LQR and MPC controller design and comparison for a stationary self-balancing bicycle robot with a reaction wheel

Abstract

A self-balancing bicycle robot based on the concept of an inverted pendulum is an unstable and nonlinear system. To stabilize the system in this work, the following three main components are required, i. e., (1) an IMU sensor that detects the tilt angle of the bicycle robot, (2) a controller that is used to control motion of a reaction wheel, and (3) a reaction wheel that is employed to produce reactionary torque to balance the bicycle robot. In this paper, we propose three control strategies: linear quadratic regulator (LQR), linear model predictive control (LMPC), and nonlinear model predictive control (NMPC). Several simulation tests have been conducted in order to show that our proposed control laws can achieve stabilizaton and make the system balance. Furthermore, LMPC and NMPC controllers can deal with state and input constraints explicitly.