Cooperative Evasion by Translating Targets with Variable Speeds

TL;DR

This paper studies a cooperative evasion problem where multiple evaders strategically choose their speeds to maximize the interception time by a pursuer executing a specific pursuit strategy, introducing an efficient algorithm and fundamental limits.

Contribution

It introduces a novel cooperative evasion model with variable speeds, analyzes conditions for evader cooperation, and proposes an efficient algorithm for evader strategy assignment.

Findings

Evaders can significantly increase interception time through cooperation.

The proposed algorithm reduces computational complexity compared to exponential search.

Fundamental limits on total evasion time are characterized for large numbers of evaders.

Abstract

We consider a problem of cooperative evasion between a single pursuer and multiple evaders in which the evaders are constrained to move in the positive Y direction. The evaders are slower than the vehicle and can choose their speeds from a bounded interval. The pursuer aims to intercept all evaders in a given sequence by executing a Manhattan pursuit strategy of moving parallel to the X axis, followed by moving parallel to the Y axis. The aim of the evaders is to cooperatively pick their individual speeds so that the total time to intercept all evaders is maximized. We first obtain conditions under which evaders should cooperate in order to maximize the total time to intercept as opposed to each moving greedily to optimize its own intercept time. Then, we propose and analyze an algorithm that assigns evasive strategies to the evaders in two iterations as opposed to performing an exponential search over the choice of evader speeds. We also characterize a fundamental limit on the total time taken by the pursuer to capture all evaders when the number of evaders is large. Finally, we provide numerical comparisons against random sampling heuristics.