Robot kabaddi

Imagine a situation in which two (or more) robots are required to capture a single rogue robot. We draw inspiration from Kabaddi, a popular team sport originating in South Asia, and study a discrete version of the game as a vehicle to study this kind of multiagent pursuit evasion problems. The game of Kabaddi involves two teams occupying opposite halves of a field, each team taking turns to send an “attacker” into the other half, in order to win points by tagging or wrestling members of the opposing team [11]. The attacker must hold his breath during the whole attack and successfully return to his own half—the attacker continuously chants “kabaddi, kabaddi, · · · ” to demonstrate holding of the breath. There are several elements of this game that distinguish it from other well-studied and similar sounding games such as man-and-the-lion [7, 10], copsand-robber [4, 1, 5], robot-and-rabbit [4], and pursuitevasion [9, 3]. Perhaps the most significant difference is that in kabaddi players of either side may capture an opponent, while in these other games one side always plays the role of captors and the other evaders. But there are several other differences as well, some of which we highlight below. In the man-and-the-lion game, for instance, the chase occurs inside a circular region, both players have the same maximum speed, and it is known that the man can evade capture indefinitely. In contrast, the game of kabbadi pits a single attacker against multiple defenders. The other games such as the cops-and-robber and pursuit-evasion differ from kabaddi in the way capture occurs as well as the information about the evader’s position. For instance, the current position of all the players is public information in kabaddi while the position of the robber or evader is often assumed to be unknown to cops or pursuers. Furthermore, it is also typically assumed that each cop (robot) follows a fixed trajectory that is known to the robber (rabbit). This makes sense in situations where the defenders (cops) have fixed patrol routes, but not in interactive games like kabaddi. The problems and results in the graph searching literature are also of a different nature than ours [2, 6]. The pursuit-evasion games have also focused on visibility based capture, where it is sufficient for some pursuer to “see” the evader—both infinite visibility or limitedrange visibility models have been considered [3, 5]. By contrast, kabaddi requires a physical capture that leads to a very different set of strategies and game outcomes. (The book by Nahin [8] offers a nice historical perspective on various pursuit-evasion type games.) With this background, let us now formalize our model of kabaddi.