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

A robot asked to "place the cup near the red plate or the blue plate" 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's intent.