  A deep-space exploration mission with low-thrust propulsion to rendezvous
with multiple asteroids is investigated. Indirect methods, based on the optimal
control theory, are implemented to optimize the fuel consumption. The
application of indirect methods for optimizing low-thrust trajectories between
two asteroids is briefly given. An effective method is proposed to provide
initial guesses for transfers between close near-circular near-coplanar orbits.
The conditions for optimality of a multi-asteroid rendezvous mission are
determined. The intuitive method of splitting the trajectories into several
legs that are solved sequentially is applied first. Then the results are
patched together by a scaling method to provide a tentative guess for
optimizing the whole trajectory. Numerical examples of optimizing three probe
exploration sequences that contain a dozen asteroids each demonstrate the
validity and efficiency of these methods.
