The linear velocity $v$ of a differential drive robot is the average of the velocities of its wheels [^]. In mathematical terms:
$$
v = \frac{v_L + v_R}{2}
$$
Where $v_L$ and $v_R$ are respectively the linear velocity of the left and right wheels. These are functions of their angular velocities and radii, such that:
$$
v_L = r_L \omega_L
$$
$$
v_R = r_R \omega_R
$$
Where $r_L$ and $r_R$ are respectively the radii (not the diameters!) of the left and right wheels, and $\omega_L$ and $\omega_R$ likewise the angular velocities.
The angular velocity $\omega$, on the other hand, is the average of the opposing contributions of left and right wheels: the left wheel contributes clockwise ("negative") motion, whereas the right wheel contributes counter-clockwise ("positive") motion. In mathematical terms:
$$
\omega = \frac{\phi_R - \phi_L}{2}
$$
Where the wheel contributions $\phi_L$ and $\phi_R$ are given by:
$$
\phi_L = \frac{r_L \omega_L}{l_L}
$$
$$
\phi_R = \frac{r_R \omega_R}{l_R}
$$
And $l_L$ and $l_R$ are respectively the left and right shaft lengths between the center of rotation and the left and right wheels.
r
and2r
labels are radii (even though drawn as diameters). Is that correct? $\endgroup$ – Ian Feb 24 '14 at 16:50