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Specification-Aware Distribution Shaping for Robotics Foundation Models

Sadık Bera Yüksel, Derya Aksaray

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.

Specification-Aware Distribution Shaping for Robotics Foundation Models

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.
Paper Structure (12 sections, 1 theorem, 26 equations, 3 figures, 2 tables)

This paper contains 12 sections, 1 theorem, 26 equations, 3 figures, 2 tables.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARIES: Signal Temporal Logic
  3. PROBLEM STATEMENT
  4. PROPOSED SOLUTION
  5. STL Policy Synthesis
  6. Specification Evaluation via $J_{\phi}$
  7. Action Distribution Optimization Under STL Constraints
  8. SIMULATION RESULTS
  9. Implementation Details
  10. Case 1: Time-Windowed Charger Reachability
  11. Case 2: Sequential Goal Visits with Safety Constraint
  12. CONCLUSION

Key Result

Proposition 1

Assume that (i) the true system dynamics satisfy $x_{t+1}=f(x_t,a_t)$ (i.e., no model mismatch between the forward-propagation model and the physical system), and (ii) the STL specification $\phi$ is satisfiable from the initial state $x_0$. If actions are sampled according to Alg. alg:main, the res

Figures (3)

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

Theorems & Definitions (4)

  • Definition 1: Signal Temporal Logic
  • Definition 2: Specification Evaluation Function
  • Proposition 1
  • proof