The Geometry of Spatial Knowledge for Navigation

导航空间知识的几何学。沃伦想象一下到达一个新的城市。 当你离开火车站，在市中心漫步时，你似乎建立了空间布局的知识，使你能够回到火车站（回家），找到去餐馆和博物馆的路，甚至走新的捷径或弯路。 人们普遍认为，这种空间知识的形式是“认知地图”，就像你头脑中的街道地图一样。 但是你对城市的布局有什么了解呢？ 通过四处走动（通过路径整合）可以建立什么样的空间知识？ 它如何取决于环境的布局，独特的地标，如雕像和摩天大楼，以及你探索城市的方式？ 什么样的导航辅助工具可以帮助您了解布局并防止您迷路（标志，地图，GPS）？该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。 研究人员通过在正在进行的步行过程中扭曲40 x 50英尺的虚拟环境来研究主动导航，并记录参与者的自然行为。 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，改变距离关系;路径和地标的位置可以被移位;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，在虚拟空间中创建“裂缝”和“折叠”。 在以往的研究中，研究人员发现，在学习新环境时，会获得多种形式的空间知识，这些知识具有不同的几何性质。但结果表明，这些知识可能不会整合到一个一致的，单一的认知地图。 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），邻里之间的关系，以及地标的顺序序列，但容忍它们之间的巨大差异。 本研究调查的度量“地图”，可以建立通过路径集成的准确性，各种类型的几何知识是如何相关的，以及它们的获取如何取决于学习过程中的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名为“博物馆”的非欧几里德虚拟世界，由六个房间组成，其中有独特的绘画和雕塑，这些绘画和雕塑不适合平面，但在空间上重叠，就像一个平面螺旋楼梯。 因此，通过绕圈行走，参与者将绕回到先前被新博物馆房间占用的物理位置。 这使得研究人员能够将邻居结构（房间）与地标的有序结构分离开来更好地理解空间知识和人类导航对于空间信息的设计和表达具有广泛的应用（标牌、地图、方向、基于网络的地图应用程序），基于GPS的导航辅助设备的视觉和语言界面（汽车，手机）和生物启发的机器人导航系统，以及建筑设计和城市规划。

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.