Implementation of Nonlinear Optimal Control of Two-wheel Robot with Extended Kalman Filter

This paper presents a nonlinear freezing optimal control (NFOC) technique combined with an extended Kalman filter (EKF) for stabilising a two-wheel robot (TWR). The balancing LEGO EV3 Robot is utilised as a prototype for simulation and practical implementation to test the performance of the NFOC with EKF, compared against the well-known linear optimal control, i.e., the linear quadratic regulator (LQR) and the stand-alone NFOC. The stabilisation of the TWR system when starting from various ranges of initial pitch angles with different types of controllers are investigated and discussed. The MATLAB simulation result demonstrates wider operation ranges from both nonlinear optimal controllers over the linear one when simulated with a high-performance motor. In the case of implementation, the two nonlinear methods also displayed slightly more comprehensive initial pitch angle ranges than the linear control. Significantly, the precision of state variable estimation from the EKF technique removes the signal drift problem in the gyro sensor, which is used to measure the pitch angle of the TWR. The effectiveness of the NFOC controller combined with EKF is demonstrated by results from MATLAB simulation and implementation on the LEGO TWR.