Velocity Measurement using Encoder

Introduction

You can get the joint velocity from the position data of an encoder. A first order approximation of the derivative gives $v\approx \Delta x/\Delta t$.

How it works

The position is updated every $T$ seconds. The computer does these steps:

1. Read and store the current encoder count $P(kT)$
2. Get the previous encoder count $P((k-1)T)$
3. Calculate the approximate velocity
4. Increase $k$ by one and repeat steps 1 to 3

$$V(kT)=\frac{P(kT)-P((k-1)T)}{T}$$

You can also use a higher order approximation of the derivative.

Choosing the update time T

• if $T$ is too large, it can violate the sampling theorem
• if $T$ is too small, the count changes very little at low speed, so low speed performance is poor