How Two Wheels Make a Robot Turn

A differential-drive robot can move forward, backward, and turn using only two independently driven sides.

The trick is that the robot's motion comes from the difference between left and right wheel speeds.

Three basic cases

left = +1    right = +1   → forward
left = -1    right = -1   → backward
left = +1    right = -1   → rotate in place

If both sides move forward but one side is slower, the robot follows a curve.

Think around the center

For ideal differential drive:

• average left/right motion contributes to forward velocity;
• difference between sides contributes to rotation.

You do not need advanced matrix math to reason about the first model.

If the left side travels farther than the right side during the same interval, the chassis must rotate toward the right.

Wheelbase matters

The distance between left and right wheel contact lines affects how a wheel-speed difference turns the robot.

A wider robot generally requires a larger difference in wheel travel to achieve the same heading change.

Geometry is part of the control system.

Real floors disagree

The ideal model assumes rolling contact without sideways slip.

Real robots experience:

• tire compression;
• scrub during turns;
• uneven traction;
• wheel diameter differences;
• floor seams;
• mechanical alignment error.

That means calculated motion and observed motion will differ.

The model is still useful because the difference becomes evidence.

Motion prediction

For each command below, sketch the expected path:

1. left 0.5, right 0.5;
2. left 0.2, right 0.6;
3. left -0.4, right 0.4;
4. left 0, right 0.5.

Label forward direction and rotation.

Then describe one real-world effect that could change each path.

The center of the robot follows from the wheels

For a differential-drive robot, the left and right wheel velocities determine both forward motion and turning.

Three simple cases:

left = +1.0   right = +1.0   → straight forward
left = +1.0   right =  0.0   → arc right
left = +1.0   right = -1.0   → rotate near center

The exact path depends on wheel spacing and the velocity difference.

If the wheelbase track width is L, one common model for angular velocity is:

ω = (v_right - v_left) / L

Suppose:

v_left  = 0.6 m/s
v_right = 1.0 m/s
L       = 0.5 m

Then:

ω = (1.0 - 0.6) / 0.5
  = 0.8 rad/s

The robot turns while also moving forward.

Geometry assumes traction

The equations describe an ideal rolling model. Real wheels slip. Carpet deforms. Tire diameter changes under load. One side may experience more friction.

That does not make the model useless. It tells you what the model predicts before physical effects are added.

Use the ideal model as a baseline, then measure the difference between prediction and behavior.