Specification-Aware Distribution Shaping for Robotics Foundation Models

Natural-language robot instructions often specify more than a coarse task goal: they may impose spatial, temporal, and logical requirements that must remain satisfied throughout execution. We present STeP, a specification-based agentic framework that uses Signal Temporal Logic (STL) as an explicit interface between high-level language reasoning and low-level robot execution. Rather than encoding such requirements implicitly in a learned policy, STeP formalizes them as task specifications that can be decomposed across multi-stage manipulation, enforced during execution, monitored online, and used as structured feedback for replanning. We evaluate STeP on standard LIBERO and LIBERO-PRO, and introduce LIBERO-Constrained, a new benchmark for manipulation tasks with spatial, temporal, and logical requirements, together with real-world tabletop experiments. On LIBERO-PRO, STeP retains 54%-89% success across five of six evaluated perturbation settings, substantially outperforming VLA and code-as-policy baselines under distribution shift. On LIBERO-Constrained, STeP achieves 80% safe success across 49 task-constraint instances; on real-world tasks, it improves safe success over a specification-free model-based baseline across all four task categories, with gains of up to 45 percentage points. These results support explicit formal specifications as a practical interface between foundation-model reasoning and reliable robot execution.

Many robotic tasks are temporally extended and demand precise specifications of subgoals, constraints, and their temporal ordering. Yet human operators typically communicate such tasks in natural language, which is inherently ambiguous, underspecified, and context dependent. Translating human instructions into formal task specifications, such as Linear Temporal Logic (LTL), is therefore essential for verifiable and safe robotic execution. Existing LLM-based translators attempt to bridge this gap through open-ended reasoning or post-hoc constraint enforcement, but the former may violate domain constraints, whereas the latter can disrupt the reasoning needed for novel instructions. This paper proposes Self-Constrained Reasoning (SCR), a framework that mitigates this trade-off by internalizing structural knowledge into the model's decision-making process rather than imposing it as an external filter. By combining a structural constraint representation with a hierarchical decision-making formulation, SCR guides reasoning within a formally grounded space while preserving adaptability to unseen instructions. Experiments show that SCR improves both domain-constraint satisfaction and generalization, providing an effective and interpretable approach for translating human intent into verifiable specifications for robotic execution.

Executing Linear Temporal Logic (LTL) instructions with learned robot policies faces two practical challenges: demonstrations may cover individual behaviors without containing the temporal compositions requested at deployment, and semantic success predicates often provide little useful motor guidance through quantitative robustness. We address these challenges by separating behavior learning from temporal composition. From the same offline demonstrations, we train an unconditioned multimodal diffusion policy and a semantic predictor that estimates which semantic outcomes are likely to follow a proposed action sequence. These predictions provide a learned guidance signal without requiring hand-designed robustness measures for semantic task objectives. At deployment, an LTL automaton tracks instruction progress and scores the policy's proposed actions according to their predicted semantic outcomes. Neither learned component receives the specification during training, allowing demonstrated behaviors to be reused in longer, previously unseen temporal compositions without retraining. For additional runtime safety constraints with informative continuous margins, an optional robustness-based controller locally refines the selected actions. Experiments in a navigation environment, CALVIN manipulation, and on a real robot demonstrate reliable execution of complex temporal instructions and additional safety constraints, with substantial improvements over temporal-logic baselines.