Feasibility Restoration under Conflicting STL Specifications with Pareto-Optimal Refinement

2026-03-06

AI Summary

In real-world scenarios, Signal Temporal Logic (STL) specifications often become unsatisfiable due to conflicts among safety rules, traffic regulations, and task objectives, causing conventional STL-based Model Predictive Control (MPC) to fall into overly conservative deadlock. This work proposes a unified two-stage framework: first restoring specification feasibility through minimal relaxation, then formulating the problem as a value-aware multi-objective optimization, which is solved via the ε-constraint method to approximate the Pareto front and enable trade-off analysis and counterfactual reasoning. By uniquely integrating feasibility recovery with Pareto-optimal refinement, the approach effectively prevents controller deadlock in autonomous driving scenarios, yielding interpretable, deadlock-free decisions that balance multiple objectives under safety-critical conditions.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Signal Temporal Logic (STL) is expressive formal language that specifies spatio-temporal requirements in robotics. Its quantitative robustness semantics can be easily integrated with optimization-based control frameworks. However, STL specifications may become conflicting in real-world applications, where safety rules, traffic regulations, and task objectives can be cannot be satisfied together. In these situations, traditional STL-constrained Model Predictive Control (MPC) becomes infeasible and default to conservative behaviors such as freezing, which can largely increase risks in safety-critical scenarios. In this paper, we proposes a unified two-stage framework that first restores feasibility via minimal relaxation, then refine the feasible solution by formulating it as a value-aware multi-objective optimization problem. Using $\varepsilon$-constraint method, we approximate the Pareto front of the multi-objective optimization, which allows analysis of tradeoffs among competing objectives and counterfactual analysis of alternative actions. We demonstrate that the proposed approach avoids deadlock under conflicting STL specifications and enables interpretable decision-making in safety-critical applications by conducting a case study in autonomous driving.

Problem

• Signal Temporal Logic
• conflicting specifications
• feasibility restoration
• safety-critical systems
• Model Predictive Control

Innovation

• Signal Temporal Logic
• Feasibility Restoration
• Pareto-Optimal Refinement
• Multi-objective Optimization
• Model Predictive Control