The Multi-pursuer Single-Evader Game

A Geometric Approach
  • Alexander Von MollEmail author
  • David Casbeer
  • Eloy Garcia
  • Dejan Milutinović
  • Meir Pachter


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.


Pursuit-evasion Differential game Voronoi diagram Optimization 

Mathematics Subject Classification (2010)

49N70 49N90 49N75 


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Copyright information

© This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2019

Authors and Affiliations

  1. 1.Controls Science Center of ExcellenceAir Force Research LaboratoryWright-Patterson AFBUSA
  2. 2.Department of Computer EngineeringUC Santa CruzSanta CruzUSA
  3. 3.Department of Electrical EngineeringAir Force Institute of TechnologyWright-Patterson AFBUSA

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