Wheel Odometry Distance
Distance a wheeled robot travels from encoder counts.
Formula
Variables
Example
r=0.05, C=500, N=1000: d ≈ 0.157 m
How it works
This formula converts wheel encoder counts into the linear distance a robot has travelled. It works because one full wheel revolution covers the wheel’s circumference, 2πr, and the fraction of a revolution completed is the fraction of encoder counts counted, C/N. Multiplying those together gives the path length the wheel has rolled along the ground, assuming the wheel does not slip.
When to use it
Use this when estimating how far a robot has moved from its wheel encoders, such as in dead reckoning, autonomous navigation, or logging travel distance. It is especially useful when you know the wheel size and encoder resolution but do not have GPS or external position sensors.
Worked example, step by step
Given: r = 0.08 m, C = 750 counts, N = 1500 counts/rev Step 1: Find the wheel circumference: 2πr = 2π(0.08) = 0.5027 m Step 2: Find the fraction of one revolution: C/N = 750/1500 = 0.5 Step 3: Multiply to get distance: d = 0.5027 × 0.5 = 0.2514 m Final answer: d ≈ 0.251 m
Common mistakes to avoid
- Using wheel diameter instead of radius in the formula
- Forgetting that C/N is a fraction of a full revolution, not the total number of turns
- Ignoring wheel slip or surface effects, which can make the encoder-based distance too large or too small
Did You Know?
Odometry drifts over time as small wheel-slip errors accumulate — hence robots fuse it with other sensors.
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