## Topological Simultaneous Localization and Mapping (SLAM): Toward Exact Localization Without Explicit Localization (2001)

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Venue: | IEEE Transactions on Robotics and Automation |

Citations: | 185 - 10 self |

### BibTeX

@ARTICLE{Choset01topologicalsimultaneous,

author = {Howie Choset and Keiji Nagatani},

title = {Topological Simultaneous Localization and Mapping (SLAM): Toward Exact Localization Without Explicit Localization},

journal = {IEEE Transactions on Robotics and Automation},

year = {2001},

volume = {17},

pages = {125--137}

}

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### Abstract

One of the critical components of mapping an unknown environment is the robot's ability to locate itself on a partially explored map. This becomes challenging when the robot experiences positioning error, does not have an external positioning device, nor the luxury of engineered landmarks placed in its free space. This paper presents a new method for simultaneous localization and mapping that exploits the topology of the robot's free space to localize the robot on a partially constructed map. The topology of the environment is encoded in a topological map; the particular topological map used in this paper is the generalized Voronoi graph (GVG), which also encodes some metric information about the robot's environment, as well. In this paper, we present the low-level control laws that generate the GVG edges and nodes, thereby allowing for exploration of an unknown space. With these prescribed control laws, the GVG (or other topological map) can be viewed as an arbitrator for a hybrid control system that determines when to invoke a particular low-level controller from a set of controllers all working toward the high-level capability of mobile robot exploration. The main contribution, however, is using the graph structure of the GVG, via a graph matching process, to localize the robot. Experimental results verify the described work. Index Terms---Exploration, localization, mapping, mobile robots, motion planning, tologoical maps, Voronoi diagrams. I.

### Citations

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Citation Context ...nning is heuristic and is limited to the plane. One class of heuristic algorithms employs a behavior-based approach in which the robot is armed with a simple set of behaviors (e.g., following a wall) =-=[4]-=-. Another heuristic approach involves discretizing a planar world into pixels of some resolution. Typically, this approach handles errors in sonar sensing readings quite well by assigning each pixel a... |

1997 |
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Citation Context ... field has produced many roadmaps: silhouette methods [5], Voronoi diagrams [21],sCHOSET 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 si... |

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Citation Context ...ecade. 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... |

407 | A robot exploration and mapping strategy based on a semantic hierarchy of spatial representations
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Citation Context ...lief that the topological and geometric structure of free space induce a natural hierarchy of symbols and connections among these symbols that represent free space. At a high level, a topological map =-=[14]-=- serves as an example of symbols and connections between them. For Kuipers, the symbols are distinct places, which are local maxima of the distance to nearby obstacles, and the connections are the gra... |

290 |
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Citation Context ...e features as low-level symbols that guide the robot from one high-level symbol to the next. At a low level, the robot’s environment can be modeled by a local map such as a fine array of pixels [20]=-=; [12]. -=-Thrun et al. [27] have been incredibly successful in demonstrating their probabilistic approach in museum environments using a grid-map representation. It is the belief of the authors that Thrun’s m... |

170 | Real-Time Obstacle Avoidance for Fast Mobile Robots
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Citation Context ...to pixels of some resolution. Typically, this approach handles errors in sonar sensing readings quite well by assigning each pixel a value indicating the likelihood that it overlaps an obstacle [20]; =-=[2]-=-. Many heuristics exist for planning with the discretized map. Many behavior-based heuristics are sometimes termed as reactive control in that low level inputs directly affect the high level behaviora... |

166 |
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Citation Context ... smallest local minimum in the sensor array. When two adjacent sensors have the same value and together form a local minimum, then assume the closest obstacle lies between the two sensors. literature =-=[1]-=-, meet points are called Voronoi vertices, but we use the term meet points because GVG edges terminate (and meet) at them. The planar GVG is . Fig. 5 has examples of planar GVGs. Prior work [21], [7] ... |

153 |
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Citation Context ...not use preplaced landmarks or GPS must employ a localization algorithm while mapping an unknown space, hence the term simultaneous localization and mapping, first coined by Leonard and Durrant-Whyte =-=[16]-=-, [25]. This paper takes a topological approach to SLAM. It is our belief that the topological and geometric structure of free space induce a natural hierarchy of symbols and connections among these s... |

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Citation Context ...evel representation: a topological map. We seek to adapt the structure of a provably correct classical motion planning scheme to a sensor-based implementation. For example, Lumelsky’s “bug” algo=-=rithm [19]-=- proves that a robot using on-line information can plan a path to the goal. This method, however, does not yield a map of an unknown space. Our approach is based on a roadmap [5], a one-dimensional su... |

133 | Learning topological maps with weak local odometric information
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Citation Context ...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] p-=-roposed 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 Thru... |

119 |
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Citation Context ...a 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. Se=-=e [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 approac... |

115 |
Robotic exploration as graph construction
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(Show Context)
Citation Context ...constantly trying to update the robot’s coordinates relative to a global frame. In this paper, we localize the robot on a topological map without ever having to do so explicitly. Others such as Dude=-=k [11]-=- and Kuipers [14] have reported localization results with the same philosophy. In [11], an agent locates itself on a graph by matching nodes and the adjacency relationships between them. This approach... |

