Objective With the advantage of the characteristic of parallel multitask and space expandability, a large-scale distributed measurement system is widely used in mechanical manufacturing. Based on the intersection-positioning mechanism of multisource observations, large-scale distributed measurement system constructs an integrated measurement network. The positioning of the system determines the performance and applicability of the whole network. The precision and quantity of orientation constraints are easily restricted by on-site conditions and environment. Represented by the angle intersection measurement system, typical distributed measurement systems consist of multiple vision measurement systems, theodolite measurement system, and workshop Measurement-Positioning System (wMPS). Considering the relative position and postural relationship among the measurement units as the optimization parameters, the objective function of the orientation process is established through redundant geometric constraints and the intersection relation between measurement units and the measured points. The final orientation parameters are obtained by the optimization method. In the conventional method, geometric constraints are constructed by auxiliary equipment, which is disadvantageous to use in complex occlusion environment.

Methods Solving the under-constraint problem for the distributed measurement system, an orientation method based on angle and length constraints is presented. It combines a high-precision dual-axis inclinometer with measurement units of distributed measurement systems. The proposed orientation method is deduced based on the wMPS. First, the general orientation principle of the distributed measurement system is established. The proposed orientation method is developed based on the general orientation principle. Second, a new orientation method is built by an dual-axis inclinometer and length constraints supported by the scalar bar. A relative postural orientation model is established according to the horizontal constraints supported by an inclinometer. The proposed method depends on the relative posture between the inclinometer and wMPS transmitter, which can be obtained by precalibration. Using internal angle constraints provided by a high-precision angle measuring instrument, the orientation parameters are processed by the multihierarchical stage, and the number of length constraints for the orientation is decreased, which can improve the orientation efficiency. Considering wMPS as the experimental platform, the combined system prototype is developed to investigate the influence of the number and distribution of orientation conditions on the orientation accuracy and robustness of the orientation method.

Results and Discussions To analyze the influence of the measuring error of inclinometer on the orientation method, some simulations are performed. In the simulation, a space of 10 m×2 m×2 m away from wMPS transmitter is used as orientation and measurement space. The measuring error of inclinometer set in simulation is 2″. The point measuring error is less than 0.1 mm (Fig.6), and length measuring error is less than 0.2 mm (Fig.7). A series of experiments are conducted. The angle resolution of high-precision dual-axis inclinometer used in the experiment is 0.0001°. The angle measurement accuracy is greater than 2″. The experimental site consists of several wMPS transmitters using a built-in inclinometer and a scalar bar. The two ends of the scalar bar are compatible with the same size spherically-mounted retroreflector and wMPS receiver. The length of the scalar bar is calibrated by the laser tracker. To analyze the influence of the horizontal constraints on the orientation result, the number of length constraints used in orientation is gradually increased from 2 to 12, and the orientation method based and not based on horizontal constraints are used to implement the orientation process, respectively. The same scalar bar is used to verify the accuracy of different positions in the measurement space 10 times. Besides, the average length measuring error is used as the evaluation index. Using two positions for orientation, the length measuring error of the conventional method (not based on horizontal constraints) is greater than 9 mm and unstable. However, the proposed method length measuring error is 0.56 mm, which is consistent with the conventional method using five positions. With the increase in the number of length constraints, the length measuring error of the two methods decreases and tends to be stable. When the number of length constraints exceeds eight, the conventional method length measuring error is close to that of the proposed method that is less than 0.2 mm (Fig.9). To verify the robustness of the proposed method, keeping the number of length constraints used in the orientation unchanged as 2, change the placement form of the scalar bar, and perform the orientation experiment based on the proposed method. After orientation, the same scalar bar is measured to test the accuracy of the system. The standard deviation of the length measuring error with 10 positions is better than 0.3 mm (Fig.10), indicating the orientation method robustness.

Conclusions In this study, an orientation method of a distributed measurement system based on hierarchical geometric constraints is investigated. Using the horizontal geometric and length constraints, the number of constraints required by the orientation model is effectively decreased. Finally, the effectiveness and adaptability of the proposed method are verified using wMPS as an experimental platform. In a complex environment, when the orientation conditions are limited, a new method can meet the measurement needs of the industrial field and has a certain application prospect.