10.1007/s13235-024-00614-2 ; arXiv: 2401.14994">
 

Complete Solution of the Lady in the Lake Scenario

Document Type

Article

Publication Date

1-3-2025

Abstract

In the Lady in the Lake scenario, a mobile agent, L, is pitted against an agent, M, who is constrained to move along the perimeter of a circle. L is assumed to begin inside the circle and wishes to escape to the perimeter with some finite angular separation from M at the perimeter. This scenario has, in the past, been formulated as a zero-sum differential game wherein L seeks to maximize terminal separation and M seeks to minimize it. Its solution is well-known. However, there is a large portion of the state space for which the canonical solution does not yield a unique equilibrium strategy. This paper provides such a unique strategy by solving an auxiliary zero-sum differential game. In the auxiliary differential game, L seeks to reach a point opposite of M at a radius for which their maximum angular speeds are equal (i.e., the antipodal point). L wishes to minimize the time to reach this point while M wishes to maximize it. The solution of the auxiliary differential game is comprised of a Focal Line, a Universal Line, and their tributaries. The Focal Line tributaries' equilibrium strategy for L is semi-analytic, while the Universal Line tributaries' equilibrium strategy is obtained in closed form.

Comments

This article was published by Springer online ahead of inclusion in an issue of Dynamic Games and Applications. The published version of record is accessible by subscription though the DOI link on this page.

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Source Publication

Dynamic Games and Applications (ISSN 2153-0785 | e-ISSN 2153-0793)

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