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Leg recirculation in horizontal plane locomotion

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Abstract

A protocol prescribing leg motion during the swing phase is developed for the planar lateral leg spring model of locomotion. Inspired by experimental observations regarding insect leg function when running over rough terrain, the protocol prescribes the angular velocity of the swing-leg relative to the body in a feedforward manner, yielding natural variations in the leg touch-down angle in response to perturbations away from a periodic orbit. Analysis of the reduced order model reveals that periodic gait stability and robustness to external perturbations depends strongly upon the angular velocity of the leg at touch-down. While the leg angular velocity at touch-down provides control over gait stability and can be chosen to stabilize unstable gaits, the resulting basin of stability is much smaller than that observed for the original lateral leg spring model with a fixed leg touch-down angle. Comparisons to experimental leg angular velocity data for running cockroaches reveal that while the proposed protocol is qualitatively correct, smaller leg angular accelerations occur during the second half of the swing phase. Modifications made to the recirculation protocol to better match experimental observations yield large improvements in the basin of stability.

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Abbreviations

k :

Spring stiffness

m :

Body mass

I :

Body moment of inertia

l :

Force-free leg length

d :

Distance between center of mass and leg attachment point

η :

Spring leg length (η(0) = l)

ζ :

Distance between foot placement and center of mass

ψ :

Angle ζ makes with local horizontal axis

v :

Center of mass velocity

δ :

Velocity heading angle

θ :

Body rotation angle

\({\dot{\theta}}\) :

Body angular velocity

β :

Leg angle with respect to body axes

\({\dot{\beta}}\) :

Leg angular velocity with respect to body axes

ω :

Leg recirculation amplitude

a :

Leg recirculation frequency

\({\phi}\) :

Leg recirculation phase shift

t des :

Desired swing phase duration

β des :

Desired leg angle at t = t des

\({\dot{\beta}_{\rm des}}\) :

Desired leg angular velocity at t = t des

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Authors and Affiliations

  1. School of Mechanical, Industrial and Manufacturing Engineering, Oregon State University, Rogers 204, Corvallis, OR, 97331, USA

    A. Wickramasuriya & J. Schmitt

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  1. A. Wickramasuriya
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  2. J. Schmitt
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Correspondence to J. Schmitt.

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Wickramasuriya, A., Schmitt, J. Leg recirculation in horizontal plane locomotion. Biol Cybern 101, 247–263 (2009). https://doi.org/10.1007/s00422-009-0333-6

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  • DOI: https://doi.org/10.1007/s00422-009-0333-6

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