A Games-in-Games Framework for Task Allocation, Path Planning, and Formation Control

This article proposes a game-theoretic framework for dealing with the integration design problem of task allocation, path planning, and formation control for multiagent systems. In this framework, an anonymous hedonic game (AHG) is established for allocating tasks according to agents' preferences, while a Stackelberg differential graphical game is nested within the AHG for path planning and controlling agents' formation. In order to capture the characteristics and interactions of the three phases, a group of coupled performance indexes is designed, based on which a backward strategy design mechanism is proposed, i.e., following the sequence of formation control $\rightarrow$ path planning $\rightarrow$ task allocation to obtain the optimal strategy of each phase. The proposed framework makes the strategies to be designed in a closed-loop form and the performance of each phase to be bidirectionally adjustable. It is rigorously proved that the designed strategies can achieve the desired performance of each phase, as well as the Gestalt Nash equilibrium of the integrated game. Finally, an integrated game algorithm is further developed to optimize the parameters of the strategies.