Outcome-Conditioned End-Effector Geometry Across Vision-Language-Action Policies

Abstract

Vision-language-action (VLA) policies solve the same manipulation task through different action interfaces, but task success alone does not establish whether their physical executions agree. We study cross-policy end-effector geometry in 15,000 closed-loop LIBERO rollouts from four policies. The primary clean-condition analysis forms 3,600 configuration-matched, and therefore dependent, policy pairs. Both-success pairs have a median normalized dynamic time warping distance of 0.0120 m versus 0.0380 m when exactly one policy succeeds. This ordering holds in every task, every policy pair, and nine sampling and band-limited representations; however, the ratio varies severalfold across representations, so we report the direction rather than a fixed multiple. Both-failure pairs are more separated again but rest on thin, uneven support, so we report them as exploratory. Within successful executions, partner replacements separate more across tasks than across initial states. A matched baseline still reveals measurable, heterogeneous residual policy differences, so a low cross-policy distance does not imply interchangeability. Successful executions sit about as far from same-task demonstrations as those demonstrations sit from each other, compatible with task-associated geometry without separating training-data overlap from task constraints. A common 72-action window preserves the ordering but reduces its magnitude; endpoint and duration adjustment likewise leaves a positive mixed-outcome coefficient relative to both-success pairs, though its magnitude is specification-dependent. Under composite visual stress, policy rankings and pair composition change together.