Backstepping-Based Inverse Optimal Attitude Control of Quadrotor

Input saturation must be taken into account for applying rapid reorientation in the large angle manoeuvre of a quadrotor. In this paper, a backstepping-based inverse optimal attitude controller (BIOAC) is derived which has the property of a maximum convergence rate in the sense of a control Lyapunov function (CLF) under input torque limitation. In the controller, a backstepping technique is used for handling the complexity introducing by the unit quaternion representation of the attitude of a quadrotor with four parameters. Moreover, the inverse optimal approach is employed to circumvent the difficulty of solving the Hamilton-Jacobi-Bellman (HJB) equation. The performance of BIOAC is compared with a PD controller in which the input torque limitation is not considered under the same unit quaternion representation using numerical simulation while the results show that BIOAC gains faster convergence with less control effort. Next, BIOAC is realized on a test bed and the effectiveness of the control law is verified by experimental studies.