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Differential Drive

Two wheels: v = (vR + vL)/2, ω = (vR − vL)/W, and the turning radius is v / ω.

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Most small robots and robot vacuums steer like a tank: no steering wheel, just two drive wheels that can run at different speeds.

Key idea

With right and left wheel speeds $v_R$, $v_L$ and the wheels $W$ apart: forward speed $v = \dfrac{v_R + v_L}{2}$, turn rate $\omega = \dfrac{v_R - v_L}{W}$ (radians per second, positive = left), and the center drives a circle of radius $v/\omega$.
Set the two wheel speeds and watch the path. Equal speeds go straight; opposite speeds spin in place.

Why it works

Picture the robot turning about a point on its axle line. Both wheels turn at the same rate $\omega$ about that point, but the outer wheel is $W$ farther away, so it must move $\omega W$ faster. That gives $v_R - v_L = \omega W$.

Worked example: Turn rate

$v_L = 0.2$, $v_R = 0.4$ m/s, $W = 0.15$ m.
  1. $v = 0.3\ \text{m/s}$.
  2. $\omega = 0.2/0.15 \approx 1.33\ \text{rad/s}$.
  3. Radius $= 0.3/1.33 \approx 0.23\ \text{m}$.

Answer: 1.33 rad/s, curving left on a 0.23 m radius.

Common mistake

Dividing by half the wheel track instead of the whole track, or mixing up which wheel is faster in a left turn (the right one).

Practice

Pass with 3 right answers, the last 2 in a row. Each right answer earns 2 XP.

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