Formula & Calculator
Robot Wheel Angular Velocity from Encoder Counts
Calculates a wheel's angular velocity from the number of encoder counts registered over a known time interval.
Interpretation
ω = (Δcounts / CPR) × (2π / Δt). Wheel angular velocity from encoder pulse counts. Used to measure wheel speeds for odometry.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| omega | Wheel angular velocity | rad/s |
| delta_counts | Number of encoder counts registered during the interval | |
| CPR | Encoder counts per revolution | |
| delta_t | Time interval over which counts were measured | s |
What it means
Encoders produce counts proportional to wheel rotation. By dividing the change in counts (Δcounts) by the counts per revolution (CPR) and the time interval Δt, the angular velocity is obtained. This is used to compute wheel speeds for differential drive robots. Understanding this is essential for deriving odometry data from encoder readings.
Worked example
Wheel Angular Velocity from Encoder Counts – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| Δcounts | 100 |
| CPR | 1000 |
| Δt (s) | 0.1 |
| Parameter | Value |
|---|---|
| Δcounts | 1000 |
| CPR | 4096 |
| Δt | 1 |
Common mistakes
- Wheel angular velocity from encoder counts: ω = (Δcounts / CPR) × (2π / Δt).
- Δcounts: Number of encoder counts between samples.
- CPR: Counts per revolution – for quadrature, this is the number of edges (multiply by 4 if using full quadrature).
- Δt: Time between samples – in seconds.
- Units: ω in rad/s.
- Noise: High‑frequency noise can be filtered – use a low‑pass filter.
Applications
Robot wheel angular velocity from encoder counts, ω = (Δ_counts/CPR)·(2π/Δt), converts the change in encoder counts over a time interval to angular velocity. This is used to measure wheel speed for feedback control and odometry. Engineers use it to estimate linear and angular velocities of the robot, to implement velocity control loops, and to detect wheel slip. By calibrating the counts per revolution (CPR), they can achieve accurate speed measurements. This formula is a standard part of motor control and robot localisation systems.
- Speed measurement for DC motor feedback control
- Velocity estimation for odometry and state estimation
- Detection of wheel slip and traction control
- Implementation of closed‑loop velocity controllers
- Integration with microcontrollers and motor drivers
Frequently Asked Questions
The angular velocity of a wheel is ω = (Δcounts / CPR) × (2π / Δt), where Δcounts is the change in encoder counts during Δt, CPR is the number of counts per revolution (including any quadrature multiplication), and Δt is the time interval.
Using the encoder's raw pulse rating as CPR when quadrature decoding actually provides several times more counts per revolution. Always use the effective CPR after decoding.
Quadrature encoding multiplies the number of counts per revolution by 4. So if the encoder has 1000 PPR (pulses per revolution), the effective CPR is 4000.
v = ω · r, where r is the wheel radius.
It is limited by the maximum frequency of the encoder pulses and the sampling rate of the controller.
Counters wrap around; you need to handle the overflow by checking for sign changes and adjusting the difference.
The resolution is determined by the minimum detectable Δcounts (1 count). The velocity resolution is (2π)/(CPR·Δt).
Odometry, motor speed feedback, and control.
Noise in the encoder counts can cause jitter in the calculated velocity. Filtering (e.g., averaging) is often used.
RPM = ω × 60 / (2π).