桥梁检测微型机器人路径规划：基于最小-最大圈覆盖的方法
Miniature Robot Path Planning for Bridge Inspection: Min-Max Cycle Cover-Based Approach
摘要：
我们研究的问题规划部署的一组移动机器人。虽然问题和公式可以用于许多不同的问题，在这里，我们使用一个桥梁检查作为激励应用的目的，阐述。机器人最初驻扎在一组遍布桥梁的仓库中。然后，每个机器人都被分配到桥上的一组站点进行检查，完成后，必须返回到存储它的同一个仓库。将机器人规划问题转化为一个有根的极小极大循环覆盖问题，其中顶点集由待检测的站点和机器人仓库组成，边的权值是（i）从一个端点到另一个端点所需的时间，或者（ii）旅行所需的能量消耗。在第一种情况下，目标函数是总检查时间，而在后一种情况下，它是所有部署的机器人之间的最大能量消耗。提出了一种新的近似比为$5 + ε$的算法，其中$0<ε<1$ .此外，所提出的算法的计算复杂性是$O\big( n^2+2^{m-1} n \log(n+k) \big)$，其中$n$是顶点的数量，和$m$是仓库的数量。
英文摘要：
We study the problem of planning the deployments of a group of mobile robots. While the problem and formulation can be used for many different problems, here we use a bridge inspection as the motivating application for the purpose of exposition. The robots are initially stationed at a set of depots placed throughout the bridge. Each robot is then assigned a set of sites on the bridge to inspect and, upon completion, must return to the same depot where it is stored. The problem of robot planning is formulated as a rooted min-max cycle cover problem, in which the vertex set consists of the sites to be inspected and robot depots, and the weight of an edge captures either (i) the amount of time needed to travel from one end vertex to the other vertex or (ii) the necessary energy expenditure for the travel. In the first case, the objective function is the total inspection time, whereas in the latter case, it is the maximum energy expenditure among all deployed robots. We propose a novel algorithm with approximation ratio of $5 + ε$, where $0<ε<1$. In addition, the computational complexity of the proposed algorithm is shown to be $O\big( n^2+2^{m-1} n \log(n+k) \big)$, where $n$ is the number of vertices, and $m$ is the number of depots.
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。
