CompCPZ: Preserving Multi-Modal Intent in Language-Guided Robot Manipulation

Abstract

A robot asked to &#34;place the cup near the red plate or the blue plate&#34; may reach the centroid between them and appear geometrically successful, while satisfying neither disjunct of the instruction. This silent semantic failure exposes a structural limitation of language-conditioned robot policies: representations that collapse a disjunctive instruction into a single connected set cannot preserve all feasible modes, and planners that commit to one action degrade under run-time mode uncertainty. We address this limitation with CompCPZ, a sound algebraic layer that language-conditioned learning systems wrap to recover multi-modal disjunctive representation, recursively composing per-primitive constrained polynomial zonotope enclosures along the language parse tree with distribution-free conformal coverage and sub-millisecond runtime. On a closed-loop ManiSkill3 tabletop-manipulation benchmark, CompCPZ outperforms convex set baselines, multi-peak decoders, and a zero-shot vision-language-action model (1,900/1,918 paired wins, p << 10^(-30)); the same compiler also transfers without retuning to planar real-robot trials on a Unitree Go2 quadruped under motion capture. These results suggest that compositional language grounding should be evaluated not only by reaching a decoded target, but by whether the represented feasibility set preserves the connected-component structure of the user&#39;s intent.