Abstract: A distributed task allocation algorithm based on potential games is proposed to address the complex task allocation problem for heterogeneous formation Earth-observation satellites equipped with diverse observation payloads and required to satisfy varied observation demands. First, a task allocation model is established that accounts for energy consumption and onboard storage constraints, reflecting the characteristics of the formation satellite task allocation problem. A proper potential function is constructed, and the task allocation process is described as a game-theoretic process. A fault-free task pre-allocation algorithm based on potential games is then designed, which effectively solves the task allocation problem while reducing computational complexity. Subsequently, to handle sensor failures on satellites, a task re-allocation algorithm is developed based on the pre-allocation results, enabling effective reassignment of tasks under sensor malfunction conditions. Finally, appropriate simulation scenarios are designed for validation. Simulation results demonstrate that the proposed algorithm improves the real-time performance of task allocation while maintaining solution effectiveness.