A New Simple Model of Balancing in the Plane

This paper presents a new model of the dynamics of balancing 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. Given this model, a high-performance balance controller can be constructed as a simple four-term control law with gains that are trivial functions of the two model parameters and a single value chosen by the user that determines the overall speed of balancing. The model is first developed for a double pendulum, and then extended to a general planar mechanism. Simulation results are presented showing the controller’s performance at following commanded motion trajectories while simultaneously maintaining the robot’s balance.