  Construction of the precise shape of an asteroid is critical for spacecraft
operations as the gravitational potential is determined by spatial mass
distribution. The typical approach to shape determination requires a prolonged
mapping phase of the mission over which extensive measurements are collected
and transmitted for Earth-based processing. This paper presents a set of
approaches to explore an unknown asteroid with onboard calculations, and to
land on its surface area selected in an optimal fashion. The main motivation is
to avoid the extended period of mapping or preliminary ground observations that
are commonly required in spacecraft missions around asteroids. First, range
measurements from the spacecraft to the surface are used to incrementally
correct an initial shape estimate according to the Bayesian framework. Then, an
optimal guidance scheme is proposed to control the vantage point of the range
sensor to construct a complete 3D model of the asteroid shape. This shape model
is then used in a nonlinear controller to track a desired trajectory about the
asteroid. Finally, a multi resolution approach is presented to construct a
higher fidelity shape representation in a specified location while avoiding the
inherent burdens of a uniformly high resolution mesh. This approach enables for
an accurate shape determination around a potential landing site. We demonstrate
this approach using several radar shape models of asteroids and provide a full
dynamical simulation about asteroid 4769 Castalia.
