The estimation of robot pose and pipe diameter is an essential task for reliable in-line inspection (ILI) operations and the accurate assessment of pipeline attributes. This paper addresses the problem of robot pose and pipe diameter estimation for natural gas pipelines based on 3D time-of-flight (ToF) sensors. To tackle this challenge, we model the problem as a non-linear least-squares optimization that fits 3D ToF sensor measurements in its local coordinates to an elliptic cylindrical model of the pipe inner surface. We identify and prove that the canonical ellipse-based estimation method (C-EPD), which uses a canonical residual function, suffers from bias in diameter estimation due to its asymmetry to depth errors. To overcome this limitation, we propose the robust and unbiased estimation of pose and diameter (RU-EPD) approach, which employs a novel error-based residual function. The proposed function is symmetric to depth errors, effectively reducing estimation bias. Extensive numerical simulations and prototype pipeline experiments demonstrate that RU-EPD outperforms C-EPD, achieving an at least six times lower estimation bias and a 2.5 times smaller estimation error range in pipe diameter and about a 2 times smaller estimation error range in pose estimation.

An accurate estimation of pipe attributes, pose of pipeline inspection gauge (PIG), and downstream pipeline topology is essential for successful in-line inspection (ILI) of underground compressible gas pipelines. Taking a 3D point cloud of light detection and ranging (LiDAR) or time-of-flight (ToF) camera as the input, in this paper, we present the simultaneous pipe-attribute and PIG-pose estimation (SPPE) approach that estimates the optimal pipe-attribute and PIG-pose parameters to transform a 3D point cloud onto the inner pipe wall surface: major- and minor-axis lengths, roll, pitch, and yaw angles, and 2D deviation from the center of the pipe. Since the 3D point cloud has all spatial information of the inner pipe wall measurements, this estimation problem can be modeled by an optimal transformation matrix estimation problem from a PIG sensor frame to the global pipe frame. The basic idea of our SPPE approach is to decompose this transformation into two sub-transformations: The first transformation is formulated as a non-linear optimization problem whose solution is iteratively updated by the Levenberg–Marquardt algorithm (LMA). The second transformation utilizes the gravity vector to calculate the ovality angle between the geometric and navigation pipe frames. The extensive simulation results from our PIG simulator based on the robot operating system (ROS) platform demonstrate that the proposed SPPE can estimate the pipe attributes and PIG pose with excellent accuracy and is also applicable to real-time and post-processing non-destructive testing (NDT) applications thanks to its high computational efficiency.

In-line inspection (ILI) is essential for maintaining the integrity of natural gas pipelines. In ILI, pipeline inspection gauges (PIGs) autonomously navigate through pipelines under real-time and resource-constrained conditions to measure pipeline irregularities. Elbow and T-junction detection and estimation (ETDE) play a critical role in enabling PIG navigation to avoid speed excursions which prevent effective data collection or even damage the PIG and pipelines. Existing approaches are often computationally intensive, incomplete, or late estimations, making them unsuitable for real-time operation in such environments. This paper proposes a real-time elbow and T-junction detection and estimation (RT-ETDE) framework that efficiently detects elbows and T-junctions and estimates their critical parameters for PIG navigation using 3D point clouds. Our framework relies on intelligent point cloud partition and feature extraction together with simple geometric solutions which greatly reduce computational complexity. Furthermore, several real-time adaptation techniques are introduced to ensure real-time operation. Experimental results on a prototype pipeline demonstrate that the RT-ETDE framework consistently detects elbows and T-junctions while achieving a 10 Hz frame rate on a real PIG processing unit, validating its suitability for next-generation pipeline inspection systems.