  This paper presents a convex approach to the optimization of a cooperative
rendezvous, that is, the problem of two distant spacecraft that simultaneously
operate to get closer. Convex programming guarantees convergence towards the
optimal solution in a limited, short, time by using highly efficient numerical
algorithms. A combination of lossless and successive convexification techniques
is adopted to handle the nonconvexities of the original problem. Specifically,
a convenient change of variables and a constraint relaxation are performed,
while a successive linearization of the equations of motion is employed to
handle the nonlinear dynamics. A filtering technique concerning the recursive
update of the reference solution is proposed in order to enhance the algorithm
robustness. Numerical results are presented and compared with those provided by
an indirect method.
