This paper addresses the problem of adaptively controlling the bias parameter in nonlinear opinion dynamics (NOD) to allocate agents into groups of arbitrary sizes for the purpose of maximizing collective rewards. In previous work, an algorithm based on the coupling of NOD with an multi-objective behavior optimization was successfully deployed as part of a multi-robot system in an autonomous task allocation field experiment. Motivated by the field results, in this paper we propose and analyze a new task allocation model that synthesizes NOD with an evolutionary game framework. We prove sufficient conditions under which it is possible to control the opinion state in the group to a desired allocation of agents between two tasks through an adaptive bias using decentralized feedback. We then verify the theoretical results with a simulation study of a collaborative evolutionary division of labor game.

翻译：本文研究通过自适应控制非线性意见动力学（NOD）中的偏置参数，将智能体分配到任意规模的群体中以最大化集体奖励的问题。在先前工作中，一种基于NOD与多目标行为优化耦合的算法已作为多机器人系统的一部分，在自主任务分配的现场实验中得到成功应用。受现场实验结果启发，本文提出并分析了一种将NOD与进化博弈框架相结合的新型任务分配模型。我们证明了在分散式反馈机制下，通过自适应偏置将群体意见状态控制到两个任务间期望智能体分配的充分条件。随后通过协作式进化分工博弈的仿真研究验证了理论结果。