Relative reachable domain for spacecraft with initial state uncertainties

The reachable domain is a geometric description of the maneuverability of a spacecraft under control and/or measurement uncertainties. In this paper, the reachable domain conceptis introduced into the field of satellite relative motion and termed the relative reachable domain. The relative reachable domain geometrically represents the effects of the initial control and/or measurement uncertainties on relative motion. A general method is developed to find the envelope of the coplanar relative reachable domain for arbitrary reference orbits, by evaluating the extremal values of the potentially accessible radius with respect to a given reference position. The relative reachable domain formulations are analytically expressed for circular reference orbits. It is shown that the relative reachable domain is a convenient tool for analyzing a variety of cluster flight mission problems. Several practical applications are suggested, including determining the upper bound on the separation distances among satellites. It is also shown that the relative reachable domain can be used for assessing the collision risk and that, in some situations, the relative reachable domain is more reliable than existing collision assessment methods. Numerical examples demonstrate the usefulness of the proposed method for finding the relative reachable domain and show that the analytical calculation of the relative reachable domain is accurate even in the case of noncoplanar perturbed motion.