Dynamic Task Allocation in Multi-Robot System Based on a Team Competition Model

In recent years, it is a trend to integrate the ideas in game theory into the research of multi-robot system. In this paper, a team-competition model is proposed to solve a dynamic multi-robot task allocation problem. The allocation problem asks how to assign tasks to robots such that the most suitable robot is selected to execute the most appropriate task, which arises in many real-life applications. To be specific, we study multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once, which defines an extensive-form game with perfect recall. We also study a common variant where one team always selects its player before the other team in each round. Regarding the robots as the players in the first team and the tasks as the players in the second team, the sub-game perfect strategy of the first team computed via solving the team competition gives us a solution for allocating the tasks to the robots-it specifies how to select the robot (according to some probability distribution if the two teams move simultaneously) to execute the upcoming task in each round, based on the results of the matches in the previous rounds. Throughout this paper, many properties of the sub-game perfect equilibria of the team competition game are proved. We first show that uniformly random strategy is a sub-game perfect equilibrium strategy for both teams when there are no redundant players. Secondly, a team can safely abandon its weak players if it has redundant players and the strength of players is transitive. We then focus on the more interesting case where there are redundant players and the strength of players is not transitive. In this case, we obtain several counterintuitive results. For example, a player might help improve the payoff of its team, even if it is dominated by the entire other team. We also study the extent to which the dominated players can increase the payoff. Very similar results hold for the aforementioned variant where the two teams take actions in turn.