Stabilization of coupled orbit–attitude dynamics about an asteroid utilizing Hamiltonian structure

The gravitationally coupled orbit–attitude dynamics, also called the full dynamics, in which the spacecraft is modeled as a rigid body, is a high-precision model for the motion in the close proximity of an asteroid. A feedback control law is proposed to stabilize relative equilibria of the coupled orbit–attitude motion in a uniformly rotating second degree and order gravity field by utilizing the Hamiltonian structure. The feedback control law is consisted of potential shaping and energy dissipation. The potential shaping makes the relative equilibrium a minimum of the modified Hamiltonian by modifying the potential artificially. With the energy-Casimir method, it is theoretically proved that an unstable relative equilibrium can always be stabilized in the Lyapunov sense by the potential shaping with sufficiently large feedback gains. Then, the energy dissipation leads the motion to converge to the relative equilibrium. The proposed stabilization control law has a simple form and is easy to implement autonomously, which can be attributed to the utilization of natural dynamical behaviors in the controller design.