If you’re looking to improve the stability of your self balancing robot you might use a
simple horrifying equation like this one. It’s part of the journey [Lauszus] took when developing a sensor filtering algorithm for his balancing robot. He’s not breaking ground on new mathematical ideas, but trying to make it a bit easier for the next guy to use a Kalman filter. It’s one method of suppressing noise and averaging data from the sensors commonly used in robotic applications.
His robot uses a gyroscope and accelerometer to keep itself upright on just two wheels. The combination of these sensors presents an interesting problem in that accelerometer input is most accurate when sampled over longer periods, and a gyroscope is the opposite. This filter takes those quirks into account, while also factoring out sensor noise. Despite the daunting diagram above, [Lauszus] did a pretty go job of breaking down the larger function and showing us where to get the data and how to use it in microcontroller code.