Wheel Odometry Formula
Reference for differential drive wheel odometry formulas.
Estimates robot position and heading from encoder ticks.
The foundation of dead-reckoning navigation.
Key Notes
- Core formula: distance = (ticks / ticks_per_rev) × 2πr: Optical or magnetic encoders count wheel rotations; multiplying by wheel circumference gives linear distance. Accuracy depends on correct wheel radius calibration.
- Differential drive heading: Δθ = (d_right − d_left) / wheel_base: For a two-wheeled robot, the change in heading is the difference between the two wheel distances divided by the distance between wheels. This accumulates into an estimated pose (x, y, θ).
- Dead reckoning drift: Odometry errors accumulate over time — small slip or calibration error compounds with every step. Even 1% wheel radius error causes significant heading drift over long distances.
- Sensor fusion improves accuracy: In practice, odometry is fused with IMU (inertial measurement unit) or GPS using a Kalman filter. Odometry is accurate short-term; GPS corrects long-term drift.
- Applications: Wheel odometry is used in warehouse robots (AMRs), autonomous vacuum cleaners (Roomba), self-driving vehicles, and any robot that must track its own position without external reference.