Exact Cell Decomposition of Arrangements used for Path
Planning in Robotics

Nora H. Sleumer / Nadine Tschichold-GurmanInstitute of Theoretical Computer Science Institute of RoboticsSwiss Federal Institute of Technology Zurich, Switzerland

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.

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.

Existing Solutions

RoadMap(Visibility Graphs)Approximate Cell Decompostition

RoadMap(Visibility Graphs) Approximate Cell Decomposition

Existing Solution

Exact Cell decomposition

The Arrangement Method

The 39 line segments (walls) result in an arrangement of 26 lines that decompose the free space into 76 cells.

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

Final Output

Arrangement decomposition with corresponding graph after cell merging. The number of cells inside the building has been reduced from 76 to 39.

Experimental Results

Questions ???