Zero-Shot Signal Temporal Logic Planning with Disjunctive Branch Selection in Dynamic Semantic Maps

Abstract: Signal Temporal Logic (STL) offers verifiable task specifications and is crucial for safety-critical control. Yet STL planning remains challenging: exact optimization-based methods are often too slow, and learning-based methods struggle to generalize across varying environments. We propose a zero-shot STL planning solver for variable-map environments that generates feasible trajectories without retraining. By integrating a map-conditioned Transformer architecture with a lightweight heuristic, our approach effectively handles complex disjunctive (OR) subformulas. Furthermore, we leverage Transitive Reinforcement Learning (TRL) to ensure consistent temporal grounding and logical coherence across decomposed sub-tasks. Experiments on dynamic semantic maps with diverse obstacle layouts demonstrate consistent gains, highlighting the framework's superior zero-shot generalization to changing environments and broad STL coverage.

• The paper introduces a zero-shot planning framework that integrates heuristic disjunctive branch selection to efficiently prune STL disjunctions in dynamic semantic maps.
• The methodology leverages a map-conditioned Transformer and TRL-based time predictor to generate robust, collision-free trajectories under varying dynamics.
• Experimental analysis demonstrates improved success rates, maintained STL robustness margins, and reduced planning time, especially in larger maze scenarios.

Zero-Shot STL Planning with Disjunctive Branch Selection in Dynamic Semantic Maps

Introduction and Motivation

The paper "Zero-Shot Signal Temporal Logic Planning with Disjunctive Branch Selection in Dynamic Semantic Maps" (2605.01222) addresses the synthesis of safe, temporally coherent trajectories under Signal Temporal Logic (STL) specifications in environments where map geometry and obstacle layout vary. Classical approaches to STL-constrained planning, particularly optimization-based and gradient-based methods, are hampered by scalability, nonconvexity, and sensitivity to environmental variability. Learning-based approaches exhibit poor generalization, particularly for complex, compositional STL formulas and changing map conditions. These limitations motivate a zero-shot planning framework capable of handling variable-map environments and disjunctive STL specifications (branching induced by logical ORs) without retraining.

Technical Contributions

The solution leverages a decompose-then-synthesize paradigm, integrating map conditioning and structured decomposition:

• Heuristic Disjunction Handling: The principal novelty lies in a lightweight heuristic for branch selection in STL formulas converted to disjunctive normal form (DNF). Candidate branches are ranked using temporal-operator complexity, map reachability, and temporal slack. This structured pruning decisively improves feasibility and success rate under dynamic conditions.
• Map-Conditioned Transformer Trajectory Generator: The main synthesis module is an autoregressive Transformer that embeds both the maze map and STL task decomposition, enabling robust, collision-free trajectory generation that generalizes to unseen environments.
• Transitive Reinforcement Learning (TRL) for Temporal Grounding: The approach trains a time predictor with TRL, enforcing consistent pairwise ordering of predicted step lengths among sub-tasks. This enhances temporal allocation between STL subgoals, bridging symbolic logic and learned trajectory synthesis.

Each component is modular: branch selection precedes temporal grounding, which is then followed by trajectory generation, all conditioned on the current map. The pipeline is agnostic to execution dynamics, relying solely on operational trajectory datasets at training.

Problem Formulation

The planning instance is specified as $(M, x_0, \varphi)$, with $M$ a binary maze, $x_0$ the initial state, and $\varphi$ an STL formula possibly containing disjunctions. Trajectories must satisfy three requirements:

1. STL Robust Satisfaction: Positive robustness margin.
2. Collision Avoidance: Trajectory avoids mapped obstacles.
3. Execution Feasibility: Trajectory adheres to unknown dynamics, validated under double-integrator and unicycle systems.

Zero-shot generalization mandates no retraining or environment-specific fine-tuning at inference, with robustness to both map variability and the intrinsic branching structure of STL.

Solving Procedure

Disjunctive Branch Selection

STL tasks are rewritten into DNF. Candidate branches are evaluated with:

• Temporal-Operator Complexity: Weighted sum of F, G, U subformulas, favoring simpler decompositions.
• Map Reachability: Branches referencing easier-to-access regions in the maze receive lower penalty.
• Temporal Slack: Greater flexibility in time intervals is rewarded, improving practical feasibility.

The combined heuristic enables efficient, structure-aware pruning, optimizing for both goal attainability and operational ease.

Time Predictor with TRL

A CNN encoder and MLP regress geometric and local map features to produce step estimates between sub-task waypoints. Training integrates TRL, imposing pairwise order consistency over predicted step lengths, which improves calibration and temporal grounding for trajectory synthesis.

Transformer-based Trajectory Generation

The Transformer model ingests context tokens (map information, region descriptors, time intervals) and trajectory prefixes, decoding feasible trajectories autoregressively. Teacher forcing with scheduled sampling mitigates exposure bias, enhancing rollout robustness in variable-map settings. No explicit dynamics information is given at inference; trajectories are executed and tested under different motion models.

Experimental Analysis

Evaluation spans three maze sizes (5×5, 7×7, 9×9) and two dynamics (double-integrator and unicycle). Metrics encompass success rate, robustness margin, and planning time. The proposed method achieves:

• Consistently Higher Success Rates: Gains magnify in larger, more complex maps. The structure-aware branch selection substantially outperforms random or unguided selection.
• Comparable or Improved Robustness Margins: Increased success does not degrade STL satisfaction margins.
• Reduced Planning Time with Heuristic Pruning: Computational overhead due to disjunctive branching is lowered by structured pruning, especially as map scale increases.
• Dynamics-Agnostic Behavior: Trajectory generator generalizes across motion models, validating the learned prior’s geometry and task-level structure.

Qualitative rollouts corroborate formal metrics: trajectory plans consistently satisfy STL constraints, remain feasible, and adaptively select map-accessible branches in the presence of disjunctions.

Implications and Future Directions

This framework advances STL planning in settings requiring real-time adaptability to dynamic environments, moving beyond the rigidity of fixed-map grounding or retraining-heavy methods. The decoupling of logical, temporal, and geometric reasoning—with Transformer-based synthesis—represents a scalable approach for mission-critical robotics and autonomous systems:

• Practical Impact: Enables deployment in heterogeneous environments, including those with semantic variability, without re-engineering control pipelines for each scenario.
• Theoretical Significance: Shows that symbolic STL reasoning can be efficiently combined with learning-based trajectory generation, preserving both robustness and generalization.
• Future Developments: Extensions may include continuous STL predicates, multi-agent planning, hierarchical semantic maps, and online dynamics adaptation. Further integration of iterative learning with symbolic reasoning could enhance specification coverage and sample efficiency.

Conclusion

The paper establishes a versatile, zero-shot STL planning pipeline for variable-map environments, addressing the challenge of compositional logical branching and dynamic obstacle layouts. Through heuristic disjunctive selection, map-conditioned trajectory generation, and transitive temporal grounding, it achieves robust, feasible planning with improved efficiency and generalization. This modular paradigm lays a foundation for further advances in adaptive, logic-constrained planning in real-world systems.