# Mobile Robot Path Planning Using a Laser Range Finder for Environments with Transparent Obstacles
## 4 Environment Map Generation Algorithm in a Transparent Obstacle Environment
The cell containing transparent obstacles have higher _WDCMap_ compared to a cell detected by irregular noise due to the regularity of the reflection noise generated by transparent obstacles. Although the value of the \(WDCMap(cell_{n-1}(t))\) is not higher than \(TH_{non-glass}\), if it is higher than the value of \(TH_{glass}\), it is marked as a candidate of transparent obstacle. 2. While the robot is moving, the reflection noise occurs continuously, but common noises occur intermittently by opaque obstacles and the surrounding environment. Using this property, it is considered as a candidate for a transparent obstacle if the \(cell_{n-1}(t)\) at time \(t\) correspond to any of \(CELL_{neighbor}(cell_{n-1}(t-1))\) at time \(t\). 3. The reflection noise generated by transparent obstacles may contain a cell that has low _WDCMap_ because it is not detected continuously; however, if it is detected regularly, it is considered to be a candidate for a transparent obstacle. The following steps progress when conditions 1 and 2 from the above are met. At time \(t\), a list \(L\) of cells is generated (Figure 9), consisting of the cells included in the virtual line segment connecting \(cell_{R}(t)\) and \(cell_{n-1}(t)\). Figure 9: Example of raster conversion. The _SDCMap_ is checked from \(cell_{L1}\), which is closest to the mobile robot, to all other elements in the list \(L\) if a cell identified as an obstacle candidate is found; (Algorithm 2) \(cell_{n-1}(t)\) is checked whether it is detected by reflection noise by the boundaries of the transparent obstacles (\(WDCMap(cell_{n-1}(t))\geq TH_{glass-surfac}\)). If \(cell_{n-1}(t)\) is detected by reflection noise, the _SDCMap_ of \(cell_{L1}\) is increased instead of \(cell_{n-1}(t)\) with a large amount. If \(cell_{n-1}(t)\) is not detected by reflection noise, the _SDCMap_ is increased with a small amount for later updates. Once the _SDCMap_ of \(cell_{L1}\) is increased by a large amount, the _SDCMap_ of those elements that belong to the list \(L\) but \(cell_{L1}\) are decreased by a large amount, and if _SDCMap_ of \(cell_{L1}\) is increased by a small amount, the _SDCMap_ of those elements that belong to the list \(L\) but \(cell_{L1}\) is decreased by a small amount. If all the elements of the list \(L\) are not detected as candidates for obstacles, \(cell_{n-1}(t)\) has a low probability of being an obstacle but would be considered for its probability of being a candidate for an obstacle; \(SDCMap(cell_{n-1}(t))\) is then increased by a small amount. If condition 3 is met, if \(cell_{n-1}(t)\) belongs to \(CELL_{0}(t)\), then it is a case of not being detected continuously but regularly; therefore, considering the probability of being a later candidate of an obstacle, \(cell_{n-1}(t)\) is increased by a small amount, and if it does not belong to \(CELL_{0}(t)\), then \(cell_{n-1}(t)\) is added to \(CELL_{0}(t)\). ## 5 Path Planning in an Environment with Transparent Obstacles

The following conditions are required when making an environment map in an environment with transparent obstacles. _[Conditions]_

1. A path planning method that can be applied to the occupancy grid map must be used. 2. A new path must be generated quickly within the environment map being updated by the sensor data being collected in real time. 3. The generated path should be close to the optimized one. Other than the above conditions, an environment map uses the _SDCMap_, and by using it, three types of cells are generated as not obstacle cell, obstacle cell, and obstacle candidate cell. Therefore, path planning is run according to the Wavefront-propagation algorithm (Table 2, Algorithm 3) with all these conditions considered [24]. Once the grid map is completed using the Wavefront-propagation algorithm, the cost of all the cells to the destination is calculated as in Figure 10a. The spot with a cost of 0 is the destination, and path planning is run based on this. The next cell is chosen by looking at the eight adjacent cells from which the robot stands.