92 |
A Retraction Method for Planning the Motion of a Disc
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Citation Context ...aces. For an indoor office-like environments, junctions and termination points of hallways represent symbols while the hallways themselves are the connections. For the generalized Voronoi graph (GVG) =-=[21]-=-; [7] (defined in Section II-A), the Voronoi vertices (we call them meet points) are the symbols while the edges form connections (Fig. 1).s126 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 17, N... |

78 | Sensor based motion planning: The hierarchical generalized voronoi graph
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(Show Context)
Citation Context ...For an indoor office-like environments, junctions and termination points of hallways represent symbols while the hallways themselves are the connections. For the generalized Voronoi graph (GVG) [21]; =-=[7]-=- (defined in Section II-A), the Voronoi vertices (we call them meet points) are the symbols while the edges form connections (Fig. 1).s126 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 17, NO. 2,... |

52 | Optimal and efficient path planning for unknown and dynamic environments
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Citation Context ...o within a tolerance, disambiguate between unscheduled and expected meet points. When the robot does indeed find an unscheduled meet point, it can find a new path using an optimal graph strategy like =-=[26]-=- or it can generate temporary edges until it re-accesses the original GVG. VIII. CONCLUSION This paper formulates a new approach to SLAM of unknown regions using a topological map annotated with some ... |

30 |
Coverage path planning: The Boustrophedon decomposition
- Choset, Pignon
- 1997
(Show Context)
Citation Context ...ault with the GVG, but rather because of a lack of richness of topological information in large open spaces. It is hard to locate oneself in the middle of the desert. Current work in robotic coverage =-=[8]-=- addresses this problem; here the robot must plan a path to pass the sensor-range of the robot over all points of the free space. B. Weak Meet Points Another problem we have encountered is the emergen... |

29 |
A “retraction” method for learned navigation in unknown terrains for a circular robot
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- 1991
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Citation Context ...oronoi 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 environment. Choset and Burdick [6] also describe a method to construct the GVG in a static -di... |

20 |
Constructing roadmaps of semi-algebraic sets
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- 1988
(Show Context)
Citation Context ...ky’s “bug” algorithm [19] proves that a robot using on-line information can plan a path to the goal. This method, however, does not yield a map of an unknown space. Our approach is based on a ro=-=admap [5], -=-a one-dimensional subset of a robot’s free space, which captures all of its important topological properties. A roadmap has the following properties: accessibility; connectivity; and departability. ... |

15 | Sensor based planning: A control law for generating the generalized Voronoi graph
- Choset, Konukseven, et al.
- 1997
(Show Context)
Citation Context ...high level behavior of the robot which guarantees 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 top... |

12 |
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- 1985
(Show Context)
Citation Context ...ing the features as low-level symbols that guide the robot from one high-level symbol to the next. At a low level, the robot’s environment can be modeled by a local map such as a fine array of pixel=-=s [20]-=-; [12]. Thrun et al. [27] have been incredibly successful in demonstrating their probabilistic approach in museum environments using a grid-map representation. It is the belief of the authors that Thr... |

9 |
Vergleich von Algorithmen zur Selbstlokalisierung eines mobilen Roboters
- Gutmann
- 1996
(Show Context)
Citation Context ..., 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,... |

7 |
Sensor based motion planning: Incremental construction of the hierarchical generalized Voronoi graph
- Choset, Burdick
- 2000
(Show Context)
Citation Context ...ensional set of points equidistant to three obstacles. Rao [22] achieves exploration by incrementally constructing the planar GVG in a two-dimensional static polygonal environment. 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, polyhedral, nor convex, which are assumptions most mot... |

6 | Sensor Based Planning: Using a Honing Strategy and Local Map Method to Implement the Generalized Voronoi Graph
- Choset, Nagatani, et al.
- 1997
(Show Context)
Citation Context ...GVG, it is significant that the robot precisely locates itself on the meet points. Thus a meet point homing algorithm was introduced to trace a path that stably converges onto the meet point location =-=[10]-=-. The control law for homing onto a meet point is similar to the one for generating GVG edges, except and its Jacobian are2 and Therefore, at a meet point, i.e., , and the robot makes the following co... |

5 |
Integrating map learning, localization and planning in a mobile robot
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- 1998
(Show Context)
Citation Context ...n. The work presented here builds upon Leonard and Durrant-Whyte’s work by determining a rigorously well-posed method for identifying features 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 outgrowth of the algorithms presented in Section II-B. Although this work does not directly impact ... |

4 | A multiple-hypothesis approach to concurrent mapping and localization for autonomous underwater vehicles
- Smith, Leonard
- 1997
(Show Context)
Citation Context ...e preplaced landmarks or GPS must employ a localization algorithm while mapping an unknown space, hence the term simultaneous localization and mapping, first coined by Leonard and Durrant-Whyte [16], =-=[25]-=-. This paper takes a topological approach to SLAM. It is our belief that the topological and geometric structure of free space induce a natural hierarchy of symbols and connections among these symbols... |

2 |
pose estimation in unknown environments by matching 2D range scans
- “Robot
- 1997
(Show Context)
Citation Context ... 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 appro... |

2 |
Probabilistic mobile robot localization and mapping
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- 1998
(Show Context)
Citation Context ...evel symbols that guide the robot from one high-level symbol to the next. At a low level, the robot’s environment can be modeled by a local map such as a fine array of pixels [20]; [12]. Thrun et al=-=. [27] h-=-ave been incredibly successful in demonstrating their probabilistic approach in museum environments using a grid-map representation. It is the belief of the authors that Thrun’s main contribution is... |