A Three-Dimensional Trajectory Measurement System for Quasi-One-Dimensional High-Speed Moving Objects

Abstract The three-dimensional (3D) trajectory measurement of a quasi-one-dimensional (quasi-1D) high-speed moving object often cannot achieve the optimizations of both the measurement range and the object’s resolution at the same time. In this paper, a 3D trajectory measurement system for quasi-1D high-speed moving objects is proposed. The system was composed of a single camera and a galvo mirror. The posture of the virtual camera is changed by adjusting the angle of the galvo mirror, thereby achieving the tracking and imaging of a quasi-1D high-speed moving object. For a background with complex textures, a measurement method based on the reconstructed homography matrix is proposed. The extrinsic matrix of the virtual camera is estimated based on the feature points on the background, and the equation of the object trajectory’s plane is estimated based on the feature points on the object. Then, by combining the extrinsic matrix and the equation of the plane, a new homography matrix is reconstructed, realizing the measurement of the 3D coordinates of the object. For a background with weak textures, a method based on the deflection angle of the galvo mirror is proposed for the calibration of the extrinsic matrix of the virtual camera. This method can calculate the extrinsic matrix of the virtual camera based on the distance from the camera to the center point of the galvo mirror and the deflection angle of the galvo mirror. The experimental results show that the proposed system is able to increase the field of view by 430%. For complex-texture backgrounds, the relative error of the system is 0.79%, and for weak-texture backgrounds, the relative error is 4.65%.