Stabilizing Two-wheeled robot using linear quadratic regulator and states estimation

A control design for two-wheeled robot (TWR) stabilization using linear quadratic regulator (LQR) method and states estimation is presented. A two-wheeled robot is an unstable system such that a control system is required to stabilize it. LQR is a control design method where the control gain is calculated by minimizing a performance index. The LQR method results in a full states feedback control law. Applying the LQR method for TWR stabilization will require feedback from pitching angle and pitching rate angle measurements. However, the common available sensor in the TWR is only a rate gyro which measures the pitching rate angle. Theoretically, time integration of the pitching rate angle results in pitching angle but it is not practically applicable because the time integration of measurement data may result in an accumulation of error and noise. Instead of the time integration, a Luenberger observer is applied to estimate the pitching angle based on the pitching rate angle measurement. Simulations of the TWR stabilization using the designed controller are presented through two scenarios: 1) both required state feedback are assumed to be available, and 2) both required state feedback are obtained through estimation using Luenberger observer. The first scenario is representing an ideal condition, while the second scenario is representing a practical condition. Simulation results show that the TWR is stabilized for the both scenarios, where the control system performance in the second scenario is slightly less than the first scenario but still acceptable.