Spacecraft hovering control for body-fixed hovering over a uniformly rotating asteroid using geometric mechanics

A spacecraft hovering scheme over a uniformly rotating asteroid in the asteroid body-fixed frame using geometric mechanics is presented. 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 asteroid trajectory, in the form of natural attitude and translational (orbital) motion of a satellite, is assumed to be available through a spacecraft on-board navigation. The spacecraft tracks a desired relative configuration with respect to the 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 employed. A Lyapunov analysis guarantees that the spacecraft asymptotically converges to the desired trajectory. Numerical simulation results demonstrate the successful spacecraft hovering control in the asteroid body-fixed frame for a selected uniformly rotating asteroid.