In this paper we present a procedure to automatically design and verify the local behavior of robots with highly limited cognition. All robots are: anonymous, homogeneous, non-communicating, memoryless, reactive, do not know their global position, do not have global state information, and operate by a local clock. They only know: (1) the relative location of their neighbors within a short range and (2) a common direction (North). We have developed a procedure to generate a local behavior that allows the robots to self-organize into a desired global pattern despite their individual limitations. This is done while also avoiding collisions and keeping the coherence of the swarm at all times. The generated local behavior is a probabilistic local state-action map. The robots follow this stochastic policy to select an action based on their current perception of their neighborhood (i.e., their local state). It is this stochasticity, in fact, that allows the global pattern to eventually emerge. For a generated local behavior, we present a formal proof procedure to verify whether the desired pattern will always eventually emerge from the local actions of the agents. The novelty of the proof procedure is that it is primarily local in nature and focuses on the local states of the robots and the global implications of their local actions. A local approach is of interest to reduce the computational effort as much as possible when verifying the emergence of larger patterns. Finally, we show how the behavior could be implemented on real robots and investigate this with extensive simulations on a realistic robot model. To the best of our knowledge, no other solutions exist for robots with such limited cognition to achieve this level of coordination with proof that the desired global property will emerge.

中文翻译：

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一群知识有限的机器人可能形成的自组织模式

在本文中，我们提出了一种程序，该程序可以自动设计和验证具有高度有限认知能力的机器人的局部行为。所有机器人都是：匿名，同质，非通信，无记忆，反应性，不知道其全局位置，不具有全局状态信息并且由本地时钟操作。他们只知道：（1）邻居在短距离内的相对位置；（2）共同方向（北）。我们已经开发了一种生成局部行为的程序，该行为允许机器人尽管有各自的局限性也可以自组织成所需的全局模式。这样做的同时还避免了碰撞并始终保持虫群的连贯性。产生的局部行为是概率局部状态-动作图。机器人遵循此随机策略，以基于其当前对邻居的感知（即其本地状态）来选择动作。实际上，正是这种随机性才使全球格局最终得以出现。对于生成的本地行为，我们提出了一种正式的证明程序，以验证所需的模式是否最终总是会从代理的本地行为中出现。证明程序的新颖性在于它本质上主要是局部的，并且着重于机器人的局部状态及其局部动作的全局含义。在验证较大模式的出现时，应该采用局部方法来尽可能减少计算量。最后，我们展示了如何在真实的机器人上实现该行为，并在真实的机器人模型上进行了广泛的仿真研究。据我们所知，对于具有如此有限的认知能力的机器人，尚无其他解决方案可以实现这种协调水平，并证明会出现所需的全局属性。