Minimum-Violation Planning for Autonomous Systems: Theoretical and Practical Considerations

TL;DR

This paper presents a novel approach for optimal trajectory planning in autonomous systems that minimizes rule violations by using prioritized safety specifications and a new class of temporal logic formulas, with practical applications demonstrated in autonomous vehicles.

Contribution

Introduction of prioritized safety specifications with temporal logic, a new class of formulas called si-FLTL_GX, and an efficient sampling-based method with asymptotic optimality guarantees for minimum-violation planning.

Findings

Effective in autonomous vehicle overtaking scenarios

Formulas are expressive enough for traffic rules

Method guarantees asymptotic optimality

Abstract

This paper considers the problem of computing an optimal trajectory for an autonomous system that is subject to a set of potentially conflicting rules. First, we introduce the concept of prioritized safety specifications, where each rule is expressed as a temporal logic formula with its associated weight and priority. The optimality is defined based on the violation of such prioritized safety specifications. We then introduce a class of temporal logic formulas called $\textrm{si-FLTL}_{\mathsf{G_X}}$ and develop an efficient, incremental sampling-based approach to solve this minimum-violation planning problem with guarantees on asymptotic optimality. We illustrate the application of the proposed approach in autonomous vehicles, showing that $\textrm{si-FLTL}_{\mathsf{G_X}}$ formulas are sufficiently expressive to describe many traffic rules. Finally, we discuss practical considerations and present simulation results for a vehicle overtaking scenario.