How Slow Should a Robot Be?: Physics of Human-Robot Coordination

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Imagine this kind of situation:
  1. A human user is requested to place his/her hand (or a grasped tool) at a given position or to move his/her hand along a given trajectory.
  2. A robot actively produces small forces to guide the human userís hand toward the desired position or along the desired trajectory.
  3. The user knows and can visually recognize the desired position or trajectory.
  4. The data of the desired position or trajectory are provided to the robot controller in advance.
  5. The robotís actuator force is so small that the user can easily deviate from the desired trajectory when s/he intends to do so.


The question we faced was: in this kind of situation, what kind of controller should be used for the robot?

Our suggestion is: use "PSMC" with the time constant 0.1 sec!!

Why PSMC?: because the controller should be stiff enough but at the same time should be damped enough. With ordinary PD control, this means high P-gain and high D-gain are required. High D-gain is technically impossible due to the noise in the velocity measurements.

How damped should it be?: From the experiments, we found the damping-to-stiffness ratio should be around 0.1 sec rather than 0.5 sec or 0.01 sec.

Why 0.1 sec?: We have no idea, frankly. But this number has good agreement with previuos studies on human response during steering vehicles. See more details in section II.B of the paper below.

The above situation may look too particular but I believe some classes of rehabilitation and human-machine coordination in manufacturing industry fall within this class of situation. I named it as a "low-force kinesthetic guidance."


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