Almost global asymptotic tracking control for spacecraft body-fixed hovering over an asteroid

Almost global asymptotic tracking control for autonomous body-fixed hovering of a rigid spacecraft over an asteroid is proposed in the framework of geometric mechanics. The configuration space for the spacecraft is the Lie group SE ( 3 ) , which is the set of positions and orientations of the rigid spacecraft in three-dimensional Euclidean space. The relative motion with respect to the spacecraft is assumed to be available through the spacecraft on-board navigation. The spacecraft tracks a desired relative configuration with respect to an asteroid in an autonomous manner. The relative configuration between the spacecraft and the asteroid is described in terms of exponential coordinates on the Lie group of rigid body motions. A continuous-time feedback tracking control using these exponential coordinates and the relative velocities is presented to perform coupled translational and rotational maneuver over an asteroid in the presence of control force saturation. A Lyapunov analysis guarantees that the spacecraft asymptotically converges to the desired trajectory. Numerical simulation results demonstrate the asymptotic tracking control achieve autonomous body-fixed hovering over a selected asteroid.