Equilibrium Adaptation-Based Control for Track Stand of Single-Track Two-Wheeled Robots

Stationary balance control is challenging for single-track two-wheeled (STTW) robots due to the lack of elegant balancing mechanisms and the conflict between the limited attraction domain and external disturbances. To address the absence of balancing mechanisms, we draw inspiration from cyclists and leverage the track stand maneuver, which relies solely on steering and rear-wheel actuation. To achieve accurate tracking in the presence of matched and mismatched disturbances, we propose an equilibrium adaptation-based control (EABC) scheme that can be seamlessly integrated with standard disturbance observers and controllers. This scheme enables adaptation to slow-varying disturbances by utilizing a disturbed equilibrium estimator, effectively handling both matched and mismatched disturbances in a unified manner while ensuring accurate tracking with zero steady-state error. We integrate the EABC scheme with nonlinear model predictive control (MPC) for the track stand of STTW robots and validate its effectiveness through two experimental scenarios. Our method demonstrates significant improvements in tracking accuracy, reducing errors by several orders of magnitude.