On the Learned Balance Manifold of Underactuated Balance Robots

Tracking control of underactuated balance robots needs to estimate balance profiles, that is, balance equilibrium manifold (BEM) of the unactuated subsystems. We present a learning-based approach to obtain the balance manifold for underactuated balance robots. We first establish the relationship between the BEM and the zero dynamics of the underactuated balance robots. The analysis shows that the BEM is a close approximation of the equilibria of the zero dynamics under perfectly tracking control. A Gaussian process learning-based method is proposed to estimate and obtain the BEM and zero dynamics, avoiding the direct inversion of the physics-based robot dynamic model. We demonstrate the analysis and applications experimentally on a rotary inverted pendulum and a bipedal robot.