## 2 Related Work  
Distributed collaborative task planning initially achieved success in ground-based multi-agent systems [9] and robot networks [10], and later gradually extended to satellite swarm applications [11]. The multi-robot task planning and \"task game\" concepts mentioned by [PERSON] [12] provided inspiration for satellite distributed task planning. [PERSON] et al. [13] further validated, in the Modular Open Network Architecture (MONARCH), that distributed simulation and task allocation optimization can significantly improve collaboration efficiency. In response to the collaborative needs within satellite systems, [PERSON] [14] realized distributed autonomous formation keeping and task planning through a multi-agent negotiation mechanism, demonstrating good robustness and adaptability, especially under highly dynamic conditions. [PERSON] et al. [15] further studied a distributed collaborative dynamic task planning algorithm based on multi-agent hybrid learning, which maintains good adaptability in multiple complex task scenarios. Additionally, [PERSON] [16] combined distributed online algorithms with game theory to provide rapid allocation and optimization ideas for multi-player space pursuit-evasion task planning, thereby greatly reducing the time required for task scheduling.  
With the enhancement of computational capabilities and the infiltration of artificial intelligence technologies, the connotation of distributed collaborative task planning in satellite mission planning has continuously expanded. [PERSON] [17] proposed a distributed autonomous task allocation model for high-density dynamic environments, improving the task completion rate and resource utilization efficiency of multi-satellite systems by adjusting task priorities and resource allocations in real time. [PERSON] [18] utilized a response threshold model for distributed task searching in unmanned aerial vehicles, providing a referential multi-agent system example for collaboration mechanism optimization in satellite mission planning. [PERSON] [19] pointed out in his study that after integrating intelligent optimization algorithms, distributed collaboration exhibits more prominent performance in task execution efficiency and dynamic adaptability. [PERSON] [20] modeled multi-satellite collaborative task scheduling using a genetic algorithm, achieving significant computational efficiency improvements in task priority ranking and resource reconfiguration. It can be observed that when the swarm size increases and the environment changes constantly, a single centralized planning model struggles to consider global optimality and real-time performance, whereas distributed collaboration can maximize global benefits through multi-node communication and local optimization.  
This paper, focusing on distributed heterogeneous cluster task planning based on Nash equilibrium, integrates methodologies from game theory and distributed optimization, achieving efficient collaboration of multiple objectives and satellites in complex constellation attack-defense confrontations and resource-limited scenarios. It addresses the deficiencies in previous studies that overlooked issues such as \"multi-objective compatibility\" and \"multi-agent joint game\", providing new solutions for task planning in heterogeneous satellite clusters. The research findings not only enrich the theoretical system of space mission planning but also provide technical support for future intelligent and distributed satellite collaborative operations.