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DMS-EPSRC: Topology of Automated Motion Planning

DMS-EPSRC：自动运动规划拓扑

基本信息

批准号：
2105553
负责人：
Shmuel Weinberger
金额：
$ 31.14万
依托单位：
University of Chicago
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-07-01 至 2025-06-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2105553&HistoricalAwards=false
关键词：
DMS EPSRC Topology Automated Motion

项目摘要

This project will investigate new mathematics useful for understanding the complexity of robotic action in a physical environment. The project thus concentrates on those aspects that are different from purely computational work. Instead, as a robot moves from place to place, it senses its environment, acts within it to achieve some goal, responds to changes in it, and might communicate with others. The interactions with the external environment are typically achieved via changes to some internal states, so that, for example, a given motion performed on two different occasions (even under identical external conditions) could be the result of different changes to the internal state of the robot. By building abstract topological models of these issues, the PI, in collaboration with M. Farber in the UK, will use algebraic and geometric tools to shed light on some of the tradeoffs (for example of stability of output against flexibility in being able to handle a variety of environments) that necessarily arise when solving such problems.The first step in this direction, a numerical invariant that measures the amount of instability necessary, no matter the computational resources available, for robotic motion planning, or equivalently the minimum amount of stochasticity necessary is the topological complexity invented almost twenty years ago by Farber, and frequently studied by cohomological tools. To understand the additional cost of flexibility", the costs imposed by needing to solve a motion planning problem but in a variety of different environments (say for a Roomba to learn its way around a room after the furniture has been moved), D. Cohen, Farber, and the PI introduced parametrized topological complexity; preliminary calculations show that it does indeed capture some new phenomena that the ordinary complexity does not. Besides further development of topological and parametrized complexity, this project aims to study the role of hidden states (e.g. moving from one fiber to another of a work map), sensing (e.g. the role of incomplete information about the environment that unfolds over time), the development of a useful technology for genus of non-fibrations, and the use of persistent homology to understand about the role of resources (e.g. the speed, path length, energy usage, sensing costs, etc.) in planning tasks.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

这个项目将研究新的数学有用的理解机器人在物理环境中的行动的复杂性。因此，该项目集中在那些方面，是从纯粹的计算工作不同。相反，当机器人从一个地方移动到另一个地方时，它会感知环境，在环境中行动以实现某个目标，对环境的变化做出反应，并可能与其他人交流。与外部环境的交互通常通过改变某些内部状态来实现，例如，在两个不同场合（即使在相同的外部条件下）执行的给定运动可能是机器人内部状态不同变化的结果。通过建立这些问题的抽象拓扑模型，PI与M。法伯在英国，将使用代数和几何工具，以阐明一些权衡（例如，输出的稳定性相对于能够处理各种环境的灵活性），这是解决此类问题时必然出现的。在这个方向上的第一步，测量必要的不稳定性的数值不变量，无论可用的计算资源如何，用于机器人运动规划，或者等价地说，所需的最小随机性是近20年前由法伯发明的拓扑复杂性，并经常被上同调工具研究。为了理解“灵活性的额外成本”，需要解决运动规划问题所带来的成本，但在各种不同的环境中（比如Roomba在家具移动后在房间里学习），D。科恩、法伯和PI引入了参数化拓扑复杂性;初步计算表明，它确实捕捉到了一些普通复杂性所不能捕捉到的新现象。除了进一步发展拓扑和参数化的复杂性，本项目旨在研究隐藏状态的作用（例如，从工作图的一个光纤移动到另一个光纤），感测（例如，关于环境的不完整信息随时间推移而展现的作用），开发用于非纤维化的有用技术，以及使用持久同源性来理解资源的作用（例如，速度、路径长度、能量使用、感测成本等）。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。