  We present a fast trajectory optimization algorithm for the soft capture of
uncooperative tumbling space objects. Our algorithm generates safe, dynamically
feasible, and minimum-fuel trajectories for a six-degree-of-freedom servicing
spacecraft to achieve soft capture (near-zero relative velocity at contact)
between predefined locations on the servicer spacecraft and target body. We
solve a convex problem by enforcing a convex relaxation of the field-of-view
constraint, followed by a sequential convex program correcting the trajectory
for collision avoidance. The optimization problems can be solved with a
standard second-order cone programming solver, making the algorithm both fast
and practical for implementation in flight software. We demonstrate the
performance and robustness of our algorithm in simulation over a range of
object tumble rates up to 10{\deg}/s.
