Displacements

A differentially steered vehicle has two displacements. One is linear, and the other one is angular. The linear displacement controls how far the vehicle goes, while the angular displacement controls how much the vehicle turns. In this text, we'll use $D_{L}$ for the linear displacement and $D_{A}$ for the angular displacement.

$D_{L}$ is the total number of steps that both motors need to perform. This is not difficult to understand. $D_{A}$, on the other hand, is a little more complicated. $D_{A}$ is the total difference of steps between the two motors. In other words, if forward is positive for both wheels, $D_{A}$ is the difference between the displacement of the right wheel and the displacement of the left wheel.

To keep track of $D_{L}$, every time either the right or the left wheel has a step forward, we add one to a counter. If a wheel has a step backward, we subtract one from the counter. To keep track of $D_{A}$, we assign positive to forward for one motor (we'll use left-forward), and assign negative to forward for the other motor. This means for each step the left wheel goes forward, it adds one to the counter. For each step the right wheel goes forward, it subtracts one from the counter.