This paper focuses on the challenge of the inability to accurately calibrate the static measurement of a laser tracker across the full scale. To address this issue, this paper proposes to add a hollow corner cube prism on a 50 m high-precision composite guide rail to achieve a double-range measurement of the laser tracker. Data analysis indicated that, in the 77 m identical-directional double-range measurement experiment, the maximum indication error of a single-beam laser interferometer was −29.5 μm, and that of a triple-beam laser interferometer was 14.6 μm, and the measurement indication error was obviously small when the Abbe error was eliminated. The single-point repeatability of the tracker was 0.9 μm. In the 50 m identical-directional verification experiment, the results of the direct measurement outperformed those of the double-range measurement, and the indication errors under standard conditions were −4.0 μm and −8.9 μm, respectively. Overall, the method used in the experiment satisfies the requirements of the laser tracker. In terms of the identical-directional measurement, the measurement uncertainty of the tracker indication error is U ≈ 1.0 μm + 0.2L (k = 2) L = (0~77 m). The proposed method also provides insights for length measurements using other high-precision measuring instruments.

Currently, there are various types of microscales and the conventional line detection system usually has only one detection method, which is difficult to adapt to the diverse calibration needs of microscales. This article investigates the high-precision measurement method of a microscale based on optoelectronics and the image integration method to solve the diversified calibration needs of microscales. The automatic measurement and processing system integrates two methods: the photoelectric signal measurement method and the photoelectric image measurement method. This article studies the smooth motion method based on ordinary linear guides, investigates the method of reducing the cosine error of a small-range interference length measurement, proposes an image-based line positioning method, and studies the edge and center recognition algorithms of the line. According to the experimental data, the system’s measurement accuracy was analyzed using the photoelectric signal measurement method to measure the 1 mm microscale, the maximum difference from the reference value was 0.105 μm, the standard uncertainty was 0.068 μm, and the absolute value of normalized error was less than 1. The accuracy of the image measurement method to measure the 1 mm microscale was consistent with that of the photoelectric signal method. The results show good consistency in the measurement results between the two methods of the integrated measurement system. The photoelectric signal method has the technical characteristics of high measurement efficiency and high accuracy, while the pixel-based measurement of the image method has two-dimensional measurement characteristics, which can realize measurements that cannot be realized by the photoelectric signal method; therefore, the measurement system of optoelectronics and image integration is characterized by high precision and a wide range of measurement adaptations.

Multi-degree-of-freedom (multi-DOF) motion systems are widely employed in precision manufacturing, intelligent robotics, semiconductor equipment, and vision-guided automation, where coordinated control across multiple axes is essential for accurate and stable operation. However, inter-axis coupling, nonlinear dynamics, actuator interactions, and external disturbances pose significant challenges to achieving precise control under dynamically varying conditions. Conventional model-based and data-driven methods often depend on predefined system models or static state-to-action mappings, which can limit their adaptability to complex and changing motion behaviors. To address these challenges, this study develops a hierarchical reinforcement learning framework, termed Option-Critic Soft Actor–Critic (OC-SAC), for adaptive continuous control of multi-DOF motion systems. The framework integrates the temporal abstraction of Option-Critic with the entropy-regularized continuous control of Soft Actor–Critic, enabling high-level option selection for long-horizon control strategies and low-level policy optimization for fine-grained motion adjustments. Double-Q learning and Prioritized Experience Replay (PER) are further incorporated to mitigate value overestimation and improve the utilization of informative experiences during off-policy learning. The proposed framework is evaluated using the Ant-v5 benchmark and a customized Gym-based multi-DOF error-state control environment. Experimental results show that OC-SAC provides improved convergence behavior and control performance compared with representative reinforcement learning algorithms, while maintaining effective error compensation in the customized multi-DOF environment. These results demonstrate the applicability of hierarchical reinforcement learning to adaptive control of complex multi-DOF motion systems under varying operating conditions.

The Laser interferometer plays an important role in the field of geometrics for large-size measuring applications. Its linear displacement error can be traced from indoor large-scale standard devices. However, the measuring range of the indoor large-scale standard device is too limited to meet the full range measurement of the laser interferometer. So, the lack of accuracy of the results is one of the key issues of laser interferometers. To solve this problem, the corner reflector is used to extend the range of indoor large-scale standard devices, which meet the indication errors in the effective measuring range of the laser interferometer. The range-extension method not only doubles the effective measuring range, but also provides a way to trace the source of other large-size measuring instruments. This work proposes a significant solution to the field of length measurement.