Wheel Speed to Robot Motion

Now connect wheel measurements to chassis motion.

Suppose over one second:

• left wheel travels 0.80 m;
• right wheel travels 1.00 m.

The average forward travel is approximately:

(0.80 + 1.00) / 2 = 0.90 m

The right side traveled farther, so the robot also rotated left.

Estimating heading change

A simplified differential-drive relationship uses:

heading change ≈ (right distance - left distance) / track width

If track width is 0.50 m:

(1.00 - 0.80) / 0.50 = 0.40 rad

That is about 23 degrees.

This is an ideal kinematic estimate. Slip and measurement error change the real result.

Why units matter

If wheel distance is in centimeters and track width is in meters, the calculation can be numerically wrong while still producing a believable number.

Robotics errors love mixed units.

Write units beside values until the conversion is obvious.

Reverse one side

If left travels -0.30 m and right travels +0.30 m with a 0.50 m track width:

heading change ≈ (0.30 - (-0.30)) / 0.50

= 1.2 rad

The robot rotates with little average translation.

Build a motion table

Create four one-second trials with different left/right wheel distances.

For each calculate:

• average forward distance;
• approximate heading change;
• qualitative path.

Then choose one trial and change only the track width. Explain how the predicted rotation changes.

The calculation is not the destination. It is the bridge between subsystem motion and whole-robot behavior.

Convert wheel rotation into ground speed

A wheel with radius r rotating at angular speed ω_wheel has ideal tangential speed:

v = r × ω_wheel

For a wheel radius of 0.05 m spinning at 12 rad/s:

v = 0.05 × 12
  = 0.60 m/s

That estimate assumes the wheel rolls without slipping.

If an encoder reports rotations per second instead, convert through circumference:

distance per rotation = 2πr

At r = 0.05 m:

circumference ≈ 0.314 m

Three wheel rotations per second would therefore predict about:

0.314 × 3 ≈ 0.94 m/s

Direction belongs in the sign

A signed velocity keeps direction in the model.

+0.8 m/s  forward
-0.8 m/s  reverse

Losing the sign early creates bugs later when left/right wheel motion is transformed into robot motion.

When you build a conversion chain, annotate every value with units. Unit labels are one of the cheapest debugging tools in robotics.