Body-fixed orbit-attitude hovering control over an asteroid using non-canonical Hamiltonian structure

The orbit-attitude hovering means that both the position and attitude of the spacecraft are kept to be stationary in the asteroid body-fixed frame. The orbit-attitude hovering is discussed in the framework of the gravitationally coupled orbit-attitude dynamics, also called the full dynamics, in which the spacecraft is modeled as a rigid body to take into account the gravitational orbit-attitude coupling naturally. A feedback hovering control law is proposed by using the non-canonical Hamiltonian structure of the problem, which is consisted of two potential shapings and one energy dissipation. The first potential shaping is to create an artificial equilibrium at the desired hovering position-attitude. Then, the second potential shaping modifies the potential further so that the artificial equilibrium is a minimum of the modified Hamiltonian on the invariant manifold. Finally, the energy dissipation leads the motion to converge asymptotically to the minimum of the modified Hamiltonian, i.e., the artificial equilibrium for hovering. The feasibility of the hovering control law is verified through numerical simulations. The proposed hovering control law has a simple form and can be implemented by the spacecraft autonomously with little computation. This feature can be attributed to the utilization of the Hamiltonian structure and natural dynamical behaviors of the system in the control law design.