Analysis of the 3D Detection Algorithm Results

Next, the ability to detect and identify pipe structures in different directions is also tested and the results are analyzed. Therefore, the 3D detection algorithm is first put to test in a 10 cm inner-diameter straight pipe with a simple reduction, a type 1 pipe structure as specified in section 2.2.1. The 45 % reduction of the diameter occurs over a distance of 20 cm, resulting in a 5.5 cm straight pipe section after the reduction. A picture of the simulated environment is appended (see figure D.10). For this simulation the ideal LiDAR sensor is used and moved towards the reduction at increments of 5 cm after each full 180° rotation of the servo. During the simulation it is observed that the reduction is first detected just 5 cm before the reduction starts. This relatively late detection of the section is due to the fact that the average radius is calculated from all detected points at each measurement instance. Because the reduction is not abrupt, but occurs gradually over the 20 cm distance, the change in radius is also small. When a type 1 pipe section is detected, the algorithm returns the smallest diameter detected and the minimum distance to this. This is generally considered to be the new pipe diameter after the reduction and the distance to the end of the reduction. During the simulation the sensor block is moved towards the end of reducing part of the pipe. The results obtained during this motion are analyzed and tabulated in table 5.1. As the distance to the end changes while moving through the reduction, the mean and standard deviation of this are not included.

Table 5.1: Analysis of the pipe properties calculated by 3D detection algorithm at distances of 25 cm to 5 cm before the end of the reduction is reached.

Reduction

(Type 1) Mean

Standard Deviation

Average Error

from the real value Unit Estimated Distance to

the end of the reduction x x 1.88 cm

Estimated Diameter of the

pipe after the reduction 5.38 0.1 0.12 cm

Due to the PIRATE its clamping method, it can easily adjust when driving through reductions. So detection of these does not have much added value for autonomous motion. The detection of bends, however, does provide notable information that will aid in autonomous navigation of these. Therefore, the 3D detection algorithm is tested in a simulated 45° pipe bend. The pipe is rotated in a way such that the direction of the bend, with respect to the horizontal initial position of the sensor (its virtualx-axis), is 136°. The point cloud obtained while driving through this pipe structure, seen in figure 5.5, gives a clear visualisation of this. The bend is first detected approximately 30 cm before its entrance. The algorithm correctly identifies the bend, as a type 2 pipe structure, up to approximately 15 cm before its entrance. The pipe properties that are estimated within this region are analyzed, of which the results are presented in table 5.2. Note that when a type 2 section is identified the diameter is assumed to remain the same, therefore it is disregarded in the analysis. A noteworthy observation from the analysis of the data, is the increasing error of the estimated direction while approaching the bend. The error increases6 from just 3° to 28°, resulting in the large statistical values

6

The actual estimated properties are presented graphically in figure D.13, where the increasing error can be observed.

Master Thesis Results & Discussion

for the direction in table 5.2. This is, likely, due to the fact that the direction is estimated using the center of the estimated ellipse from the outline points. Since these points might not exactly form a circle or ellipse from every measurement, the resulting estimation varies every time. The statistical properties of the estimated angle of the bend, on the other hand, are satisfactory during the entire detection. It should also be noted that when the sensor is very close to the bend, this gets identified as a type 1 section. This is expected, since the algorithm cannot identify an outline anymore.

Figure 5.5: 3D Point cloud, with respect to the global (x,y,z) coordinate frame, obtained while driving through a simulated 45° pipe bend. The pipe is oriented with the bend at an angle of 44° from the positive y-axis.

Table 5.2: Analysis results of the pipe properties estimated by the 3D detection algorithm in the range between 30 cm and 15 cm before the entrance of the 45° bend.

Bend (Type 2) Mean Value Standard Deviation Average Error

from real value Unit Distance to the

Entrance x x 4.04 cm

Direction 147.33 11.14 11.35 °

Angle 45.87 1.31 1.2 °

Lastly, the 3D detection algorithm is put to the ultimate test of identifying multiple junctions. For this test a horizontally oriented cross-junction, a type 3 pipe structure, is simulated in Gazebo. During this test, the structure is detected when the sensor is at a distance between 15 cm and 5 cm from the center of the cross-junction. The algorithm again correctly identifies the structure and returns that there are three possible options. The estimated properties of the first two options are analyzed, whereas the third option is simply the option to keep going forward. The results of the statistical analysis are presented in table 5.3. In these results it is noticeable that the standard deviations are much smaller than before. This because, the outline of pipe sections orthogonal to the centerline7 has a more elliptical form than that of pipe sections at a different angle from the centerline. Due to

Master Thesis Results & Discussion

this, the similar ellipse parameters are estimated at each position of the sensor (within the detection range).

Table 5.3: Statistical analysis results of the estimated pipe properties, calculated by the 3D detection algorithm at distances between 15 cm and 5 cm from the center of a cross-junction.

Cross Junction

(Type 3) Option Mean

Standard Deviation

Average Error

from real value Unit Distance to the Entrance 1 x x 2.10 cm 2 x x 2.09 Diameter 1 8.93 0.24 1.07 cm 2 9.16 0.21 0.84 Direction 1 0.03 0.33 0.29 ° 2 187.75 0.75 7.75 Angle 1 89.58 0.94 0.83 ° 2 89.17 1.51 1.27