A Sampled Common-Translation Latch for Nominal Double Integrators

Abstract

We study a sampled common-translation latch coupled to equal-gain nominal double integrators. The sampled branches follow the recovery callbacks in the Flying Cats version cited by the parent article: settled bodies are skipped, recomputation precedes a possible priority update, and the returning branch holds the translation while its timer advances. For a fixed finite cohort, convergent goals and vanishing disturbance integrals on fixed sampling cells, exact nominal flow and every sequence of holds or recomputations produce vanishing tracking error and velocity. The source-bound guard consequently stops recomputing after finitely many samples. The endpoint contains the actual frozen translation. We prove augmented translation equivariance, well-posedness, a last-recomputation error formula, and separate timer, impulse and bounded-residual statements. Complete-cohort information and a common clock are explicit resources. The result does not establish a rigid-body, airflow or floating-point realization.