Torque commands for velocity reference motor

Question

I have a controller board for a motor, where I can read the motor current (to transform to torque), the position, the velocity and I can give a velocity command. There is not really a torque mode on this controller, that is I can only command velocity and read torque but I cannot give a torque reference.

How can use it to give a torque reference?, hence to comply with the standard robotic equation of the type

$\tau = m \ddot{q} + H(\dot{q},q) + G(q)$

That is that I get the $\tau$ value to send as reference, but in my case the controller board I have receives $\dot q$ and sends $\tau$. Is there a way to still use the standard equation for control ?

Answer 1

The $m$ in your equation looks like the symbol for mass. Really it should be $M$, the inertia matrix, but maybe you meant this.

If you are only dealing with a dual-link arm in a single plane, then you should be able to determine the inverse. This is dealt with in a lot of books, but the clearest explanation I have found is in an old MIT AI Lab paper. See p.12ff.