• Proceedings of the KSME Conference
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• 2003.04a
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• pp.822-827
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• 2003

Topological maps have drawn more attention recently because they are compact, provide natural interfaces, and are applicable to path planning easily. To build a topological map incrementally, Voronoi diagram was used by many researchers. The Voronoi diagram, however, has difficulty in applying to arbitrarily shaped objects and needs long computation time. In this paper, we present a new method for global topological map from the local topological maps incrementally. The local topological maps are created through a thinning algorithm from a local grid map, which is built based on the sensor information at the current robot position. A thinning method requires simpler computation than the Voronoi diagram. Localization based on the topological map is usually difficult, but additional nodes created by the thinning method can improve localization performance. A series of experiments have been conducted using a two-wheeled mobile robot equipped with a laser scanner. It is shown that the proposed scheme can create satisfactory topological maps.

• The Journal of Korea Robotics Society
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• v.6 no.3
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• pp.247-254
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• 2011

This paper presents a method of sonar grid map matching for topological place recognition. The proposed method provides an effective rotation invariant grid map matching method. A template grid map is firstly extracted for reliable grid map matching by filtering noisy data in local grid map. Using the template grid map, the rotation invariant grid map matching is performed by Ring Projection Transformation. The rotation invariant grid map matching selects candidate locations which are regarded as representative point for each node. Then, the topological place recognition is achieved by calculating matching probability based on the candidate location. The matching probability is acquired by using both rotation invariant grid map matching and the matching of distance and angle vectors. The proposed method can provide a successful matching even under rotation changes between grid maps. Moreover, the matching probability gives a reliable result for topological place recognition. The performance of the proposed method is verified by experimental results in a real home environment.

• Proceedings of the KIEE Conference
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• 2004.07d
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• pp.2450-2452
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• 2004

Map building is essential to a mobile robot navigation system. Localization and path planning methods depend on map building strategies. A topological map is commonly constructed using the GVG(Generalized Voronoi Graph). The advantage of the GVG based topological map is compactness. But the GVG method have many difficulties because it consists of collision-free path. In this paper, we proposed an extended map building method, the AVG (Areal Voronoi Graph) based topological map. The AVG based topological map consists of collision-free area. This feature can improve map building, localization and path planning performance.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.6
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• pp.492-497
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• 2002

Map building is the process of modeling the robot's environment. The map is usually built based on a grid-based or topological approach, which has its own merits and demerits. These two methods, therefore, can be integrated to provide a better way of map building, which compensates for each other's drawbacks. In this paper, a method of building the topological map based on the occupancy grid map through a Voronoi diagram is presented and verified by various simulations. This Voronoi diagram is made by using a labeled Voronoi diagram scheme which is suitable for the occupancy grid maps. It is shown that the Proposed method is efficient and simple fur building a topological map. The simple path-planning problem is simulated and experimented verify validity of the proposed approach.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.7
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• pp.693-699
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• 2006

An accurate and compact map is essential to an autonomous mobile robot system. For navigation, it is efficient to use an occupancy grid map because the environment is represented by probability distribution. But it is difficult to apply it to the large environment since it needs a large amount of memory proportional to the environment size. As an alternative, a topological map can be used to represent it in terms of the discrete nodes with edges connecting them. It is usually constructed by the Voronoi-like graphs, but in this paper the topological map is incrementally built based on the local grid map using the thinning algorithm. This algorithm can extract only meaningful topological information by using the C-obstacle concept in real-time and is robust to the environment change, because its underlying local grid map is constructed based on the Bayesian update formula. In this paper, the position probability is defined to evaluate the quantitative reliability of the end nodes of this thinning-based topological map (TTM). The global TTM can be constructed by merging each local TTM by matching the reliable end nodes determined by the position probability. It is shown that the proposed TTM can represent the environment accurately in real-time and it is readily extended to the global TTM.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.38.3-38
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• 2002

$\textbullet$ The topological map using a thinning needs much simpler computation than that using a Voronoi. $\textbullet$ A thinning can provide much information on the environment (additional nodes). $\textbullet$ Each node created in a local map is considered as temporary and redundant nodes are discarded. $\textbullet$ A global topological map can be built fast and correctly through a thinning algorithm. $\textbullet$ Path planning can be easily achieved with a topological map.

• The Journal of Korea Robotics Society
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• v.6 no.2
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• pp.189-196
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• 2011

This paper presents a method of topological modeling using only low-cost sonar sensors. The proposed method constructs a topological model by extracting sub-regions from the local grid map. The extracted sub-regions are considered as nodes in the topological model, and the corresponding edges are generated according to the connectivity between two sub-regions. A grid confidence for each occupied grid is evaluated to obtain reliable regions in the local grid map by filtering out noisy data. Moreover, a convexity measure is used to extract sub-regions automatically. Through these processes, the topological model is constructed without predefining the number of sub-regions in advance and the proposed method guarantees the convexity of extracted sub-regions. Unlike previous topological modeling methods which are appropriate to the corridor-like environment, the proposed method can give a reliable topological modeling in a home environment even under the noisy sonar data. The performance of the proposed method is verified by experimental results in a real home environment.

• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2834-2836
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• 2000

This paper introduces the behavior-based learning controller for mobile robot using topological map. When the mobile robot navigates to the goal position, it utilizes given information of topological map and its location. Under navigating in unknown environment, the robot classifies its situation using ultrasonic sensor data, and calculates each motor schema multiplied by respective gain for all behaviors, and then takes an action according to the vector sum of all the motor schemas. After an action, the information of the robot's location in given topological map is incorporated to the learning module to adapt the weights of the neural network for gain learning. As a result of simulation, the robot navigates to the goal position successfully after iterative gain learning with topological information.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.5
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• pp.450-456
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• 2006

Monte Carlo localization is known to be one of the most reliable methods for pose estimation of a mobile robot. Although MCL is capable of estimating the robot pose even for a completely unknown initial pose in the known environment, it takes considerable time to give an initial pose estimate because the number of random samples is usually very large especially for a large-scale environment. For practical implementation of MCL, therefore, a reduction in sample size is desirable. This paper presents a novel approach to reducing the number of samples used in the particle filter for efficient implementation of MCL. To this end, the topological information generated through the thinning technique, which is commonly used in image processing, is employed. The global topological map is first created from the given grid map for the environment. The robot then scans the local environment using a laser rangefinder and generates a local topological map. The robot then navigates only on this local topological edge, which is likely to be similar to the one obtained off-line from the given grid map. Random samples are drawn near the topological edge instead of being taken with uniform distribution all over the environment, since the robot traverses along the edge. Experimental results using the proposed method show that the number of samples can be reduced considerably, and the time required for robot pose estimation can also be substantially decreased without adverse effects on the performance of MCL.

• Bulletin of the Korean Mathematical Society
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• v.61 no.4
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• pp.1137-1159
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• 2024

In the paper, we prove that if a continuous map of a compact uniform space is equicontinuous and pointwise topologically stable, then it is persistent. We also show that if a sequence of uniformly expansive continuous maps of a compact uniform space has a uniform limit and the uniform shadowing property, then the limit is topologically stable. In addition, we introduce the concepts of shadowable points and topologically stable points for a continuous map of a compact topological space and obtain that every shadowable point of an expansive continuous map of a compact topological space is topologically stable.