A simple model of balancing in the plane and a simple preview balance controller

This paper presents a new model of the dynamics of a general planar robot balancing on a point in the plane, in which the essential parameters of the robot’s balancing behaviour are reduced to just two numbers, both of which are simple functions of basic physical properties of the robot mechanism. A third number describes the effect of other movements on the robot’s balance. This model gives rise to a simple preview balance controller consisting of a four-term control law with easily calculated gains and a reverse-time low-pass filter acting on a preview of the command signal. The filter makes the robot lean in anticipation of future movements. Simulation results are presented showing the balance controller achieving excellent tracking of large fast motion commands while simultaneously maintaining the robot’s balance and accurately rejecting disturbances caused by other motions being performed by the robot. The controller is also robust to effects such as actuator saturation and sensor noise.