Controllability Study of Two-Wheel Robot for Nonlinear Optimal Control and Implementation

This paper presents the benefits of controllability study, used to facilitate the implementation of a nonlinear optimal controller. The controllability technique can be applied to investigate the controllable ranges of different state-space models from the same physical system. Once the controllability of each mathematical model is established, controllable parts from different models are selected to build a new joint model before implementing the nonlinear freezing optimal control and extended Kalman filter. When applied to a two-wheel LEGO EV3 robot, the novel mixing model demonstrates excellent stabilising control results compared against both previous models by: 1) producing smoother transient behaviour with less oscillations and 2) demonstrating a broader initial pitch angle range for stabilisation using a nonlinear optimal controller.