Closed-loop control for global coverage and equatorial hovering about an asteroid

The purpose of this work is to develop a simple control law to implement stable orbits about a small rotating celestial body to achieve global coverage as well as fixed-body hovering on the equatorial plane. The celestial body is assumed to be rotating about a principal axis, with constant rotational velocity along the largest moment of inertia. A simple three dimensional closed-loop guidance law function of position and velocity is defined and analyzed, enabling the determination of the guidance constants to assure convergence to any desired circular orbit about the irregular celestial body, controlling independently five orbital parameters: inclination, right ascension of the ascending node, orbital radius, orbital rate and equatorial longitude. Representative numerical results are presented for an Eros type asteroid.