Tasks in the real world are complex and often require multiple robots to collaborate to be serviced. In many cases, a task might require different sensory inputs and actuation outputs. However, allocating a large variety of sensors and/or actuators on a single robot is not a cost-effective solution—robots with different attributes must be considered. In this paper, we study coalition formation for such a set of heterogeneous robots to be allocated instantaneously to a set of tasks. Our proposed solution employs a hedonic coalition formation strategy based on a weighted bipartite matching algorithm. In our setting, a hedonic coalition game, a topic rooted in game theory, is used to form coalitions by minimizing the total cost of the formation and maximizing the overlap between required and allocated types of robots for each of the tasks. This approach guarantees a polynomial time complexity and Nash-stability. Numerical results show that our approach finds similar quality near-optimal solutions to existing approaches while significantly reducing the time to find them. Moreover, it easily scales to large numbers of robots and tasks in negligible time (1.57 sec. with 2000 robots and 400 tasks).

现实世界中的任务很复杂，通常需要多个机器人协作才能得到服务。在许多情况下，一项任务可能需要不同的感官输入和驱动输出。然而，在单个机器人上分配多种传感器和/或执行器并不是一种具有成本效益的解决方案——必须考虑具有不同属性的机器人。在本文中，我们研究了这样一组异构机器人的联盟形成，以立即分配给一组任务。我们提出的解决方案采用享乐联盟形成基于加权二分匹配算法的策略。在我们的设置中，享乐联盟游戏是一个植根于博弈论的主题，用于通过最小化形成的总成本并最大化每个任务所需和分配的机器人类型之间的重叠来形成联盟。这种方法保证了多项式时间复杂度和纳什稳定性。数值结果表明，我们的方法找到了与现有方法类似的质量接近最优的解决方案，同时显着减少了找到它们的时间。此外，它可以在极短的时间内轻松扩展到大量机器人和任务（1.57 秒，2000 个机器人和 400 个任务）。