Estimation of inclination angle for balancing robots based on physical model

This paper presents a method for calculating the accurate inclination angle of a balancing robot using accelerometers and optionally angular rate sensor (rate gyroscope), based on systematic correction of sensor errors. The correction is calculated on the basis of physical model of the system. The basic idea of accelerometer-based inclination measurement is that accelerometers can measure the direction of gravity and thus its angle relative to the upright position. The problem is that in a moving robot not only gravitational acceleration is present, but also the acceleration and angular acceleration of the robot itself, hence the measurement is distorted with these parasitic accelerations. That is why often gyroscopes are used instead or beside the accelerometers. However, gyros have also systematic errors and are more expensive then accelerometers. In this paper we propose to use two accelerometers, each having 2 axes, and compensate the above parasitic accelerations based on a physical model. We developed an algorithm to accurately estimate the inclination angle.