Lexicographic Minimum-Violation Motion Planning using Signal Temporal Logic

2026-04-22

AI Summary

This work addresses the challenge in autonomous driving motion planning where multiple specification constraints—often conditionally conflicting—cannot be simultaneously satisfied and must instead be violated minimally according to a prescribed priority order. The authors reformulate the lexicographic multi-objective optimization problem as a single scalar objective and introduce an efficient solution method based on non-uniform quantization and shift-based encoding. They further design a predicate robustness metric that integrates spatiotemporal information. Built upon Signal Temporal Logic (STL) and Model Predictive Path Integral (MPPI) control, the proposed framework enables interpretable and scalable minimum-violation planning, preserving priority semantics while significantly improving computational efficiency.

Technology Category

• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Multiagent Systems: Multiagent Planning
• Search and Optimization: Learning to Search

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
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Motion planning for autonomous vehicles often requires satisfying multiple conditionally conflicting specifications. In situations where not all specifications can be met simultaneously, minimum-violation motion planning maintains system operation by minimizing violations of specifications in accordance with their priorities. Signal temporal logic (STL) provides a formal language for rigorously defining these specifications and enables the quantitative evaluation of their violations. However, a total ordering of specifications yields a lexicographic optimization problem, which is typically computationally expensive to solve using standard methods. We address this problem by transforming the multi-objective lexicographic optimization problem into a single-objective scalar optimization problem using non-uniform quantization and bit-shifting. Specifically, we extend a deterministic model predictive path integral (MPPI) solver to efficiently solve optimization problems without quadratic input cost. Additionally, a novel predicate-robustness measure that combines spatial and temporal violations is introduced. Our results show that the proposed method offers an interpretable and scalable solution for lexicographic STL minimum-violation motion planning within a single-objective solver framework.

Problem

• lexicographic optimization
• minimum-violation motion planning
• signal temporal logic
• autonomous vehicles
• specification prioritization

Innovation

• lexicographic optimization
• signal temporal logic
• minimum-violation planning
• non-uniform quantization
• predicate robustness