# An Approach for Indoor Path Computation among Obstacles that Considers User Dimension

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## Abstract

**:**

## 1. Introduction

**Figure 1.**Minkowski sums of obstacles to a user and the minimum distance between obstacles. (

**a**) Minkowski sum of obstacles for a user approximated as a circle; (

**b**) union of the Minkowski sum of obstacles and the minimum distance.

**Figure 2.**The union of Minkowski sums contains inner rings and self-intersections. (

**a**) Union of Minkowski sums with one inner ring (the circle denotes a user); (

**b**) self-intersection and inner rings of the Minkowski sums.

**Figure 3.**Creating polygonal boundaries of objects according to inaccessible gaps between the objects (the circle denotes a user with tools, and red lines represent inaccessible gaps). (

**a**) The polygonal boundary for the six objects without inner rings; (

**b**) the simple boundary for the nine objects.

**Figure 4.**Computing a path with simple boundaries of obstacle groups for a user. (

**a**) Selecting groups of obstacles between two locations (the circle denotes the user; boundaries of obstacles are yellow; and the blue line is the direct path); (

**b**) the navigation network considering the inaccessible gaps between obstacles and walls (blue lines denote the buffer of walls; red lines denote inaccessible gaps; and black lines form the network); (

**c**) a schematic representation of the computed shortest path on the network (the path is black); (

**d**) a realistic path by taking into account the size of the user (circles denote the user; and black lines are the path).

## 2. Related Work

## 3. The Proposed Approach

#### 3.1. Compute MD between Obstacles and Find Inaccessible Gaps

#### 3.2. Group Obstacles

- Step 1. Pick an unchecked obstacle as the current obstacle obs. If there is no unchecked obstacle, then go to Step 5. Otherwise, create an empty group gop; add obs to gop; and go to Step 2.
- Step 2. In the linked list of obs, add all of the unchecked members to gop.
- Step 3. For the previously-added members, add all of the unchecked members in their linked lists to the gop.
- Step 4. Repeat Step 3 until no unchecked members are found. Then, the obstacles in the gop form a group. Go to Step 1.
- Step 5. All of the groups have been identified. Count the number of groups and assign each group an ID.

#### 3.3. Select Obstacle Groups

- Step 1. Find the obstacles intersecting the direct path.
- Step 2. Select all of the obstacles from the groups that have an obstacle intersecting the direct path.
- Step 3. Compute a CH with the nodes of all of the selected obstacles and the direct path.
- Step 4. If the current CH intersects or contains new obstacles, look up the groups of the new obstacles, and select all of the obstacles from the new groups. Re-compute a CH.
- Step 5. Iterate Step 4 until there are no other obstacles included by the current CH.

**Figure 8.**Selecting obstacle groups with respect to the start and target location of a user. (

**a**) The direct path intersects two obstacles; (

**b**) selecting the groups of the intersected obstacles; (

**c**) computing a convex hull (CH), and the CH intersects other obstacles; (

**d**) selecting the group of new obstacles in and re-computing the CH; (

**e**) no more obstacles intersect the CH, and then, three groups are selected.

#### 3.4. Create Boundaries for Selected Groups

- Step 1. For a selected obstacle group, check the number of obstacles. If the group includes only one obstacle, then the obstacle’s polygon is the boundary. Otherwise, go to Step 2.
- Step 2. Create a DT with the vertices of all obstacles in the group, and assign the given dimension of the user to the alpha value.
- Step 3. Compute all of the lengths of edges of each triangle in the DT. Preserve a triangle if its edges’ lengths are all less than the alpha value.
- Step 4. In all of the preserved triangles, find the edges only used for one triangle. Form the edges into a boundary.

#### 3.5. Create a Network Considering Inaccessible Gaps with Walls

**Figure 11.**Detecting bottlenecks between a wall and the boundary of an obstacle group and identifying inaccessible edges crossing the bottlenecks.

**Figure 12.**Creating a visibility graph (VG) and a room buffer, removing the inaccessible edges and computing a path for users with a size of 0.8 m. (

**a**) Creating a VG; (

**b**) computing a room buffer; (

**c**) finding inaccessible edges in the bottlenecks; (

**d**) removing the inaccessible edges; (

**e**) the computed path.

## 4. Use Cases

**Figure 13.**The floor plans of two buildings. (

**a**) The floor of the conventional neonatal intensive care unit (CNICU) at the hospital; (

**b**) ground floor of the Architecture Faculty building.

**Figure 14.**Testing the complete approach between two locations for a user with a size of 0.6 m. (

**a**) Computing the bottlenecks between obstacles; (

**b**) grouping the obstacles; (

**c**) selecting obstacle groups; (

**d**) creating the boundaries of the selected groups; (

**e**) creating a VG and removing the inaccessible edges.

**Figure 15.**Path-finding for the sizes of 0.5 m, 0.6 m and 0.8 m on the hospital floor plan. (

**a**) The shortest path for the 0.5 m size; (

**b**) the shortest path for the 0.6 m size; (

**c**) no path for the 0.8 m size.

**Figure 16.**The shortest paths for the sizes 0.5 m, 0.8 m and 1.0 m on the floor plan of the campus building. (

**a**) Path for the 0.5 m size; (

**b**) path for the 0.8 m size; (

**c**) path for the 1.0 m size.

**Figure 17.**(

**a**) The VG regardless of a user’s dimension and (

**b**–

**d**) all of the shortest paths between all doors for the sizes of 0.5 m, 0.6 m and 0.8 m. (a) The complete VG of all obstacles without respect to a user’s dimension; (b) all of the shortest paths for the user with a size of 0.5 m; (c) all of the shortest paths for a user with a size of 0.6 m; (d) all of the shortest paths for the user with a size of 0.8 m.

## 5. Conclusions

**Figure 18.**The computed and genuine minimum distances (MDs) between a convex and a non-convex obstacle. (

**a**) The computed MD in our approach; (

**b**) the genuine MD.

**Figure 19.**The boundaries of three obstacles in our method and in a strict condition. (

**a**) Three obstacles; (

**b**) our boundary for the group of three obstacles; (

**c**) a strict boundary for the group of three obstacles.

**Figure 20.**(

**a**) A user can pass through a gap larger than the diameter of the user’s circle; (

**b**) the user cannot pass through the gap when the diameter is larger; and (

**c**) the user can pass through the gap after a 90-degree turn. (a) The user can pass through the gap when its length is longer than the diameter of the circle; (b) the user cannot pass the gap when its length is shorter than the diameter of the circle; (c) the user can pass through the gap because the user’s short side is smaller than the gap, though the diameter of the circle is larger than the gap.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Liu, L.; Zlatanova, S. An Approach for Indoor Path Computation among Obstacles that Considers User Dimension. *ISPRS Int. J. Geo-Inf.* **2015**, *4*, 2821-2841.
https://doi.org/10.3390/ijgi4042821

**AMA Style**

Liu L, Zlatanova S. An Approach for Indoor Path Computation among Obstacles that Considers User Dimension. *ISPRS International Journal of Geo-Information*. 2015; 4(4):2821-2841.
https://doi.org/10.3390/ijgi4042821

**Chicago/Turabian Style**

Liu, Liu, and Sisi Zlatanova. 2015. "An Approach for Indoor Path Computation among Obstacles that Considers User Dimension" *ISPRS International Journal of Geo-Information* 4, no. 4: 2821-2841.
https://doi.org/10.3390/ijgi4042821