Reactive and Risk-Aware Control for Signal Temporal Logic

TL;DR

This paper introduces ReRiSITL, an extension of STL that incorporates uncontrollable propositions and risk measures, enabling reactive planning and control for autonomous systems in uncertain environments.

Contribution

It presents ReRiSITL, a new logic for specifying complex, risk-aware, and reactive behaviors, along with algorithms for satisfiability checking and control synthesis.

Findings

ReRiSITL effectively models uncontrollable environmental factors.

The satisfiability algorithm uses game-based abstraction.

The framework enables risk-aware reactive control in uncertain settings.

Abstract

The deployment of autonomous systems in uncertain and dynamic environments has raised fundamental questions. Addressing these is pivotal to build fully autonomous systems and requires a systematic integration of planning and control. We first propose reactive risk signal interval temporal logic (ReRiSITL) as an extension of signal temporal logic (STL) to formulate complex spatiotemporal specifications. Unlike STL, ReRiSITL allows to consider uncontrollable propositions that may model humans as well as random environmental events such as sensor failures. Additionally, ReRiSITL allows to incorporate risk measures, such as (but not limited to) the Conditional Value-at-Risk, to measure the risk of violating certain spatial specifications. Second, we propose an algorithm to check if an ReRiSITL specification is satisfiable. For this purpose, we abstract the ReRiSITL specification into a timed signal transducer and devise a game-based approach. Third, we propose a reactive planning and control framework for dynamical control systems under ReRiSITL specifications.