Horizon-Dependent Tube MPC for Elliptical-Orbit Rendezvous Under Mass Uncertainty

Abstract

A spacecraft closing on a target from three hundred kilometres to contact flies one guidance law across five orders of magnitude of range, and a controller that is provably safe at close range can lose that guarantee completely at long range while continuing to fly as though nothing were wrong. This paper derives the range at which the guarantee lapses and uses it as a design rule. The bound compares the prediction model's own linearisation error against the disturbance set the controller was built to reject, and needs only the sampling period, the orbit and that disturbance bound, so it can be evaluated before any simulation. On a Mars Sample Return approach it disqualifies the homing phase, where most of the propellant is spent, and clears the other two. Re-posing the disqualified phase in relative orbital elements restores the guarantee; re-posing a phase the rule already clears, in a frame two orders of magnitude more accurate, changes propellant by under a tenth of one per cent, and it is that second prediction that makes the rule falsifiable rather than descriptive. The constraint tightening also ties the prediction horizon to feasibility, so the horizon search limit becomes a mission parameter rather than a solver setting. Against a reimplementation of a published benchmark that reproduces its propellant to within one per cent, over five hundred dispersed Monte Carlo transfers per case on matched seeds, the controller saves 29% of the propellant on a circular target orbit and 40% on an eccentric one, docking inside the 0.20 m capture requirement on essentially every draw at a median miss near 5 cm. Two results run the other way: the saving is bought with time of flight and computation, and it comes from what the guarantee demanded of the terminal condition rather than from better disturbance rejection. Recursive feasibility and asymptotic stability are not claimed.