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Orbit-attitude hovering of a spacecraft at the natural relative equilibria inthe body-fixed frame of a uniformly rotating asteroid is discussed in theframework of the full spacecraft dynamics, in which the spacecraft is modeledas a rigid body with the gravitational orbit-attitude coupling. In thishovering model, both the position and attitude of the spacecraft are kept to bestationary in the asteroid body-fixed frame. A Hamiltonian structure-basedfeedback control law is proposed to stabilize the relative equilibria of thefull dynamics to achieve the orbit-attitude hovering. The control law isconsisted of two parts: potential shaping and energy dissipation. The potentialshaping is to make the relative equilibrium a minimum of the modifiedHamiltonian on the invariant manifold by modifying the potential artificially.With the energy-Casimir method, it is shown that the unstable relativeequilibrium can always be stabilized in the Lyapunov sense by the potentialshaping with sufficiently large feedback gains. Then the energy dissipationleads the motion to converge asymptotically to the minimum of the modifiedHamiltonian on the invariant manifold, i.e., the relative equilibrium. Thefeasibility of the proposed stabilization control law is validated throughnumerical simulations in the case of a spacecraft orbiting around a smallasteroid. The main advantage of the proposed hovering control law is that it isvery simple and is easy to implement autonomously by the spacecraft with littlecomputation. This advantage is attributed to the utilization of dynamicalbehaviors of the system in the control design.

Body-fixed orbit-attitude hovering at equilibria near an asteroid using non-canonical Hamiltonian structure