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Dynamic modelling of a four-legged robot

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Abstract

A unified dynamic modelling approach of closed and/or open kinematic chain mechanisms is established. It is based on the use of the Newton-Euler formalism and the explicit formulation of kinematic holonomic constraints for the closed loop mechanisms. The approach is then applied to derive the dynamic modelling of a four-legged robot adopting a walking gait. The different movement sequences of the gait are analysed in order to calculate the all necessary terms in the dynamic equations of the quadruped robot.

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Abbreviations

g :

acceleration vector due to the gravity

m i :

mass of bodyS i

G i :

mass centre of bodyS i

I i :

inertia tensor of the bodyS i about its mass centre

f :

coefficient of viscous friction

V Gi :

3-dim absolute velocity vector

Ωi :

3-dim absolute angular velocity vector

t i :

6-dim twist vector of the bodyS i defined as\(t_i = \left[ {V_{G_i }^T ,\Omega _i^T } \right]^T \)

n, l :

number of bodies, joints

d i :

number of degree of freedom of the jointi

I d :

3×3 identity matrix

T suprinfi :

6-dim wrench vector acting on the bodyS i in whichr stands for:l (constraint wrench),g (gravity wrench),f (friction wrench),e (external wrench),m (driving wrench)

θi :

joint angle of the bodyS i

O(3) :

3-dim zero vector

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Bennani, M., Giri, F. Dynamic modelling of a four-legged robot. J Intell Robot Syst 17, 419–428 (1996). https://doi.org/10.1007/BF00571701

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  • DOI: https://doi.org/10.1007/BF00571701

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