Title

The Multi-pursuer Single-Evader Game: A Geometric Approach

Document Type

Article

Publication Date

11-2019

Abstract

We consider a general pursuit-evasion differential game with three or more pursuers and a single evader, all with simple motion (fixed-speed, infinite turn rate). It is shown that traditional means of differential game analysis is difficult for this scenario. But simple motion and min-max time to capture plus the two-person extension to Pontryagin’s maximum principle imply straight-line motion at maximum speed which forms the basis of the solution using a geometric approach. Safe evader paths and policies are defined which guarantee the evader can reach its destination without getting captured by any of the pursuers, provided its destination satisfies some constraints. A linear program is used to characterize the solution and subsequently the saddle-point is computed numerically. We replace the numerical procedure with a more analytical geometric approach based on Voronoi diagrams after observing a pattern in the numerical results. The solutions derived are open-loop optimal, meaning the strategies are a saddle-point equilibrium in the open-loop sense.

Comments

The "Link to Full Text" on this page loads the PDF of the article, furnished open-access through the Springer Nature SharedIt content-sharing initiative. © This is a U.S. government work and its text is not subject to copyright protection in the United States; however, its text may be subject to foreign copyright protection 2019.

Please attribute the work using the citation indicated below.

DOI

10.1007/s10846-018-0963-9

Source Publication

Journal of Intelligent and Robotic Systems: Theory and Applications

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