  In this paper we present a fast method based on successive convexification
for generating fuel-optimized spacecraft rendezvous trajectories in the
presence of mixed-integer constraints. A recently developed paradigm of
state-triggered constraints allows to efficiently embed a subset of discrete
decision constraints into the continuous optimization framework of successive
convexification. As a result, we are able to solve difficult trajectory
optimization problems at interactive speeds, as opposed to a mixed-integer
programming approach that would require significantly more solution time and
computing power. Our method is applied to the real problem of transposition and
docking of the Apollo command and service module with the lunar module. We
demonstrate that, within seconds, we are able to obtain trajectories that are
up to 90 percent more fuel efficient (saving up to 45 kg of fuel) than
non-optimization based Apollo-era design targets. Our trajectories take
explicit account of minimum thrust pulse width and plume impingement
constraints. Both of these constraints are naturally mixed-integer, but we
handle them as state-triggered constraints. In its current state, our algorithm
will serve as a useful off-line design tool for rapid trajectory trade studies.
