GVG-based Topological SLAM：无明确定位下的精确位置确定

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本文档探讨的是"5.拓扑同时定位与建图（Topological Simultaneous Localization and Mapping, SLAM）：向精确定位无需明确定位技术的发展"这一关键领域。SLAM是机器人在未知环境中导航的重要组成部分，它涉及到机器人如何在部分探索的地图上确定自己的位置，尤其是在面临定位误差、缺乏外部定位设备以及没有人为设计的地标的情况下。作者Howie Choset和Keiji Nagatani作为IEEE会员，提出了一个新颖的SLAM方法，该方法利用机器人自由空间的拓扑结构进行精确定位，即使在部分构建的地图上也能实现。传统SLAM面临的挑战促使研究者转向拓扑信息来辅助定位。论文的核心概念是将环境的拓扑结构编码进一种称为广义Voronoi图（Generalized Voronoi Graph, GVG）的拓扑地图中。GVG不仅提供了环境的拓扑信息，还能包含关于机器人周围空间的一些度量信息，如邻近性和距离。这种方法的优势在于能够处理复杂的、非结构化的环境，而不仅仅是依赖于几何特征。在本文中，作者详细阐述了生成GVG边和节点的低级控制策略，这些策略允许机器人有效地探索未知空间。通过这种方式，机器人能够一边收集环境信息，一边不断更新其自身的地图，逐步接近精确的位置估计。这种拓扑SLAM方法减少了对精确外部定位设备的依赖，提高了机器人的自主性，并为在动态变化的环境中实现精确定位提供了新的可能性。这篇论文对SLAM技术的未来发展产生了深远影响，特别是在那些对精确定位有严格需求但受限于环境条件的机器人系统中。通过利用拓扑信息，机器人可以在一定程度上自我校准，从而增强其在复杂环境中的导航性能，这为未来的自主机器人研究开辟了新的道路。

CHOSET AND NAGATANI: TOPOLOGICAL SLAM: TOWARDS EXACT LOCALIZATION WITHOUT EXPLICIT LOCALIZATION 127

visibility graphs [15], etc. (see [15] for a survey of roadmaps).

The roadmap used in this work is the GVG [7], which is the

one-dimensional set of points equidistant to

obstacles in

dimensions. In the plane, the GVG is simply the generalized

Voronoi diagram, which is the set of points equidistant to two

obstacles [21]. In a three-dimensional Euclidean space

, the

GVG is the one-dimensional set of points equidistant to three

obstacles.

Rao [22] achieves exploration by incrementally constructing

the planar GVG in a two-dimensional static polygonal envi-

ronment. Choset and Burdick [6] also describe a method to

construct the GVG in a static

-dimensional environment, but

their approach does not require obstacles to be polygonal, poly-

hedral, nor convex, which are assumptions most motion plan-

ners require. Both methods assume that the robot only uses

line-of-sight information.

Both Rao’s and Choset and Burdick’s methods also assume

that the robot is equipped with a 360

field-of-view high az-

imuth infinite range sensor that detects nearby obstacles. They

do not consider how real range readings can be integrated into

a control law to direct a mobile robot. In this paper, we present

control laws that take low level sensor information and then di-

rects the robot to follow the GVG edges without knowing the

GVG ahead of time. This has the affect of incrementally con-

structing the GVG. Here, low level reactive-style control has a

direct affect on high level behavior of the robot which guaran-

tees that the robot explores an unknown space. This control law

works well in small environments with a mobile robot equipped

with a ring of sonar sensors [9]. Unfortunately the control laws,

by themselves, are not enough for deploying a robot in large

environments because of errors in encoder readings. The main

contribution of this paper is to use the topology encoded in the

GVG to overcome these errors and to localize the robot.

B. Localization

Localization is a major area of mobile robotics that has

received increased attention over the past decade. Again, the

literature in this field is vast, so only work which has influenced

this paper’s results are mentioned. See [3] for a complete

overview of current localization techniques. Lu et al. [17], [18],

[13] use gradient ascent to update various location estimates

forward and backward in time. As a result, this approach has

led to significantly larger maps that are more accurate than

previous approaches, but is still limited to situations with

bounded odometric error. Shatkay and Kaelbling [24] proposed

an approach that uses probabilistic representations, along

with the well-known Baum–Welch algorithm for efficient

estimation. Their approach is similar in nature to the one

described by Thrun [27], in that they both employ probabilistic

representations and both use the Baum–Welch algorithm.

However, the method in [24] does not consider orientation

dead-reckoning error.

Thrun has recently completed a localization approach that

has been successfully verified in very large environments on

a mobile robot where a map is known a priori or the robot

is driven (currently by an external agent) to acquire environ-

mental information [27]. This approach poses a maximum-like-

lihood estimation problem, where both the location of land-

marks and the robot’s position have to be estimated. Likelihood

is maximized under probabilistic constraints that arise from the

physics of robot motion and perception. Just like [27], they use

a Baum–Welch (or alpha–beta) algorithm. Unfortunately, this

approach requires a user to specify the landmarks, as opposed

to the robot self-selecting them. Also, their approach does not

include an exploration strategy. In other words, there is nothing

in their approach that directs the robot to explore new areas, or

that guides the robot to specific locations to reduce dead-reck-

oning error.

C. Localization with Topological Maps

The above localization techniques took the approach of con-

stantly trying to update the robot’s

coordinates relative

to a global frame. In this paper, we localize the robot on a topo-

logical map without ever having to do so explicitly. Others such

as Dudek [11] and Kuipers [14] have reported localization re-

sults with the same philosophy. In [11], an agent locates itself

on a graph by matching nodes and the adjacency relationships

between them. This approach assumes that the agent can label

each node by depositing a marker at the nodes. The approach in

this paper and in [14] has the robot automatically identify nodes

in the topological graph from geometric environmental infor-

mation.

The basic thrust of this paper’s work is quite similar to

Kuiper’s. In [14], the robot essentially traces points that are

equidistant from two portions of the environment until it

reaches a point that is three-way equidistant or until it reaches a

point where a distance threshold is met, at which point the robot

follows the obstacle boundaries. The nodes in this graph are

termed distinct places, which are local maxima of the distance

to nearby obstacles. The robot can easily self-determine distinct

places from sensor data. Distinct places are a subset of the

nodes of the GVG, which are the set of points equidistant

to three obstacles (in other words, there exist examples of

triple equidistance that are not local maxima). Localization is

achieved again by matching distinct places of the graph.

D. Simultaneous Localization and Mapping (SLAM)

Leonard and Durrant-Whyte coined the term SLAM, which

as its name suggests, enables a robot to construct a map of an

unknown environment while using the same map to bound or

nullify positioning errors [16]. With SLAM, the robot must au-

tomatically determine landmarks while constructing the map.

Smith and Leonard [25] developed a feature-based approach to

address SLAM by generating multiple hypothesis and selecting

among them while mapping an unknown region. The work pre-

sented here builds upon Leonard and Durrant-Whyte’s work by

determining a rigorously well-posed method for identifying fea-

tures and the topological relations among them.

Schultz et al. [23] present a more conventional approach to

SLAM that uses certainty grids. This approach is more of an

outgrowthof the algorithms presented in Section II-B. Although

this work does not directly impact the SLAM algorithm pre-

sented in this paper, Schultz and our approaches share some

common ideas and problems.

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