## 6 Results
### Experiment Setups  
To evaluate our proposed approach, we develop a pull-rig robot and a 20-inch prototype pipeline. Figure 15 shows the prototype pipeline consisting of four 6-m straight pipes, one 1.5D elbow, and one T-junction with the same shape and size as the real gas pipeline. The 1.5D elbow has a radius of 1.5 times the pipe diameter, which is 762 mm. The elbow angle is 90\({}^{\circ}\), which has a length of 1.196 m. The T-junction branch has the same radius as the main pipe. Figure 16 shows the robot and its components. The robot consists of two parts: a head and a tail, each of which is equipped with passive wheels to move along the pipeline. Figure 14: Sequence diagram of the multi-processor offloading scheme. A rope is attached to the front and the end of the robot to pull the robot forward and backward. The main components of the robot include a Helios2 3D ToF camera, an IMU, an odometer, and a processing unit which are distributed on the tail and head parts, as in Figure 16. The robot speed is approximately 0.5 m/s when approaching the elbow and T-junction. The processing unit is the Xilinx Zynq 7000 system, which is the same as the one used in the real PIG. To address the high-pressure environment in gas pipelines, the 3D ToF camera needs a pressure-resistant enclosure with a cover glass that is strong enough for the pressure and has minimal effect on the measurement. Types of glass are considered for the cover glass, including tempered glass, polycarbonate, and polymethyl methacrylate. The selection criteria for the cover glass are twofold: (1) the flexural strength, i.e., the strength against the bending, and (2) the transmittance, i.e., the ratio of light that can go through the glass. Table 2 shows these criteria on 10-mm thickness glasses of each type. We choose polymethyl methacrylate as the cover glass material which has the best transmittance and the second highest flexural. We verify with the pressure test that the enclosure with polymethyl methacrylate cover glass can endure the real pipe pressure. On the other hand, we address another key issue of the cover glass, which is the interference from the internal reflection,  
Figure 16: Pull-rig robot. Figure 15: Prototype pipeline. as shown in Figure 17. When the light travels from the glass to the outer environment, part of it is reflected back into the glass (red arrow). Through multiple reflections, it may reach the receiver and interfere with the actual returning light from the object (orange arrow). To alleviate this issue, the anti-reflection coating is applied to the glass. Table 3 shows the transmittance before and after coating on one or both sides. We select both-side coating since it has the highest transmittance, i.e., the lowest interference. The Helios2 3D ToF camera has a resolution of \(640\times 480\) and a field of view of \(69^{\circ}\times 51^{\circ}\). The frame rate is fixed at 10 Hz. Figure 18 shows three point clouds without and with the existence of the elbow and T-junction. Data points with an \(X\)-position below 0.5 m do not completely cover the circumferential direction of the pipe while data points with an \(X\)-position above 2.0 m do not show the correct pipe shape or are randomly invalid, as illustrated in Figure 18a. Therefore, we choose the data points with an \(X\)-position between 0.5 and 2 for processing. Moreover, the data points within \((1.2,2)\) m are used for ETDE, while the range \((0.5,1.2)\) is used for camera pose estimation. Figure 18b,c show the point cloud of the elbow and T-junction in this range. We perform four experiments with different robot roll angles at the entry point, i.e., \((0^{\circ},90^{\circ},180^{\circ},270^{\circ})\). Figure 19 shows the camera coordinate system and the first straight pipe coordinate system, as well as the rear view of the robot at the entry point of the pipeline. Note that the robot Z-axis has the same direction as the 3D ToF camera Z-axis.