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Exact Cell Decomposition of Arrangements used for Path Planning in Robotics
The document presents an algorithm for generating a map of an indoor environment for mobile service robots, using a CAD description of a building's walls. It employs an exact cell decomposition method that transforms wall segments into infinite lines, resulting in a connectivity graph for path planning and position verification. The algorithm successfully reduces the number of cells from 76 to 39 while providing environmental information for each cell.
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Exact Cell Decomposition of Arrangements used for Path Planning in Robotics
- 1. Exact Cell Decompositionof 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. Abstract We present apractical 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. Problem Statement A CADrepresentation of a building defined by 39 line segments representing the walls. The robot A moves in the white workspace outlined by grey obstacles.
- 4. Existing Solutions RoadMap(Visibility Graphs) ApproximateCell Decomposition
- 5. Existing Solution ● ● Exact Celldecomposition
- 6. The Arrangement Method The39 line segments (walls) result in an arrangement of 26 lines that decompose the free space into 76 cells.
- 7. Algorithm Steps ● ● ● ● Extend theline 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
- 9. Final Output Arrangement decompositionwith corresponding graph after cell merging. The number of cells inside the building has been reduced from 76 to 39.
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