A Hölder-continuous Extended State Observer for Rigid Body Attitude Dynamics

Abstract

Estimating rigid body attitude dynamics in the presence of unknown or uncertain torques, has applications to unmanned aerial, ground, (under)water and space vehicles. This work provides a new approach to estimating the attitude states and unknown, time-varying, (disturbance) torque vector acting on a rigid body, using an extended state observer. The observer design uses the concept of geometric homogeneity to obtain its stability. A Lyapunov stability analysis is carried out to prove its stability properties. The resulting observer for the attitude states and disturbance torque is smooth, Hölder-continuous, and exhibits almost globally finite-time stable (AG-FTS) with a constant disturbance torque in body frame. These properties are theoretically shown, and a numerical simulation is carried out to demonstrate how the observer works in a realistic attitude estimation scenario.