摘要： 针对光伏电站异构多功能清洗机器人集群在多约束条件下的协同任务分配问题，提出了一种基于重叠联盟形成博弈的分布式任务分配方法。首先，构建面向光伏运维的多约束异构机器人集群协同任务优化模型。系统分析异构机器人与多元运维任务的资源适配机理，设计了光伏组件污染等级与机器人清洗能力的匹配机制，建立融合综合资源匹配度、挽回发电损失、运维总成本、最大完工时间和冗余惩罚机制的综合效用函数，该任务分配问题的目标函数构建为最大化联盟总效用，结合工程实际引入任务优先级、任务唯一性与安全距离等约束条件，完成机器人集群运维任务的精细化数学建模，显著提升了机器人与任务间的资源匹配度与运维调度适配性。其次，构建基于双边互利准则的重叠联盟形成博弈框架。该框架将全局组合优化问题转化为分布式联盟划分问题，依托所定义的偏好关系与交换操作，可支持机器人跨联盟动态协作与自主形成重叠联盟结构，进一步提出一种可以描述个体自私逐利与系统全局最优映射关系的双边互利交换准则，显著提升了资源调度灵活性，有效协调了个体理性与系统整体效用；该博弈被证明为势博弈，当机器人最大化自身效用而改变资源分配结构时，目标函数的差异与效用函数的差异是一致的，且博弈框架中至少存在一个纳什均衡即稳定的联盟结构。最后，设计一种融合偏好引力引导与扰动机制的重叠联盟形成算法。算法引入偏好引力机制为机器人选择联盟提供方向性指引，利用边际收益评估机制与提出的双禁忌列表剔除低效联盟、规避无效搜索，结合协同设计的动态资源调整策略与随机扰动机制有效摆脱局部最优；该算法被证明可以在有限次迭代内收敛到T-稳定状态，通过分析其复杂度处于可控范围；最终该算法在求解由任务优化模型与博弈框架所构成的任务分配数学模型时，能够满足异构机器人集群在复杂多元任务协同场景下的任务分配需求，并快速收敛至高质量的纳什均衡解。仿真实验结果表明，本文所提方法在保证全局解质量的前提下，兼备显著的实时性与稳定性。在消融实验中，验证了各改进策略能全面提升算法综合性能；在验证算法解质量与运维指标实验中，相较于基线算法，本文算法挽回发电损失提升了6.63%，运维总成本降低了2.55%，平均作业时间缩短了13.29%；在规模变化下性能对比分析实验中，本文算法在不同机器人与任务数量变化情况下各项指标均为最优；在实时性与稳定性实验中，本文算法平均运行时间不超过6.09s，标准差与Wilcoxon秩和检验具有统计显著性。可制定经济高效的任务分配方案，为光伏电站精细化运维提供了有效技术支撑。

Abstract: This paper proposes a distributed task allocation method based on overlapping coalition formation game, to address the collaborative task allocation problem of heterogeneous multi-functional cleaning robot clusters in photovoltaic (PV) power stations under multiple constraints. First, this paper constructs a multi-constraint cooperative task optimization model of heterogeneous robot clusters for PV operation and maintenance (O&M). It systematically analyzes the resource adaptation mechanism between heterogeneous robots and diverse O&M tasks. It designs a matching mechanism between PV module pollution levels and robot cleaning capabilities. It establishes a comprehensive utility function integrating comprehensive resource matching degree, recovered power generation loss, total O&M cost, maximum completion time and redundancy penalty mechanism. The objective function of this task allocation problem is constructed to maximize the total coalition utility. Combined with engineering practice, it introduces constraint conditions including task priority, task uniqueness and safety distance. It completes the refined mathematical modeling of robot cluster O&M tasks. It significantly improves the resource matching degree and O&M scheduling adaptability between robots and tasks. Second, this paper constructs an overlapping coalition formation game framework based on the bilateral mutual benefit criterion. This framework converts the global combinatorial optimization problem into a distributed coalition partition problem. Relying on the defined preference relation and exchange operation, it supports robots to realize cross-coalition dynamic cooperation and independently form an overlapping coalition structure. This paper further proposes a bilateral mutual benefit exchange criterion to describe the mapping relationship between individual selfish profit-seeking and global system optimization. The criterion significantly improves the flexibility of resource scheduling. It effectively coordinates individual rationality and overall system utility. This game is proven to be a potential game. When robots change the resource allocation structure to maximize their own utility, the difference of the objective function is consistent with the difference of the utility function. And there exists at least one Nash equilibrium, namely a stable coalition structure, in the game framework. Finally, this paper designs an overlapping coalition formation algorithm integrating preference gravity guidance and disturbance mechanism. The algorithm introduces a preference gravity mechanism to provide directional guidance for robots to select coalitions. It uses the marginal revenue evaluation mechanism and the proposed double tabu list to eliminate inefficient coalitions and avoid invalid searches. Combined with the co-designed dynamic resource adjustment strategy and random disturbance mechanism, it effectively gets rid of local optimum. This algorithm is proven to converge to a T-stable state within a finite number of iterations. Its complexity is analyzed to be within a controllable range. When solving the task allocation mathematical model composed of the task optimization model and the game framework, the algorithm can meet the task allocation requirements of heterogeneous robot clusters in complex and diverse task cooperation scenarios. It can quickly converge to a high-quality Nash equilibrium solution. Simulation experimental results show that the proposed method has remarkable real-time performance and stability on the premise of ensuring the quality of the global solution. Ablation experiments verify that each improvement strategy can comprehensively improve the comprehensive performance of the algorithm. In experiments verifying algorithm solution quality and O&M indicators, compared with the baseline algorithm, the proposed algorithm increases the recovered power generation loss by 6.63%, reduces the total O&M cost by 2.55%, and shortens the average operation time by 13.29%. In performance comparison experiments under scale changes, all indicators of the proposed algorithm are optimal under different numbers of robots and tasks. In real-time and stability experiments, the average running time of the proposed algorithm does not exceed 6.09s. Its standard deviation and Wilcoxon rank-sum test results have statistical significance. It can formulate economical and efficient task allocation schemes. It provides effective technical support for the refined O&M of PV power stations.