Dynamical Modeling and LQR Control of a Gyroscopically Stabilized Bicycle

Abstract

This contribution focuses on the dynamical modeling and control of a self-balancing bicycle. The bicycle is equipped with two flywheels rotating at constant speed mounted via a hinge that is actuated by an additional motor and allows for rotation about the vertical axis. Due to the balance of angular momentum, a torque is generated around the axis perpendicular to the hinge and spinning axis, i.e. an axis along the forward motion direction. This gyroscopic effect is exploited for the stabilization of the bicycle. Two cases are distinguished: 1) For the stabilization of the non-moving bicycle an LQ-controller based on a linear model is used. 2) For the moving bicycle, a non-linear dynamic model in terms of non-holonomic velocities is derived and based on the linearized model at constant driving speeds the stability of the bicycle is analyzed. The model reveals the self-stabilization behavior of a bicycle without flywheels. At a speed of about 17km/h, the linearized model has only eigenvalues with negative real parts and is hence stable. Experimental as well as simulation results are presented.This is an open access article under the terms of the Creative Commons Attribution-Non-Commercial-NoDerivs Licence 4.0, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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