that increased damping contributes significantly to task-level stability; however, this benefit quickly plateaus after only a small amount of damping. These results suggest that the low intrinsic damping values observed experimentally may have stability benefits and are not simply minimized for energetic reasons. All Python code and data needed to generate our results are available open source.

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Section: Introductionmentioning

confidence: 99%

A little damping goes a long way: a simulation study of how damping influences task-level stability in running

et al. 2020

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“…Differing from the LIPM, the SLIP model includes two complaint legs with a certain stiffness and a centralised mass point [19]. Especially, the SLIP model naturally performs characteristics similar to human walking dynamics, including the CoM fluctuation, double support period and double-peak ground reaction force profile [20,21]. The SLIP model was initially proposed for focusing on the important kinematic features of animal locomotion in biomechanical studies [22].…”

Section: Spring-loaded Inverted Pendulum Modelmentioning

confidence: 99%

An overview on bipedal gait control methods

Hu,

Xie,

Gao

et al. 2023

IET Collab Intel Manufact

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Bipedal gait control has always been a very challenging issue due to the multi‐joint and non‐linear structure of humanoid robots and frequent robot–environment interactions. To realise stable and robust bipedal walking, many aspects including robot modelling, gait stability and environmental adaptivity should be considered to design the gait control method. In this paper, a general description of bipedal gait and the corresponding evaluation indicators are introduced. Moreover, the existing bipedal gait control methods are classified into model‐based gait, stability criterion‐based gait and learning strategy‐based gait and a comprehensive review is conducted. Finally, the existing challenges and development trends of bipedal gait control are presented.

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Asymptotic Solution of a Boundary Value Problem for a Spring–Mass Model of Legged Locomotion

Okrasińska-Płociniczak

Płociniczak

2020

J Nonlinear Sci

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Running is the basic mode of fast locomotion for legged animals. One of the most successful mathematical descriptions of this gait is the so-called spring–mass model constructed upon an inverted elastic pendulum. In the description of the grounded phase of the step, an interesting boundary value problem arises where one has to determine the leg stiffness. In this paper, we find asymptotic expansions of the stiffness. These are conducted perturbatively: once with respect to small angles of attack, and once for large velocities. Our findings are in agreement with previous results and numerical simulations. In particular, we show that the leg stiffness is inversely proportional to the square of the attack angle for its small values, and proportional to the velocity for large speeds. We give exact asymptotic formulas to several orders and conclude the paper with a numerical verification.

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A Detailed Look at the SLIP Model Dynamics: Bifurcations, Chaotic Behavior, and Fractal Basins of Attraction

Cited by 7 publications

References 34 publications

A little damping goes a long way: a simulation study of how damping influences task-level stability in running

A little damping goes a long way: a simulation study of how damping influences task-level stability in running

An overview on bipedal gait control methods

Asymptotic Solution of a Boundary Value Problem for a Spring–Mass Model of Legged Locomotion

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