paper: Power consumption limits and total motor power in FRC drives

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Power consumption limits and total motor power in FRC drives
by: Oblarg

Investigates the theoretical effect of limiting of total robot drive power consumption on drive performance.

The effect of adding more motors to a FRC drive is subject to some interesting subtleties when considering the limitations of the FRC batteries and common current-limiting implementations. A particularly-counterintuitive effect is derived and discussed, and some directions for future inquiry are highlighted.

Power_Limited_Motor_Analysis (2).pdf (182 KB)

Supplemental: I had a bit more spare time and decided to make the extended force-versus-speed plot that I mentioned at the end of the paper.

As with the calculations in the paper, everything is based around a drive geared to 15 ft/s free speed, and no frictional losses are taken into account. If you’re wondering why the lines are different lengths, recall that the speed at which a drive becomes no longer power-limited depends on the total motor power.

Edit: And here’s the R script used to generate the plot, in case anyone wants to play around with it or implement the calculations in their own thing or whatever.

Supplemental 2:

I have updated the previous graph to include the linear solution representing performance with no current-limiting applied:

This serves to isolate the subtle (and perhaps not-so-big as I had initially thought) effect of the H-bridge duty cycle. Note, curiously, that the 8x 775pro is actually less powerful at stall in the absence of current limiting - this is because it actually draws enough current at stall to fall on the wrong side of the battery’s power curve (which peaks, as one can easily calculate, at the current draw which drops the battery to half voltage).

As before, here is the code used to generate the plot.

Given that most wheels top out at a COF of 1.2, shouldn’t each of these graphs have a traction-limited flat top around ~180 lbf or below?

In principle, yes; but that depends on wheel COF, robot mass, and frictional losses in the drive (which are usually in the neighborhood of 30%, but can be as big as 50%). In practice, I don’t think (based on my experience) that any of these drives at this gearing could actually slip their wheels, unless the robot were very light.

Including that cutoff would require making assumptions about more variables than I think is prudent to maintain generality and interpretability of the results, so I left it out. It shouldn’t be hard to intuit where the cutoff ought to be given your own values for those constants, however, and the code is included so you can even generate your own graph with them if you’d like.