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arXiv 1707.07083cs.RO
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同步多机器人系统的$k$弹性计算

Computing the $k$-resilience of a Synchronized Multi-Robot System

University of Texas at Dallas(德克萨斯大学达拉斯分校);University of Seville(塞维利亚大学);University of Denver(丹佛大学)

Sergey Bereg, Luis-Evaristo Caraballo, José-Miguel Díaz-Báñez, Mario A. Lopez

摘要:

研究了多机器人系统覆盖策略设计中的一个优化问题。考虑一组$n$协作机器人沿着预定的封闭且不相交的轨迹行进。每个机器人都需要定期与附近的机器人进行信息通信。在两个轨迹在彼此范围内的地方,建立通信链路,允许两个机器人交换信息,只要它们是“同步的”,即,他们同时访问链接。在这种设置中,定义了通信图,并且如果每对邻居都同步,则机器人系统被称为\emph{synchronized}。如果一个或多个机器人离开系统,那么一些轨迹将无人看管。为了在同步系统中处理这种情况,当现场机器人到达通信链路并检测到邻居的不存在时,它转移到相邻的轨迹以承担无人值守的任务。如果足够多的机器人离开,可能会发生一个活的机器人进入\emph{starvation}状态,在飞行期间无法永久地与其他机器人相遇。为了测量系统在这种现象下的容忍度,我们将\emph{$k$-resilience}定义为移除可能导致$k$幸存机器人进入饥饿状态的机器人的最小数量。我们表明,计算的$k$弹性的问题是NP难的,如果$k$是输入的一部分,即使通信图是一棵树。我们提出的算法来计算$k$ -弹性的$k$在一般的通信图中的常数值,并显示更有效的算法,其通信图是一棵树的系统。

英文摘要:

We study an optimization problem that arises in the design of covering strategies for multi-robot systems. Consider a team of $n$ cooperating robots traveling along predetermined closed and disjoint trajectories. Each robot needs to periodically communicate information to nearby robots. At places where two trajectories are within range of each other, a communication link is established, allowing two robots to exchange information, provided they are "synchronized", i.e., they visit the link at the same time. In this setting a communication graph is defined and a system of robots is called \emph{synchronized} if every pair of neighbors is synchronized. If one or more robots leave the system, then some trajectories are left unattended. To handle such cases in a synchronized system, when a live robot arrives to a communication link and detects the absence of the neighbor, it shifts to the neighboring trajectory to assume the unattended task. If enough robots leave, it may occur that a live robot enters a state of \emph{starvation}, failing to permanently meet other robots during flight. To measure the tolerance of the system under this phenomenon we define the \emph{$k$-resilience} as the minimum number of robots whose removal may cause $k$ surviving robots to enter a state of starvation. We show that the problem of computing the $k$-resilience is NP-hard if $k$ is part of the input, even if the communication graph is a tree. We propose algorithms to compute the $k$-resilience for constant values of $k$ in general communication graphs and show more efficient algorithms for systems whose communication graph is a tree.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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