Slosh-augmented tube MPC for spacecraft proximity operations: Coupled dynamics and partial robustness guarantees

Kurzfassung

Fuel slosh in partially filled tanks perturbs the translational dynamics of a spacecraft executing close-range proximity manoeuvres. Standard model predictive control treats slosh as an unmodelled disturbance, discarding the structure encoded in the classical equivalent-mechanical model. This paper embeds a three-axis linearised mass–spring-damper slosh model into the prediction dynamics of a tube-based controller, producing a twelve-state augmented system whose off-diagonal coupling block maps slosh displacement and velocity into body-velocity perturbations through the reaction force, a coupling absent from the block-diagonal formulations in the existing literature. Because the slosh modes complete several oscillation cycles within one sampling interval, element-wise error bounds on the slosh states diverge under box propagation; constraint tightening is therefore applied only to the rigid-body states, the slosh feedthrough is bounded through an energy-dissipation argument on the slosh tracking error, and robust constraint satisfaction is proved for the rigid-body sub-state under bounded additive disturbances. A structured controller ablation over paired Monte Carlo trials on an eccentric Mars orbit isolates the contributions of augmented-state prediction, coupled dynamics, and slosh cost weighting: coupled prediction, not cost weighting, drives the improvement. In simulation the coupled tube controller holds the approach corridor in the large majority of trials, whereas nominal predictive control fails the strict zero-violation criterion in every trial, and a failure-mode decomposition shows most of those failures are tracking-accurate, so the gain from coupling is safety certification rather than tracking precision. The added solve time remains a small fraction of the sampling period.