Stabilization of a Wheeled Inverted Pendulum by a Continuous-Time Infinite-Horizon LQG Optimal Controller

An LQG control strategy is proposed and tested for a wheeled inverted pendulum robot. We show how a reduced set of sensors, as compared to other solutions that can be found in the literature, can be used to observe all state variables of interest for stabilization. A Kalman-Bucy estimator is used to estimate the unmeasured variables and to filter those that are directly measured. An LQR feedback strategy is then used to stabilize the upright equilibrium state. The resulting LQG controller is tested under simulation and the results are verified on an OpenGL virtual environment developed for this purpose.