Making Task Abstractions Executable: Control-Aware Layout Repair for a Fixed Controller

Natural-language manipulation instructions specify qualitative relations, whereas continuous controllers require state-evaluable task quantities, differentials, and completion conditions. Because a qualitative relation generally leaves part of the relative configuration unspecified, expanding it into a complete pose can introduce unintended constraints. We present a typed semantic-to-geometric interface in which language specifies entities, relations, and phases, while each relation indexes a registered specification of its task-relevant distinctions and preserved freedoms. A robot-side compiler grounds these specifications, constructs relation-specific task maps and consistent differentials using conformal geometric algebra, and composes the resulting policies through RMPflow. To evaluate the division of responsibility between the language model and the compiler, we compared a Semantic Topology interface with one that additionally requires relation-specific geometric specifications over 60 instructions. Both produced correct shared semantic content in 41/60 cases, but critical errors under their respective interface requirements occurred in 19/60 and 58/60 cases. Across 64 grounded evaluations spanning eight geometric relation forms, the task maps preserved registered null directions and responded to relation-relevant perturbations; analytic directional derivatives agreed with finite differences, and Jacobian ranks matched the registered dimensions. In three closed-loop ablations using a simulated Franka Emika Panda in MuJoCo, fixing a relation-preserved coordinate increased median terminal progress error by 20.24--71.00~mm while the retained relation errors remained within their evaluation bounds. These results support compiling relation-visible geometry and preserved freedom together into composable continuous objectives.

Existing indoor layout generators produce globally plausible layouts yet may retain local violations such as collisions, out-of-bounds placements, obstructed openings, and blocked circulation. Most prior work focuses on full-scene synthesis or scene-level optimization, with limited support for identifying responsible objects and locally repairing affected regions. We present Roomer, a reflective repair framework that casts these violations as sparse, object-grounded repair problems. Roomer encodes layouts as RoState'' and uses RoReview'' to bind measured violations to implicated objects. A geometry-conditioned vision-language model planner proposes a structured local edit, while a deterministic solver validates it and generates a finite set of candidate edits when needed. Each candidate is committed only if full-scene verification confirms that it resolves the target violation without new hard violations or broken protected constraints. We train the planner on Roomer-CC, a controlled-corruption dataset that pairs faulty layouts with object-grounded violation evidence and known-feasible inverse StatePatches. Since existing benchmarks rarely assess whether physically valid layouts are usable, we introduce Roomer-Eval to assess distributional quality, physical validity, and practical usability. Experiments show that Roomer repairs residual violations while preserving valid regions, improves physical validity and usability, and transfers across external generators.

In this study, we propose a layout-independent control allocator capable of zero-shot deployment across diverse actuator configurations. The proposed method utilizes a learning pipeline that integrates a Graph Neural Network (GNN) and a Transformer to represent the robot's geometric layout as a graph, along with a Mixture Density Network (MDN) to predict multi-modal control command distributions. Furthermore, by incorporating a differentiable physics surrogate model, we achieve command refinement during inference to minimize target wrench tracking error and energy consumption. A single generalized model using randomly generated actuator layout data demonstrated high trajectory tracking performance on different actuator layout robots outside the training distribution. Additionally, in real-world pool experiments, our approach achieved performance nearly equivalent to conventional controllers designed to specific layouts.