Position and pose are two basic parameters describing the position and attitude of an object in space, and they are extensively researched in robot grasping, automatic driving, and industrial inspection. Traditional attitude estimation methods such as using mechanical, laser tracker, inertial unit, and other attitude measurement systems have their drawbacks, including the need for contact measurement or susceptibility to interference by ambient light, and optical path complexity. As an optical measurement method, the digital image correlation (DIC) method features strong anti-interference ability and a simple optical path without contact. Meanwhile, it has been widely employed in the measurement of displacement, strain, and mechanical properties, but less research on attitude measurement is conducted. At present, there is a position measurement system based on the DIC method, which adopts the space vector method. This method requires the calculation of the inverse tangent function in rotation angle calculation, which has a large error and requires more calculation points. To deal with the shortcomings of the traditional position measurement system, we propose a position estimation system based on the three-dimensional digital correlation (3D-DIC) method to complete the measurement of multiple position parameters of a rigid body in space. Meanwhile, a new position solution method is put forward for the weaknesses of the existing space vector method, and a new matching calculation method is also proposed to solve the problem of DIC in measuring large rotation angles.

The mathematical model of position solution based on singular value decomposition (SVD) is first derived, and then the position measurement system is built for experiments. The specimen which has been sprayed with scattering spots is fixed on a moving platform, and the specimen moves along with the movement of the platform. After calibrating the binocular camera, the image sequences before and after the specimen movement are captured by the binocular camera, and the 3D-DIC is employed to match the image sequences before and after the movement and thus obtain the spatial three-dimensional coordinates of the calculation points. After obtaining a set of 3D coordinates before and after the movement of the calculation points, the SVD method is adopted to solve the rotation matrix and translation matrix, with the movement position parameters of the specimen solved. For the large errors of 3D-DIC in measuring large rotational deformation, we propose the matching calculation method of adding intermediate images. The feasibility and accuracy of the proposed method are verified by the translational degree of freedom and rotational degree of freedom experiments. Finally, a set of accuracy comparison experiments with the space vector method are conducted to verify whether this proposed method is better.

After experimental validation, the position estimation system based on the proposed 3D digital correlation method can realize the measurement of multiple position parameters of a rigid body in space. The absolute errors of the three translational degrees of freedom in the transverse, longitudinal, and elevation are less than 0.07 mm (Fig. 6), and the absolute errors of the yaw and roll angles are less than 0.02° when the rotation angle is less than 10° (Figs. 7 and 9). Meanwhile, the proposed matching calculation method of adding intermediate images also reduces the error of large angle measurement (Fig. 10). The accuracy comparison experiments with the existing space vector method show that the proposed method has smaller measurement errors in rotation angle measurement and requires fewer calculation points (Table 2).

We establish a position estimation system based on the 3D digital image correlation method, and propose a position solution method based on singular value decomposition. The 3D coordinates of the computation point are obtained by taking the image sequence before and after the motion of the object to be measured for the position solution, and multiple position parameter measurement of the spatial rigid body is realized. The results of the three translational degrees of freedom measurement experiments validate that the proposed 3D-DIC-based position measurement system is suitable for measuring the spatial translational degrees of freedom of the rigid body. Additionally, the large-angle measurement experiments verify that the proposed improved matching calculation method which adds intermediate images has obvious improvement in large-angle measurements, and the results of yaw angle and roll angle measurements show that the present measurement system is also applicable to the rotational degree of freedom position measurements of small and large angles. Compared with the traditional position estimation system, our method features high accuracy and a simple optical path without contact. Compared with the existing space vector method, our study has small measurement errors in both yaw and roll angles, and the required number of calculation points is also greatly reduced. In summary, the position and pose measurement system based on our 3D digital image correlation method is suitable for spatial rigid body position measurement, and the measurement accuracy is high, which meets the measurement requirements.