Specification-Aware Distribution Shaping for Robotics Foundation Models

Sadık Bera Yüksel; Derya Aksaray

cs.ROMar 18, 2026

Specification-Aware Distribution Shaping for Robotics Foundation Models

Authors: Sadık Bera Yüksel, Derya Aksaray

Organizations: Department of Electrical and Computer Engineering at Northeastern University.

Abstract

Robotics foundation models have demonstrated strong capabilities in executing natural language instructions across diverse tasks and environments. However, they remain largely data-driven and lack formal guarantees on safety and satisfaction of time-dependent specifications during deployment. In practice, robots often need to comply with operational constraints involving rich spatio-temporal requirements such as time-bounded goal visits, sequential objectives, and persistent safety conditions. In this work, we propose a specification-aware action distribution optimization framework that enforces a broad class of Signal Temporal Logic (STL) constraints during execution of a pretrained robotics foundation model without modifying its parameters. At each decision step, the method computes a minimally modified action distribution that satisfies a hard STL feasibility constraint by reasoning over the remaining horizon using forward dynamics propagation. We validate the proposed framework in simulation using a state-of-the-art robotics foundation model across multiple environments and complex specifications.

Figures & tables

Panel of Figure 1 — Fig. 1 : A robot is instructed to “find a bowl” while ensuring that at least one charging station (green circles) is visited within designated time intervals. The trajectories illustrate [left] execution under a pretrained robotics foundation model policy (SPOC) and [right] the same model augmented with specification-aware action distribution shaping to enforce the spatio-temporal constraint.

$\phi$	$t^{*}$	$\ell$
$G_{[a,b]}\,\varphi$	$t^{*}=a$	$\displaystyle\frac{1}{t^{*}}\ln\!\left(\frac{\gamma_{0}-\gamma_{\infty}}{\rho_{\max}-\gamma_{\infty}}\right)$
$F_{[a,b]}\,\varphi$	$t^{*}\in[a,b]$	$\displaystyle\frac{1}{t^{*}}\ln\!\left(\frac{\gamma_{0}-\gamma_{\infty}}{\rho_{\max}-\gamma_{\infty}}\right)$
$F_{[a,c_{1}]}G_{[c_{2},b]}\varphi$	$t^{*}\in[a+c_{2},c_{1}+c_{2}]$	$\displaystyle\frac{1}{t^{*}}\ln\!\left(\frac{\gamma_{0}-\gamma_{\infty}}{\rho_{\max}-\gamma_{\infty}}\right)$

TABLE I : Selection of funnel parameters

\ell

and

t^{*}

[ 24 ] .

Panel of Figure 3 — Fig. 2 : Top-down view of an AI2-THOR house environment (left) and the corresponding 2D occupancy map abstraction used for training and forward propagation (right). In the occupancy map, black regions denote occupied space (walls and static obstacles), white regions represent free space, and the robot is depicted as a red circular footprint.

Case	STL (%)	Main (%)	STL (%)	Main (%)
	Unmodified SPOC		Proposed
Case 1 ( $\phi_{1}$ )	0	93.5	100	92.5
Case 2 ( $\phi_{2}$ )	0	99	100	82.5

TABLE II : Empirical success rates over 200 independent simulation runs.

Panel of Figure 5 — Fig. 3 : Trajectory comparison for Case 2: (left) execution under the unmodified SPOC policy and (right) execution under the proposed specification-aware framework.

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Robotic control studies how machines use sensing and computation to produce reliable movement and interaction in changing environments.

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STeP: Signal Temporal Logic for Precise Specifications for Action Generation with Vision Language Models

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Language-Conditioned Robot Control VLMs for Robotics Robustness of VLA Models

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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.

Abstract

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