# Mobile Robot Path Planning Using a Laser Range Finder for Environments with Transparent Obstacles
## 4 Environment Map Generation Algorithm in a Transparent Obstacle Environment
\begin{table}
\begin{tabular}{c c} \hline \hline
**Terminology** & **Explanation** \\ \hline \(g(x)\) & A function emphasizing the extent of increase of the _SDCMap_(cell) (default function: \(g(x)=x\)) \\ \hline \(TH_{non-glass}\) & The threshold number of _WDC_ to determine opaque obstacle (default value = 5, WDC = weakly detected counter) \\ \hline \(TH_{glass}\) & The threshold number of WDC to determine the transparent obstacle candidate (default value = 1, \(TH_{glass}<TH_{non-glass}\)) \\ \hline \(TH_{glass-surface}\) & The threshold number of WDC to determine the surface of transparent obstacle (default value = 3) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(Cont.\)In Algorithm 1, whether \(d_{n}(t)\) belongs to the range of \(D_{min}\leq d_{n}(t)\leq D_{max}\) is checked first to delete all inaccurate distance information about \(d_{n}(t)\) according to its \(\theta_{n}(t)\) measured from LRF at time \(t\). The distance is calculated using Equation (1) if it belongs to the range. In this paper, LRF's angular resolution is 0.25 degrees, and the size of the cell is 15 cm in the grid map; therefore, two beams detect the same \(cell_{n}(t)\) for a cell that has an opaque obstacle [28]. The angle between the \(n\)-\(1\)th beam and the \(n\)th beam is 0.25 degrees, more than 35 m distance is needed if two beams point to different cells (Figure 8). The value of \(D_{max}\) is 20 m. Therefore, a cell that has an opaque obstacle is always detected by more than two beams. Based on the above information, if \(cell_{n}(t)\) and \(cell_{n\text{ - }1}(t)\) point to the same cell, the probability of \(cell_{n\text{ - }1}(t)\) being an obstacle is increased by adding 1 to \(WDCMap(cell_{n\text{ - }1}(t))\). If (\(cell_{n}t\)) and \(cell_{n\text{ - }1}(t)\) are different, the \(SDCMap(cell_{n\text{ - }1}(t))\) is updated according to the value of \(WDCMap(cell_{n\text{ - }1}(t))\). The algorithm proposed in this paper uses the common feature of reflection noises generated from transparent obstacles while the robot is moving; if the \(SDCMap\) is updated while the robot is not moving, redundant detections are accumulated. Therefore, the \(SDCMap\) may not be updated while the robot is not moving. Updates to the \(SDCMap\) are provided through different methods according to measurements of \(WDCMap(cell_{n\text{ - }1}(t))\). If the \(WDCMap(cell_{n\text{ - }1}(t))>TH_{non\text{ - }glass}\), this denotes that many beams are indicating the same cell simultaneously. This denotes that the probability of (\(cell_{n\text{ - }1}t\)) being an opaque cell is high; therefore, the value of the \(SDCMap(cell_{n\text{ - }1}(t))\) should be increased significantly. ```
Input:\(cell_{L1}\leftarrow\) Result of function finding the closest but not the same cell from \(cell_{R}(t)\) in the list \(L\)\(L\leftarrow\) List of cells included in the virtual line segment \(\text{NUM\_CELLS}\leftarrow\) Last index number of list \(L\) Output:\(SDCMap\leftarrow\) The global map representing the accumulated number of detected sensor beams in a certain cell to decide obstacle cell Begin Algorithm Detect Obstacle Candidate
1 If\(SDCMap(cell_{L1})>0\)then
2 If\(WDCMap(L[\text{NUM\_CELLS}])\geq TH_{glass\text{-}surfac}\)then//\(L[\text{NUM\_CELLS}]\):\(cell_{n-1}(t)\)
3\(SDCMap(cell_{L1})\) += \(g(WDCMap(L[\text{NUM\_CELLS}]))\)
4 Else
5\(SDCMap(cell_{L1})\) += 1 \(\text{INIT\_CELL}\gets 1\)
6\(cell_{L}\leftarrow\)Find\(\_\)NearCell(\(cell_{L1}\), \(L[\text{INIT\_CELL:NUM\_CELLS}]\)) // Function finding the closest but not the same cell from \(L[0]==cell_{L1}\) in the list \(L\)
7 loop:

Figure 8: The relationship between the cell and the laser beam. If the value of the _WDCMap(\(cell_{n-1}(t)\))_ is not high, whether \(cell_{n-1}(t)\) is detected by reflection noise or common noise should be distinguished. For this purpose, the following three conditions are provided. _[Conditions]_

1.