用全局博弈框架解决异构机器人多任务分配问题
A Global Games-Inspired Approach to Multi-Robot Task Allocation for Heterogeneous Teams
- 基于全局信号设计线性目标函数，引导机器人理性分配任务
- 通过参数调节实现混合纳什均衡，避免所有机器人集中于单一任务
- 仅需矩阵求逆即可生成分配概率，适合大规模团队部署
本文提出一种基于全局博弈的多机器人任务分配方法。每个任务关联一个全局信号（实数值），反映任务执行进度或紧急程度。系统为每台机器人设计线性目标函数，其值随全局信号增加而上升，随分配机器人数量增加而下降。通过设定目标函数超参数条件，可诱导出混合纳什均衡解，即避免所有机器人集中于单个任务。所提算法仅需一次矩阵求逆即可确定机器人分配的概率分布。我们在仿真中验证了算法性能，并指明了应用场景与未来研究方向。
原文摘要 · Abstract (English)
In this article we propose a game-theoretic approach to the multi-robot task allocation problem using the framework of global games. Each task is associated with a global signal, a real-valued number that captures the task execution progress and/or urgency. We propose a linear objective function for each robot in the system, which, for each task, increases with global signal and decreases with the number assigned robots. We provide conditions on the objective function hyperparameters to induce a mixed Nash equilibrium, i.e., solutions where all robots are not assigned to a single task. The resulting algorithm only requires the inversion of a matrix to determine a probability distribution over the robot assignments. We demonstrate the performance of our algorithm in simulation and provide direction for applications and future work.
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