This paper proposes two algorithms, namely "back-tracking" and "history following", to reach consensus in case of communication loss for a network of distributed agents with switching topologies. To reach consensus in distributed control, considered communication topology forms a strongly connected graph. The graph is no more strongly connected whenever an agent loses communication.Whenever an agent loses communication, the topology is no more strongly connected. The proposed back-tracking algorithm makes sure that the agent backtracks its position unless the communication is reestablished, and path is changed to reach consensus. In history following, the agents use their memory and move towards previous consensus point until the communication is regained. Upon regaining communication, a new consensus point is calculated depending on the current positions of the agents and they change their trajectories accordingly. Simulation results, for a network of six agents, show that when the agents follow the previous history, the average consensus time is less than that of back-tracking. However, situation may arise in history following where a false notion of reaching consensus makes one of the agents stop at a point near to the actual consensus point. An obstacle avoidance algorithm is integrated with the proposed algorithms to avoid collisions. Hardware implementation for a three robots system shows the effectiveness of the algorithms.

中文翻译：

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使用回溯和历史跟随算法的多代理系统的共识

本文提出了两种算法，即“回溯”和“历史跟踪”，以在具有切换拓扑的分布式代理网络的通信丢失的情况下达成共识。为了在分布式控制中达成共识，考虑的通信拓扑形成了一个强连接图。每当代理失去通信时，图就不再是强连通的。每当代理失去通信时，拓扑就不再是强连通的。所提出的回溯算法确保代理回溯其位置，除非重新建立通信，并且改变路径以达成共识。在历史跟踪中，代理使用他们的记忆并移动到先前的共识点，直到重新获得通信。恢复沟通后，根据代理的当前位置计算新的共识点，并相应地改变他们的轨迹。模拟结果，对于六个代理的网络，表明当代理遵循先前的历史时，平均共识时间小于回溯的时间。然而，历史上可能会出现以下情况，即达成共识的错误概念使其中一个代理停止在接近实际共识点的点。避障算法与所提出的算法相结合以避免碰撞。三机器人系统的硬件实现显示了算法的有效性。平均共识时间小于回溯。然而，历史上可能会出现以下情况，即达成共识的错误概念使其中一个代理停止在接近实际共识点的点。避障算法与所提出的算法相结合以避免碰撞。三机器人系统的硬件实现显示了算法的有效性。平均共识时间小于回溯。然而，历史上可能会出现以下情况，即达成共识的错误概念使其中一个代理停止在接近实际共识点的点。避障算法与所提出的算法相结合以避免碰撞。三机器人系统的硬件实现显示了算法的有效性。