  Ranging from cart-pole systems and autonomous bicycles to bipedal robots,
control of these underactuated balance robots aims to achieve both external
(actuated) subsystem trajectory tracking and internal (unactuated) subsystem
balancing tasks with limited actuation authority. This paper proposes a
learning model-based control framework for underactuated balance robots. The
key idea to simultaneously achieve tracking and balancing tasks is to design
control strategies in slow- and fast-time scales, respectively. In slow-time
scale, model predictive control (MPC) is used to generate the desired internal
subsystem trajectory that encodes the external subsystem tracking performance
and control input. In fast-time scale, the actual internal trajectory is
stabilized to the desired internal trajectory by using an inverse dynamics
controller. The coupling effects between the external and internal subsystems
are captured through the planned internal trajectory profile and the dual
structural properties of the robotic systems. The control design is based on
Gaussian processes (GPs) regression model that are learned from experiments
without need of priori knowledge about the robot dynamics nor successful
balance demonstration. The GPs provide estimates of modeling uncertainties of
the robotic systems and these uncertainty estimations are incorporated in the
MPC design to enhance the control robustness to modeling errors. The
learning-based control design is analyzed with guaranteed stability and
performance. The proposed design is demonstrated by experiments on a Furuta
pendulum and an autonomous bikebot.
