# Is it possible to control joint torque using the position input and torque feedback?

So I am working with a UR10 manipulator which doesn't have a direct torque interface. However, it provides torque/velocity/position feedback for each joint as well as position/velocity interfaces for joint control.

I have a feeling the answer is "yes", but I've been having trouble finding examples and comments on the feasibility of this approach.

Thanks!

• I don't understand your question. You have both position and force feedback of each joint. What exactly do you think you miss? – JJM Driessen May 21 '17 at 7:34

$$\tau = I \alpha \\$$
Where $\tau$ is joint torque, $I$ is the moment of inertia, and $\alpha$ is the joint angular acceleration. It's a linear relationship and should be pretty straightforward to control with a PID controller.
$$\tau_{\mbox{err}} = \tau_{\mbox{ref}} - \tau_{\mbox{fbk}} \\ e_P = \tau_{\mbox{err}} \\ e_I = e_I + e_P*\Delta t \\ e_D = \frac{e_P - e_{P_{\mbox{prev}}}}{\Delta t} \\ e_{P_{\mbox{prev}}} = e_P \\ a_{\mbox{ref}} = (K_P e_P) + (K_I e_I) + (K_D e_D) \\ v_{\mbox{ref}} = v_{\mbox{ref}} + a_{\mbox{ref}} * \Delta t \\$$