Nonlinear Optimal Stabilising Control of a Two-wheel Robot

The stabilisation of a two-wheel robot is a classical benchmarking problem for determining the effectiveness of a control technique. In this paper, a nonlinear optimal control technique is applied to a two-wheel robot which demonstrates excellent control performance comparing against the LQR technique. Simulation results demonstrated that this nonlinear optimal controller can achieve accurate tracking of wheel angular displacement and effective stabilisation of the robot from a very large range of initial pitch angles. Practical factors such as maximum motor voltages are considered and analysed using an extended state-space model to embed such control saturations. Significantly, the two-wheel robot can be balanced from a body pitch angle of up to 88.0° with a maximum motor voltage of 48 V using the proposed nonlinear optimal control technique, larger than any other methods achieved in the literature. Controllability studies are also performed throughout this research to facilitate understanding and visualisation of the substantial stabilisation ranges with and without control saturations.