# The speed�?curvature power law of movements: a reappraisal

[From Erling Jorgensen (2017.11.08 1005 EST)]

Bruce Nevin (2017.11.07.18:57 ET)

As I belatedly realized (Bruce Nevin 2017.11.07.18:50 ET),

The “minimum-jerk model” that Huh and Sejnowski present is an ‘optimal control’ model; it is not a control-theory model. So it is pointless to ask how to disturb “minimum jerk” or how it might be perceived or controlled by a control system.

And it is likewise pointless to ask for a functional diagram. Wrong tree, and nothing to bark at.

Hi Bruce,

EJ: I agree that the ‘optimum control’ model, as I understand it, does not produce “minimum jerk” by controlling input, but by calculating and generating output. However, I believe it is possible to control for minimum jerk, or smoothness of acceleration, in a PCT manner.

EJ: My father-in-law was notorious for driving with a very erratic use of the accelerator, even at running speed on straight roads with minimal disturbances. The accelerator was constantly surging or easing off, and it made for a noticeably uncomfortable ride as a passenger. I think that sensitized me to what a passenger might be feeling if I was being too aggressive with acceleration or deceleration (even at steady rates.) I’ve tried to notice, and minimize, that last bit of jerk just before coming to a full stop, by slightly easing up on the brake with a slight mini-coast to a stop for the final second. I’ve tried to be smoother or steadier with changes in accelerating.

EJ: I think I am perceptually noticing a couple of things, in order to control for smoothness. One is the pressure of the accelerator on the bottom of my right foot, and the degree of perceived effort. Along with that is the rate of change in the angle of my right ankle, trying to minimize sudden changes. A more pronounced indicator of jerkiness in the ride is whether my upper torso is making small uncontrolled movements forward or back. As the driver, these get buffered somewhat by the muscle tone of my arms gripping the steering wheel, and even by the pressure back against my right foot by the springy accelerator pedal itself. Because I have those dynamic buffers online by virtue of driving, I try to realize that the passengers may not be bracing themselves in a similar way, and so that is a reminder to try to make the journey even smoother than it feels to me.

EJ: I haven’t yet thought through how this may be applied to drawing ellipses or scribbles or other results of curved-path movements. Nor have I thought yet about potential disturbances to smoothness in those activities. But it seems the third derivative of position may have some applicability, at least for some situations of PCT control.

All the best,

Erling

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