Robust and Unbiased Estimation of Robot Pose and Pipe Diameter for Natural Gas Pipeline Inspection Using 3D Time-of-Flight (ToF) Sensors

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.