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arXiv 2409.03120cs.RO
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利用子模集覆盖进行机器人覆盖规划的近似环境分解

Approximate Environment Decompositions for Robot Coverage Planning using Submodular Set Cover

University of Waterloo(滑铁卢大学);Avidbots Corp.(Avidbots公司)

Megnath Ramesh, Frank Imeson, Baris Fidan, Stephen L. Smith

AI总结:

针对机器人覆盖路径规划中的环境分解问题,提出基于子模集覆盖的重叠矩形扇区分解方法,并通过贪心算法给出扇区数量近似保证,实验表明其优于现有方法。

摘要:

本文研究了为机器人覆盖规划分解二维环境的问题。覆盖路径规划(CPP)涉及为配备覆盖或传感工具的机器人计算一条成本最小化路径,使该工具访问环境中的所有点。CPP是一个NP难问题,因此现有方法通过将环境分解为最少数量的扇区来简化问题。扇区是环境的子区域,每个子区域都可以使用以某一角度定向的割草机路径(即沿平行直线路径)进行覆盖。然而,传统方法要么将覆盖方向限制为轴平行(水平/垂直),要么无法保证分解中扇区的数量。我们提出了一种将环境分解为可能重叠的矩形扇区的方法。对于给定环境,我们为使用该方法计算出的扇区数量提供了近似保证。我们通过利用扇区覆盖函数的子模特性来实现这一点,这使我们能够将分解问题表述为子模集覆盖(SSC)问题,而贪心算法在该问题上具有众所周知的近似保证。正如使用复杂真实环境地图进行的评估所证明的那样,我们的方法改进了现有的覆盖规划方法。

英文摘要:

In this paper, we investigate the problem of decomposing 2D environments for robot coverage planning. Coverage path planning (CPP) involves computing a cost-minimizing path for a robot equipped with a coverage or sensing tool so that the tool visits all points in the environment. CPP is an NP-Hard problem, so existing approaches simplify the problem by decomposing the environment into the minimum number of sectors. Sectors are sub-regions of the environment that can each be covered using a lawnmower path (i.e., along parallel straight-line paths) oriented at an angle. However, traditional methods either limit the coverage orientations to be axis-parallel (horizontal/vertical) or provide no guarantees on the number of sectors in the decomposition. We introduce an approach to decompose the environment into possibly overlapping rectangular sectors. We provide an approximation guarantee on the number of sectors computed using our approach for a given environment. We do this by leveraging the submodular property of the sector coverage function, which enables us to formulate the decomposition problem as a submodular set cover (SSC) problem with well-known approximation guarantees for the greedy algorithm. Our approach improves upon existing coverage planning methods, as demonstrated through an evaluation using maps of complex real-world environments.

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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