Position Tracking - 2 encoder or 3 encoder?

[theol0403]

Yeah, as you have found, it is impossible to determine heading from the third wheel unless you turn on a dime.
You can’t differentiate horizontal movement from rotational movement, and it is affected by the center of turning.
The only way of getting heading is from the two parallel wheels, then the expected movement of the third wheel for that rotation is canceled out, leaving the horizontal displacement.

I explained it here:

@theol0403

Finally, in odometry the horizontal tracking wheel is not used for angle. It is impossible to differentiate the movement of the horizontal wheel between horizontal displacement or rotation of the robot. What tracking algorithms do is measure the orientation of the robot using the two vertical wheels with this formula:
dRadians = (dLeftInch - dRightInch) / chassisWidthInch;
Then, it can calculate how much it expects the horizontal wheel to move given that rotation.
It cancels out that movement from the horizontal wheel, and what remains is the horizontal displacement.