  External and internal convertible (EIC) form-based motion control is one of
the effective designs of simultaneously trajectory tracking and balance for
underactuated balance robots. Under certain conditions, the EIC-based control
design however leads to uncontrolled robot motion. We present a Gaussian
process (GP)-based data-driven learning control for underactuated balance
robots with the EIC modeling structure. Two GP-based learning controllers are
presented by using the EIC structure property. The partial EIC (PEIC)-based
control design partitions the robotic dynamics into a fully actuated subsystem
and one reduced-order underactuated system. The null-space EIC (NEIC)-based
control compensates for the uncontrolled motion in a subspace, while the other
closed-loop dynamics are not affected. Under the PEIC- and NEIC-based, the
tracking and balance tasks are guaranteed and convergence rate and bounded
errors are achieved without causing any uncontrolled motion by the original
EIC-based control. We validate the results and demonstrate the GP-based
learning control design performance using two inverted pendulum platforms.
