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What would the equations be for the robot's angular and linear velocity at P and also P2? I think I'm doing it wrong...
WL = left wheels angular velocity WR = right wheels angular velocity
For P I had for example the linear velocity = (1/3)rWL + (2/3)2rWR
Am I on right track?
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.
rand2rlabels are radii (even though drawn as diameters). Is that correct? $\endgroup$ – Ian Feb 24 '14 at 16:50