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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- 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