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.

This paper presents a nonlinear control design for highly underactuated balance robots, which possess more numbers of unactuated degree-of-freedom (DOF) than actuated ones. To address the challenge of simultaneously trajectory tracking of actuated coordinates and balancing of unactuated coordinates, the proposed control converts a robot dynamics into a series of cascaded subsystems and each of them is considered virtually actuated. To achieve the control goal, we sequentially design and update the virtual and actual control inputs to incorporate the balance task such that the unactuated coordinates are balanced to their instantaneous equilibrium. The closed-loop dynamics are shown to be stable and the tracking errors exponentially converge towards a neighborhood near the origin. The simulation results demonstrate the effectiveness of the proposed control design by using a triple-inverted pendulum cart system.

External and internal convertible (EIC) form-based motion control (i.e., EIC-based control) is one of the effective approaches for underactuated balance robots. By sequentially controller design, trajectory tracking of the actuated subsystem and balance of the unactuated subsystem can be achieved simultaneously. However, with certain conditions, there exists uncontrolled robot motion under the EIC-based control. We first identify these conditions and then propose an enhanced EIC-based control with a Gaussian process data-driven robot dynamic model. Under the new enhanced EIC-based control, the stability and performance of the closed-loop system is guaranteed. We demonstrate the GP-enhanced EIC-based control experimentally using two examples of underactuated balance robots.