An Almost Global Attitude Controller for Rigid Bodies Subject to Unknown Disturbances and Sensor Bias

This paper studies the attitude trajectory tracking problem of rigid bodies subject to unknown constant disturbances and angular velocity measurements corrupted by constant bias. We employ the exponential coordinates of rotation and the angular velocity to describe the state of the rigid body. Exploiting the structural properties of the attitude kinematics and dynamics of the rigid body, we propose a bias observer that compensates for biased measurements and a nonlinear control law with integral action that achieves attitude tracking for almost all initial conditions and compensates for constant disturbances. We design the control law based on a Barrier Lyapunov function to circumvent the exponential coordinates' singularity. Finally, numerical simulations and experimental tests illustrate the efficacy of our control law and bias observer.