The Geometry of Spatial Knowledge for Navigation

航海空间知识的几何学调查者：威廉·H·沃伦想象来到一个新的城市。当你离开火车站，在市中心漫步时，你似乎建立了对空间布局的了解，使你能够回到火车站(回家)，找到去餐馆和博物馆的路，甚至走新的捷径或绕道。人们普遍认为，这种空间知识以“认知地图”的形式存在，就像你脑中的街道地图一样。但你对这座城市的布局到底学到了什么？你可以通过走来走去(通过路径整合)建立什么样的空间知识？它如何取决于环境的布局、雕像和摩天大楼等独特的地标，以及你探索城市的方式？什么类型的导航辅助工具可以帮助你学习布局并防止你迷路(标志、地图、GPS)？这个项目旨在通过利用最先进的虚拟现实技术来回答这些问题。研究人员通过在持续行走过程中扭曲40x50英尺的虚拟环境，并记录参与者的自然行为来研究主动导航。例如，当参与者在环境中学习或导航时，虚拟世界可以被拉伸，从而改变距离关系；路径和地标的位置可以被移动；或者可以插入“虫洞”以将参与者从一个地方传送到另一个地方，从而在虚拟空间中产生“撕裂”和“折叠”。这些操作使研究人员能够探索空间知识的几何结构以及它是如何获得的。在之前的研究中，研究人员发现，当学习一个新的环境时，会获得具有不同几何性质的多种形式的空间知识。但结果表明，这些知识可能不会被整合到一致的、单一的认知地图中。特别是，参与者似乎获得了一些关于距离和方向的局部度量信息，但未能将其整合到一致的全球地图中。他们学习拓扑结构，如连接地点的路径(图)、邻居之间的关系以及地标的有序序列，但容忍它们之间的巨大差异。本研究调查了通过路径整合建立的度量“地图”的准确性，各种类型的几何知识是如何相关的，以及它们的习得如何依赖于学习过程中环境的结构和稳定性。例如，在一项研究中，研究人员将创建一个非欧几里得风格的虚拟世界，名为“埃舍尔博物馆”，由六个房间组成，里面有独特的绘画和雕塑，它们不属于一个平面，但在空间上重叠，有点像一个平坦的螺旋楼梯。因此，通过绕圈行走，参观者将返回到以前被新博物馆房间占据的物理位置。这使得研究人员可以将邻里结构(房间)从地标(雕塑)的顺序结构以及它们之间的度量距离和方向中分离出来。更好地理解空间知识和人类导航在设计和呈现空间信息(标志、地图、方向、基于网络的地图应用程序)、基于GPS的导航辅助工具(汽车、手机)的视觉和语言界面以及生物启发的机器人导航系统以及建筑设计和城市规划方面有着广泛的应用。

The Geometry of Spatial Knowledge for NavigationInvestigator: William H. WarrenImagine arriving in a new city. As you leave the train station and walk around the downtown area, you seem to build up knowledge of the spatial layout that enables you to get back to the train station (homing), find your way to restaurants and museums, and even take new shortcuts or detours. It is commonly believed that this spatial knowledge takes the form of a "cognitive map," something like a street map in your head. But what have you really learned about the layout of the city? What sort of spatial knowledge can you build up by walking around (by path integration)? How does it depend on the layout of the environment, on distinctive landmarks like statues and skyscrapers, and the manner in which you explore the city? What kinds of navigation aids might help you learn the layout and keep you from getting lost (signs, maps, GPS)?This project aims to answer such questions by taking advantage of state-of-the-art virtual reality techniques. Investigators study active navigation by distorting a 40 x 50 ft virtual environment during ongoing walking, and recording the participant's natural behavior. For instance, as a participant learns or navigates in the environment, the virtual world may be stretched, changing distance relationships; the locations of paths and landmarks may be shifted; or "wormholes" may be inserted to teleport the participant from one place to another, creating "rips" and "folds" in virtual space. These manipulations allow the investigators to probe the geometric structure of spatial knowledge and how it is acquired.In previous research, the investigators have found that multiple forms of spatial knowledge, with different geometric properties, are acquired when learning a new environment. But the results suggest that such knowledge may not be integrated into a consistent, unitary cognitive map. In particular, participants seem to acquire some local metric information about distances and directions, but fail to integrate it into a consistent global map. They learn topological structure such as the paths that connect places (a graph), relations among neighborhoods, and ordinal sequences of landmarks, but tolerate large discrepancies between them. The present research investigates the accuracy of the metric "map" that can be built up through path integration, how the various types of geometric knowledge are related, and how their acquisition depends on the structure and stability of the environment during learning. For example, in one study the investigators will create a non-Euclidean virtual world called the "Escher Museum," consisting of six rooms with distinctive paintings and sculptures that do not fit into a plane, but overlap in space, something like a flat spiral staircase. Thus, by walking around a loop the participant will circle back to previous physical locations that are occupied by new Museum rooms. This allows the investigators to dissociate the neighborhood structure (rooms) from the ordinal structure of landmarks (sculptures) and metric distances and directions between them.A better understanding of spatial knowledge and human navigation has broad applications to the design and presentation of spatial information (signage, maps, directions, web-based mapping applications), visual and verbal interfaces for GPS-based navigation aids (autos, cell phones), and biologically-inspired robot navigation systems, as well as to architectural design and city planning.