Lion and man game in the presence of a circular obstacle

Authors:
Nikhil Karnad;Volkan Isler
Affiliations:
Department of Computer Science and Engineering at the University of Minnesota, Minneapolis, Minnesota;Department of Computer Science and Engineering at the University of Minnesota, Minneapolis, Minnesota
Venue:
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Year:
2009

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Abstract

In the lion and man game, a lion tries to capture a man who is as fast as the lion. We study a new version of this game which takes place in a Euclidean environment with a circular obstacle. We present a complete characterization of the game: for each player, we derive necessary and sufficient conditions for winning the game. Their (continuous time) strategies are constructed using techniques from differential games and arguments from geometry. Our main result is a decision algorithm which takes arbitrary initial positions as input, declares one of the players as the winner of the game and outputs a winning strategy for that player. We extend our approach to explicitly construct, in closed form, the decision boundary that partitions the arena into win and lose regions.