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arXiv 1802.00898cs.RO
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最小化期望成本直至成功的路径规划

Path Planning for Minimizing the Expected Cost until Success

University of California Santa Barbara(加州大学圣巴巴拉分校)

Arjun Muralidharan, Yasamin Mostofi

摘要:

考虑机器人在具有边成本的图上的一般路径规划问题,并且其中每个节点具有给定概率的成功或失败(相对于某些任务)的布尔值。目标是在图上为机器人规划一条路径,使预期成本最小化,直到成功。在本文中,我们的目标是对这个问题有一个基本的理解。我们首先展示了如何将这个问题最优地解决,将其制定为无限时域马尔可夫决策过程,但具有指数空间复杂度。然后,我们正式证明其NP-硬度。为了解决空间复杂度,我们提出了一个路径规划,使用博弈论的框架,渐近任意接近最优解。此外,我们还提出了两个快速和非近视路径规划。为了展示我们的框架的性能,我们对两种场景进行了广泛的模拟:火星上的漫游者正在寻找一个用于科学研究的物体,以及一个机器人正在寻找一个连接到远程站的点(来自旧金山市中心的真实数据)。我们的数值结果表明,现有的国家的最先进的方法有相当大的性能改善。

英文摘要:

Consider a general path planning problem of a robot on a graph with edge costs, and where each node has a Boolean value of success or failure (with respect to some task) with a given probability. The objective is to plan a path for the robot on the graph that minimizes the expected cost until success. In this paper, it is our goal to bring a foundational understanding to this problem. We start by showing how this problem can be optimally solved by formulating it as an infinite horizon Markov Decision Process, but with an exponential space complexity. We then formally prove its NP-hardness. To address the space complexity, we then propose a path planner, using a game-theoretic framework, that asymptotically gets arbitrarily close to the optimal solution. Moreover, we also propose two fast and non-myopic path planners. To show the performance of our framework, we do extensive simulations for two scenarios: a rover on Mars searching for an object for scientific studies, and a robot looking for a connected spot to a remote station (with real data from downtown San Francisco). Our numerical results show a considerable performance improvement over existing state-of-the-art approaches.

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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