Controllability Analysis of Spacecraft with Only Attitude Actuation Near Small Solar System Bodies

Abstract

Abstract: This paper investigates the nonlinear controllability of the translational and rotational motion of an under actuated spacecraft near small Solar System bodies (asteroids and comets) using attitude actuation only The coupled dynamics of the spacecraft and small body is analyzed in the framework of the full two body problem, with the coupling provided by their mutual gravity Due to the symmetry in their mutual gravity the problem of analyzing the dynamics of the spacecraft is obtained by reducing it to that of a single body (the spacecraft) under the gravitational interaction provided by the spacecraft-small body pair. It has been previously shown that the rotational (attitude) dynamics of the spacecraft is strongly coupled with its translational (orbital) dynamics in this weak-gravity environment. For spacecraft missions to small bodies, this coupling can be used to obtain controlled trajectories within a bounded neighborhood of the small body using only attitude control, as the analysis here shows. Prior to designing guidance and control schemes for such spacecraft missions, it is important to show the controllability of the spacecraft dynamics on the 12-dimensional state space, i.e., the tangent bundle TSE(3), with only attitude control. Sufficient conditions for controllability are shown using the Lie Algebra Rank condition (LARC), and the weakly positively Poisson stable (WPPS) property of the drift vector field under certain initial conditions.