Admissibility Over Winning: A New Approach to Reactive Synthesis in Robotics

TL;DR

This paper introduces a new approach to reactive synthesis in robotics by using admissibility to generate strategies that are more flexible than traditional winning strategies, enabling robots to act reasonably even when winning strategies do not exist.

Contribution

It proposes the concept of admissibly rational strategies, an ordering of strategies beyond winning, and provides an efficient synthesis algorithm for robotic applications.

Findings

Admissibly rational strategies improve robot behavior in complex scenarios.

The proposed method is computationally efficient.

Case studies demonstrate practical effectiveness.

Abstract

Reactive synthesis is a framework for modeling and automatically synthesizing strategies in robotics, typically through computing a \emph{winning} strategy in a 2-player game between the robot and the environment. Winning strategies, however, do not always exist, even in some simple cases. In such situations, it is still desirable for the robot to attempt its task rather than "giving up". In this work, we explore the notion of admissibility to define strategies beyond winning, tailored specifically for robotic systems. We introduce an ordering of admissible strategies and define \emph{admissibly rational strategies}, which aim to be winning and cooperative when possible, and non-violating and hopeful when necessary. We present an efficient synthesis algorithm and demonstrate that admissibly rational strategies produce desirable behaviors through case studies.