4-DOF pose estimation of a pipe crawling robot using a Collimated Laser, a conic mirror, and a fish-eye camera

A vision-based pose estimation technique for a pipe crawling robot moving inside a pipe is presented with applications in quality control and inspection. The robot carries an on-board sensor that comprises of a Collimated Laser, a 45-degree conic mirror, and a camera with a wide-angle fish-eye lens. The laser reflected on the mirror would project as a circle on the inner wall of the pipe. This would form the image of a perfect circle when viewed by a camera as long as (1) the pipe is perfectly round, (2) the camera is perfectly aligned and calibrated with the laser/mirror, and (3) the whole sensing unit is centered inside the pipe. A novel non-linear optimization method is presented to estimate four degrees of motion, namely the two orthogonal translational sways and the pan and tilt in the robot based on the lasers image. The proposed algorithm assumes that the pipe is round and that the laser/mirror/camera are perfectly aligned. However, a learning component can be readily added to the existing algorithm for uncalibrated systems as well. First, a novel set of image moments with a full-rank interaction matrix is introduced to estimate the aforementioned four degrees of motion. Second, a non-linear polynomial solver is employed. Simulations and experimental results show promising robustness in the proposed method. Also, the pose estimations are comparable to that obtained via expensive military-grade Inertial Measurement Units (IMU) with a much lower cost factor.