In the large hybrid observer design for rigid body with quaternion measurements

In this paper we present a hybrid observer for rigid body angular velocity estimation, which equilibrium point in closed loop with the system is asymptotically stable in the large¹, i.e. we prove that the error states are stable and asymptotically converging towards the origin for all initial rotations and angular velocities. Stability results for quaternion based observers have until now typically only been valid for a bounded set of initial conditions. To overcome this issue our observer design is based on dynamic scaling and switching logic. Simulation results for the proposed observer together with a PD-based state feedback control law are presented to corroborate our theoretical findings.