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As convex programming offers deterministic convergence properties, this algorithm is suitable for onboard implementation and real-time use. A set of hardware-in-the-loop experiments substantiates this claim. To cast the guidance problem as a collection of convex programming problems, the capture maneuver is divided into two simultaneously occurring sub-maneuvers: a system-wide translation and an internal re-configuration. These two sub-maneuvers are optimized in two consecutive steps. A sequential convex programming procedure, overcoming the presence of non-convex constraints and nonlinear dynamics, is used on both optimization steps. A proof of convergence is offered for the system-wide translation, while a set of structured heuristics\u2014trust regions\u2014is used for the optimization of the internal re-configuration sub-maneuver. 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