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# Exact Cell Decomposition of Arrangements used for Path Planning in Robotics

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This is short overview of research paper.

We present a practical algorithm for the automatic generation of a map that describes the operation environment of an indoor mobile service robot. The input is a CAD description of a building consisting of line segments that represent the walls. The algorithm is based on the exact cell decomposition obtained when these segments are extended to infinite lines, resulting in a line arrangement. The cells are represented by nodes in a connectivity graph. The map consists of the connectivity graph and additional environmental information that is calculated for each cell. The method takes into account both the path planning and position verification requirements of the robot and has been implemented.

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### Exact Cell Decomposition of Arrangements used for Path Planning in Robotics

1. 1. Exact Cell Decomposition of Arrangements used for Path Planning in Robotics Nora H. Sleumer / Nadine Tschichold-Gurman Institute of Theoretical Computer Science Institute of Robotics Swiss Federal Institute of Technology Zurich, Switzerland
2. 2. Abstract We present a practical algorithm for the automatic generation of a map that describes the operation environment of an indoor mobile service robot. The input is a CAD description of a building consisting of line segments that represent the walls. The algorithm is based on the exact cell decomposition obtained when these segments are extended to infinite lines, resulting in a line arrangement. The cells are represented by nodes in a connectivity graph. The map consists of the connectivity graph and additional environmental information that is calculated for each cell. The method takes into account both the path planning and position verification requirements of the robot and has been implemented.
3. 3. Problem Statement A CAD representation of a building defined by 39 line segments representing the walls. The robot A moves in the white workspace outlined by grey obstacles.
4. 4. Existing Solutions RoadMap(Visibility Graphs) Approximate Cell Decomposition
5. 5. Existing Solution ● ● Exact Cell decomposition
6. 6. The Arrangement Method The 39 line segments (walls) result in an arrangement of 26 lines that decompose the free space into 76 cells.
7. 7. Algorithm Steps ● ● ● ● Extend the line segments representing the walls to lines. Compute the arrangement and store in an appropriate data structure Merge the cells that are split unnecessarily Calculate the environmental information for each cell
8. 8. Final Output Arrangement decomposition with corresponding graph after cell merging. The number of cells inside the building has been reduced from 76 to 39.
9. 9. Experimental Results
10. 10. Questions ???