Anytime computation algorithms for approach-evasion differential games

TL;DR

This paper introduces novel anytime algorithms for approach-evasion differential games, enabling efficient computation of optimal strategies with proven convergence, outperforming existing multi-grid methods through theoretical analysis and numerical simulations.

Contribution

The paper presents a new class of anytime algorithms for approach-evasion differential games, combining incremental sampling and viability theory, with improved performance over traditional methods.

Findings

Algorithms converge reliably and efficiently.

Significant performance improvements over multi-grid methods.

Validated through numerical simulations.

Abstract

This paper studies a class of approach-evasion differential games, in which one player aims to steer the state of a dynamic system to the given target set in minimum time, while avoiding some set of disallowed states, and the other player desires to achieve the opposite. We propose a class of novel anytime computation algorithms, analyze their convergence properties and verify their performance via a number of numerical simulations. Our algorithms significantly outperform the multi-grid method for the approach-evasion differential games both theoretically and numerically. Our technical approach leverages incremental sampling in robotic motion planning and viability theory.