Distributed Task Scheduling for Multiple EOSs via a Game Theory Approach

In this study, we investigate the task scheduling problem for multiple earth observation satellites (EOSs) to achieve the maximal task observation ratio with the least repeated tasks. To begin, we build a task graph to describe feasible observation sequences for each EOS while satisfying its kinematic constraints. Next, we construct local utility functions for individual EOSs as metrics, and show that the task scheduling problem is indeed an exact potential game problem. Based on this finding, the collaborative goal for task scheduling is converted to the problem of solving for the Nash equilibrium (NE) of the game. Then, a sequential iterative algorithm and a simultaneous iterative algorithm are developed to solve for the NE in a distributed manner. Also, in the algorithms, a sieving scheme for EOSs is proposed to reduce the searching spaces. It is proved that our algorithms converge to the NE in finite steps and the global utility is shown to be monotonically increasing under certain conditions. Finally, the Bézier curve is used to smoothen the target observation path, based on which a model predictive control scheme is employed to design the control law of EOSs.