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The craig(p.180) states that equations can be made to represent the dynamic equations. The first one being the state space equation.

$\tau=M(\Theta)\cdot\ddot{\Theta} + V(\Theta,\dot{\Theta}) + G(\Theta)$

The other one being the configuration state space equation.

$\tau=M(\Theta)\cdot\ddot{\Theta} + B(\Theta)[\dot{\Theta} \dot{\Theta}]+ C(\Theta)[\dot{\Theta}^2] + G(\Theta)$

Why would one need to split the velocity term into a Coriolis and centrifugal part? I need one of these versions to make a controller but can't see why one should be desirable than the other. Why is this important for computer control of a robot?

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  • $\begingroup$ What is the difference between $\dot{\Theta} \dot{\Theta}$ and $\dot{\Theta}^2$? $\endgroup$
    – fibonatic
    Commented Nov 29, 2020 at 16:47
  • $\begingroup$ That this is the angular velocities of the different joints. $\dot{\Theta}_{n}, \dot{\Theta}_{n+1}$ $\endgroup$
    – Hamzalihi
    Commented Nov 30, 2020 at 16:38

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They are exactly the same equation, being the former only a compact version of the latter.

From the Euler-Lagrange approach to the dynamics of a manipulator, you can build the $B$ and $C$ terms distinctively from the knowledge of your robot (e.g. distribution of masses of the links).

Thus, for constructing the dynamics that you aim to control, you have to deal with the second equation. This knowledge is way important (oftentimes a prerequisite) to design a good controller.

However, when it comes to designing the controller, you can conveniently group up terms in $\Theta$ and $\dot{\Theta}$ (first equation) as their influence can be aggregated.

Differently, if you don't have available the inertial parameters of your manipulator, you could think of estimating those dynamical terms, perhaps by means of adaptive control. In this specific case, you will most likely estimate $V$ rather than $B$ and $C$ separately, right because their effects accumulate and it is not straightforward to observe them in isolation.

Hope it helps out.

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