A Simply Stabilized Running Model

Ghigliazza, R. M.; Altendorfer, Richard; Holmes, Philip; Koditschek, D. E.

doi:10.1137/050626594

Cited by 90 publications

(38 citation statements)

References 54 publications

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“…This model differs from some recent approaches in that (i) no small angle assumptions are made in the equations of motion (19) and (ii) gravity is not ignored (39). This approach necessitates a numerical solution but provides a more realistic approximation of guinea fowl behavior.…”

Section: Methodsmentioning

confidence: 99%

Running over rough terrain reveals limb control for intrinsic stability

Daley

Biewener

2006

Proc. Natl. Acad. Sci. U.S.A.

190

228

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Legged animals routinely negotiate rough, unpredictable terrain with agility and stability that outmatches any human-built machine. Yet, we know surprisingly little about how animals accomplish this. Current knowledge is largely limited to studies of steady movement. These studies have revealed fundamental mechanisms used by terrestrial animals for steady locomotion. However, it is unclear whether these models provide an appropriate framework for the neuromuscular and mechanical strategies used to achieve dynamic stability over rough terrain. Perturbation experiments shed light on this issue, revealing the interplay between mechanics and neuromuscular control. We measured limb mechanics of helmeted guinea fowl (Numida meleagris) running over an unexpected drop in terrain, comparing their response to predictions of the mass-spring running model. Adjustment of limb contact angle explains 80% of the variation in stance-phase limb loading following the perturbation. Surprisingly, although limb stiffness varies dramatically, it does not influence the response. This result agrees with a mass-spring model, although it differs from previous findings on humans running over surfaces of varying compliance. However, guinea fowl sometimes deviate from mass-spring dynamics through posture-dependent work performance of the limb, leading to substantial energy absorption following the perturbation. This posture-dependent actuation allows the animal to absorb energy and maintain desired velocity on a sudden substrate drop. Thus, posture-dependent work performance of the limb provides inherent velocity control over rough terrain. These findings highlight how simple mechanical models extend to unsteady conditions, providing fundamental insights into neuromuscular control of movement and the design of dynamically stable legged robots and prosthetic devices.biomechanics ͉ locomotion ͉ motor control ͉ mass-spring model A ll legged terrestrial animals use similar basic mechanisms for steady locomotion (1-7). In the stance phase of bouncing gaits, such as hopping and running, kinetic energy (KE) and gravitational potential energy of the body cycle in phase, decreasing during the first half of stance and increasing during the second half (1). Elastic recoil allows this energy to be stored and returned by the elastic structures of the limb (8-11). Consequently, a simple mass-spring model is often used to describe the stance phase dynamics of these gaits. The model consists of a point mass and a linear compression spring (2-4). Despite the simplicity of this model, it appears that humans and animals maintain mass-spring dynamics over a broad range of locomotor conditions by adjusting model parameters: limb contact angle ( o ), effective limb length (L o ), and leg stiffness (k leg ) (4, 5, 12, 13). Nonetheless, the mass-spring model is a conservative system, meaning that the total mechanical energy of the body (E com ) does not change over a stride. If energy must be absorbed or produced to change E com (in acceleration or deceleration, fo...

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Section: Methodsmentioning

confidence: 99%

Running over rough terrain reveals limb control for intrinsic stability

Daley

Biewener

2006

Proc. Natl. Acad. Sci. U.S.A.

190

228

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“…To create a self-contained model of running, we first examined the simplest alternative-the mean parameter-SLIP model-which is closest to the traditional SLIP models of the 1990s [8,29,30]. In the mean parameter-SLIP model, we held the SLIP parameters of left and right steps constant, with values that correspond to a periodic motion with the same step durations, nadir heights and apex states as the average empirical left and right steps.…”

Section: Resultsmentioning

confidence: 99%

Constructing predictive models of human running

Maus

Revzen

Ludwig

et al. 2015

J. R. Soc. Interface.

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Running is an essential mode of human locomotion, during which ballistic aerial phases alternate with phases when a single foot contacts the ground. The spring-loaded inverted pendulum (SLIP) provides a starting point for modelling running, and generates ground reaction forces that resemble those of the centre of mass (CoM) of a human runner. Here, we show that while SLIP reproduces within-step kinematics of the CoM in three dimensions, it fails to reproduce stability and predict future motions. We construct SLIP control models using data-driven Floquet analysis, and show how these models may be used to obtain predictive models of human running with six additional states comprising the position and velocity of the swing-leg ankle. Our methods are general, and may be applied to any rhythmic physical system. We provide an approach for identifying an event-driven linear controller that approximates an observed stabilization strategy, and for producing a reduced-state model which closely recovers the observed dynamics.

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“…Based on simple models, researchers have also analytically examined running motion. Ghigliazza et al [15] used a spring-loaded inverted pendulum (SLIP) as a running model. Their model consisted of a rigid body equipped with a massless springy leg, and it was periodically controlled so that its leg angle relative to the inertial space was constant when this model touched the ground.…”

Section: Introductionmentioning

confidence: 99%

Self-stability of a simple walking model driven by a rhythmic signal

Aoi

Tsuchiya

2007

Nonlinear Dyn

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In this paper, we analyzed the dynamic properties of a simple walking model of a biped robot driven by a rhythmic signal from an oscillator. The oscillator receives no sensory feedback and the rhythmic signal is an open loop. The simple model consists of a hip and two legs that are connected at the hip. The leg motion is generated by a rhythmic signal. In particular, we analytically examined the stability of a periodic walking motion. We obtained approximate periodic solutions and the Jacobian matrix of a Poincaré map by the powerseries expansion using a small parameter. Although the analysis was inconclusive when we used only the first order expansion, by employing the second order expansion it clarified the stability, revealing that the periodic walking motion is asymptotically stable and the simple model possesses self-stability as an inherent dynamic characteristic in walking. We also clarified the stability region with respect to model parameters such as mass ratio and walking speed.

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A Simply Stabilized Running Model

Cited by 90 publications

References 54 publications

Running over rough terrain reveals limb control for intrinsic stability

Running over rough terrain reveals limb control for intrinsic stability

Constructing predictive models of human running

Self-stability of a simple walking model driven by a rhythmic signal

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