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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!

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    $\begingroup$ I don't understand your question. You have both position and force feedback of each joint. What exactly do you think you miss? $\endgroup$ – JJM Driessen May 21 '17 at 7:34
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If you're trying to do torque control, then you'll probably get best results if you could work with joint accelerations, because:

$$ \tau = I \alpha \\ $$

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.

You don't have an acceleration input for your joint, though. What you have is a speed input for your joint. SO, what you could do is to setup a PID controller with torque error as your input, joint acceleration reference as your output, and then perform a numeric integration of the output to get a speed reference. This would look like:

$$ \tau_{\mbox{err}} = \tau_{\mbox{ref}} - \tau_{\mbox{fbk}} \\ e_P = \tau_{\mbox{err}} \\ e_I = e_I + e_P*\Delta t \\ e_D = \frac{e_P - e_{P_{\mbox{prev}}}}{\Delta t} \\ e_{P_{\mbox{prev}}} = e_P \\ a_{\mbox{ref}} = (K_P e_P) + (K_I e_I) + (K_D e_D) \\ v_{\mbox{ref}} = v_{\mbox{ref}} + a_{\mbox{ref}} * \Delta t \\ $$

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