Lexicographic Minimum-Violation Motion Planning using Signal Temporal Logic

TL;DR

This paper introduces a scalable, single-objective optimization approach for lexicographic minimum-violation motion planning in autonomous vehicles using Signal Temporal Logic, extending MPPI and introducing a new robustness measure.

Contribution

It transforms multi-objective lexicographic STL optimization into a single-objective problem and extends MPPI to efficiently solve it, with a novel predicate-robustness measure.

Findings

The method efficiently solves lexicographic STL optimization problems.

It provides an interpretable and scalable solution for motion planning.

The approach outperforms standard methods in computational efficiency.

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.