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Quantity causing acceleration in the state space of a mechanical system.

1
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, respectively, responsible for generating the attractive force toward the target (stiffness) as well as a drag (damping) that suitably decelerates the robot avoiding oscillations around $x_d$. Once you have … $\ddot{x}$, you can integrate it twice in time to get the temporal evolution. The extension to the 2D and 3D cases is pretty immediate, whereas to account for the repulsive force yielded by the obstacle $x_o$, you have to invert the sign of the term $K\cdot\left(x_o-x\right)$. …
answered Aug 4 '19 by Ugo Pattacini
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As a general remark, a PID controller can be designed to take into account only constraints occurring at the commanded variable - the end-effector velocity in your case - through the so-called antiwin …
answered Mar 9 '19 by Ugo Pattacini