Analysis and design of second-order sliding-mode algorithms for quadrotor roll and pitch estimation

The problem addressed in this paper is that of quadrotor roll and pitch estimation without any assumption about the knowledge of perturbation bounds when Inertial Measurement Units (IMU) data or position measurements are available. A Smooth Sliding Mode (SSM) algorithm is first designed to provide reliable estimation under a smooth disturbance assumption. This assumption is next relaxed with the second proposed Adaptive Sliding Mode (ASM) algorithm that deals with disturbances of unknown bounds. In addition, the analysis of the observers are extended to the case where measurements are corrupted by bias and noise. The gains of the proposed algorithms were deduced from the Lyapunov function. Furthermore, some useful guidelines are provided for the selection of the observer turning parameters. The performance of these two approaches is evaluated using a nonlinear simulation model and considering either accelerometer or position measurements. The simulation results demonstrate the benefits of the proposed solutions.