Balancing riderless electric scooters at zero speed in the presence of feedback delay

Abstract

The nonlinear dynamics of electric scooters is investigated using a spatial mechanical model. The equations of motion are derived with the help of Kane's method. Two control algorithms are designed in order to balance the e-scooter in a vertical position at zero longitudinal speed. Hierarchical, linear state feedback controllers with feedback delay are considered. In the case of a delay-free controller, the linear stability properties are analyzed analytically, with the help of the Routh-Hurwitz criteria. The linear stability charts of the delayed controllers are constructed with the help of the D-subdivision method and semi-discretization. The control gains of the controllers are optimized with respect to the robustness against perturbations. The effects of the feedback delay of the controllers, the rake angle, the trail, and the center of gravity of the handlebar on the linear stability are shown. The performance of the control algorithms is verified by means of numerical simulations. Mathematics Subject Classification (2020) MSC 34A30 · MSC 34A34 · MSC 34D08 · MSC 34H05 · MSC 37C75 · MSC 93B52