Approximate Solutions to a Class of Reachability Games

TL;DR

This paper introduces a computationally efficient method for approximating Nash equilibria in reachability games, applicable to multi-player scenarios with high-dimensional state spaces, and adaptable to single-player optimal control.

Contribution

It presents a novel approximation approach for reachability games that is efficient, scalable, and connects to existing gradient-based optimization methods.

Findings

Operates in real-time for multi-player, high-dimensional scenarios

Provides a hierarchy of increasingly accurate approximations

Reduces to local gradient-based optimization in single-player cases

Abstract

In this paper, we present a method for finding approximate Nash equilibria in a broad class of reachability games. These games are often used to formulate both collision avoidance and goal satisfaction. Our method is computationally efficient, running in real-time for scenarios involving multiple players and more than ten state dimensions. The proposed approach forms a family of increasingly exact approximations to the original game. Our results characterize the quality of these approximations and show operation in a receding horizon, minimally-invasive control context. Additionally, as a special case, our method reduces to local gradient-based optimization in the single-player (optimal control) setting, for which a wide variety of efficient algorithms exist.