I am curious how you found those “magic” numbers (1.2, 1.0356, 0.2) for the function. Aside from trial and error, it seems a bit un-intuitive. I like to use power functions, because it is straight-forward to visualize how their curvature changes as power changes. I explained these power functions a while back here. I explained my motivation for using these functions here. I encourage anyone to read how to use these functions, and try them out for themselves. I also enjoy graphing in Desmos, so I created some interactive graphs which visualize these functions. You can enable/disable the each of the graphs by pressing the circles to the right of the equations. You can change power of the curve using the n slider.
Pay attention to my note about even and odd values of n from the first link:
As you can see when
n = 1(blue), it actually results in the traditional output. Also note that they all intersect the points(0, 0)and(127, 127). Please be aware that if you choose an even value forn, the output will be positive even when you push the joystick backwards! You can solve this by multiplying the sign of the raw joystick value and the output of your function. Whennis an odd number, the direction of the output will work as expected. Remember there is no correct value ofn, and it’s up to the driver’s preferences.
If you press the ‘play arrow’ next to the x_joystick you can see a circle follow the mapping curve. The radius of the circle shows the rate of change of the curve (its derivative). For reference, I have graphed OP’s equation in orange and [-127, 127] on the domain and range. I use motor.move() in PROS meaning [-127, 127]is the range for the joysticks and motors.