Calculating wheel velocities for differentail drive.

Question

I really want to know how to determine formulas for velocity in a differential drive? I found these formulas that work for me:

$$v_r = \frac{(2 \cdot v) + (w \cdot L)}{2 \cdot R}$$ $$v_l = \frac{(2 \cdot v) - (w \cdot L)}{2 \cdot R}$$ But even knowing kinematics of differentail robot, I don't know how to solve this to achive velocity foreach wheel. Here is kinematics: differential drive unicycle model

Thanks for your help.

Answer 1

Hint.

This is a consequence of the Euler-Poisson kinematic law for a rigid body.

$$ \vec v_1 = \vec v_2 + \vec \omega \times (p_1-p_2) $$

Here $p_1, p_2$ are the wheel floor contact points.