Conceptual Research and Verication of a Single-stage High-precision Pointing Technology

 Abstract: High - precision pointing plays a critical role in optical equipment and laser communication systems. In order to reach the level of sub mrad for pointing accuracy, a two - stage pointing technology is currently widely used. However, this results in significant technical complexity. Therefore, the realization of a high - precision pointing technology under single - stage control is highly challenging. In this study, we find that erase the floating errors of the middle link of the mechanism can effectively improve the pointing accuracy. Based on this assumption, we propose the concept of a single - stage high - precision pointing technology and also establish its mathematical model of drive and an error elimination algorithm. Using modern computer technology, we study the working principle of this single - stage high - precision pointing technology in detail. We also build a prototype and test its performance. The test results show that the uniaxial error of the prototype is no greater than 0.004°, while its spatial synthetic error is no greater than 0.006° and the stability time is less than 100 ms. The test results show that this concept is completely feasible. It is also found that the accuracy of the pointing system can further be improved when the vibration is suppressed, which also represents an important concept for further research. We anticipate that an ultra - high - precision pointing system with single - stage control will be established in the near future.


Introduction
As a key technology of optical equipment for aerospace, high-precision pointing technology is widely used in the fields of aviation and aerospace. Furthermore, even with the rapid development of laser communication systems in recent years, there is still a strong demand for this technology in civil applications.
In the aerospace field, the optical systems of various spacecraft have very stringent requirements for pointing technology, for example, the James Web telescope requires a pointing accuracy that can reach 0.004" [1], while the Large UV Optical Infrared Telescope (LUVOIR, America) currently under development requires a pointing accuracy of no less than 0.00034" [2]. Recently, the staring imaging system of a small satellite and an X-ray imager of a special solar observation satellite, both developed in China, have revealed high accuracy requirements for their pointing systems [3][4]. Furthermore, even the accuracy of the pointing system of China's "Mozi" quantum satellite has reached 2 μrad [5]. The photoelectric tracking and aiming ·2· system is also the core component of the aviation fighter's pod system, it requires the pointing system to meet the accuracy level of sub mrad, for example, the airborne laser communication's pod adopts a composite pointing mechanism and its pointing accuracy reaches 10 μrad [6].
High-precision pointing technology is also key for photoelectric equipment for the landing guidance of carrier-based aircraft [7].
In civil applications, the cluster control of modern unmanned aerial vehicles adopts laser communication, with one of its core components being high-precision pointing systems [8]. In addition, this technology is also the core component of underwater laser communication systems [9]. Therefore, research into high-precision pointing technology still has important significance and value.
At present, only single-stage pointing systems using piezoelectric ceramic material, micro electromechanical system or flexure mechanism can achieve the performance of high-precision pointing [10][11][12], but their workspace is very small and their control is complex [13][14]. Therefore, current high-precision pointing technology must adopt a two-stage technology, i.e., a double stability system with a primary pointing mechanism and a secondary stability of fast mirror. However, the complexity of this two-stage system hinders its application and only recently studies reported that it has been used on satellite photoelectric equipment [15][16]. The realization of high-precision pointing on a single stage is therefore an important research direction for the future. The latest international report is that the accuracy of a single-stage pointing system has reached 80 μrad (0.004°) [17]. Under this background, we propose a concept of single-stage high-precision pointing technology and studied it through theoretical analysis and experiments. This study expounds working principle and verification results of this technology in detail.
These research results lay a foundation for further research in the near future.

Configuration
Although significant progress has been made regarding the development of high-precision pointing systems, further improving the accuracy of pointing systems remains a substantial challenge. The current two-stage pointing system has reached sub mrad accuracy but it also brings technical complexity and instability. A single-stage pointing system is proposed here, with high pointing accuracy achieved by eliminating the floating errors of the middle link of the mechanism, thereby making it a relatively simple system. The research objective of this project is that the uniaxial error is not greater than 0.005°, the spatial synthesis error is not greater than 0.008° and the load is not less than 100 kg. Considering the engineering requirements, researchers have adopted the embedded control technology and write the control software in C, with an upper computer used to simulate the instructions. The composition of this single-stage high-precision pointing system is shown in Figure 1

Pointing mechanism
Because of the high stiffness characteristics of the parallel mechanism [18], its transmission accuracy is better than that of the series mechanism. Therefore, researchers have proposed a two degree of freedom (DOF) parallel mechanism known as the 2RPS mechanism. This mechanism is composed of two sliding pairs Pi (i = 1,2), four ball joint pairs Sj (j = 1-4) and a cylindrical pair R1 and its composition and principle are shown in Figures 2 and 3  Many opinions of the calculation method of the DOF of the spatial mechanism have been proposed but the more recognized method is to convert the spatial mechanism into the solution relationship in the plane [19][20]. Equation (1) is used to calculate the DOF of the parallel mechanism: where W is the number of DOFs for the spatial mechanism, PX is the total number of DOFs for the motion pair, λ is the number of redundant DOFs for the motion pair and N is the number of closed rings of the mechanism. The pointing mechanism has three closed rings, namely, rings I, II and III, as shown in Figure 3. For ring I, its number of DOFs is WⅠ = 10-6-3 × 1 = 1. For ring II, its number of DOFs is WⅡ = 12-8-3 × 1 = 1. For ring III, its number of DOFs is WⅢ = 8-5-3 × 1 = 0. The number of DOFs of the pointing mechanism is W = WⅠ + WⅡ + WⅢ = 2, so the number of DOFs of the pointing mechanism meets the design requirements.

Control strategy
Only when the mechanism has an effective control strategy can it achieve optimal performance. The comprehensive errors are the main reason leading to the loss of precision of parallel mechanism [21][22]. It is necessary for researchers to study a control algorithm with error compensation. Therefore, researchers have proposed a control strategy with error elimination as the core goal, as shown in Figure 4. . If the pointing error is greater than 0.005 °, the controller will continue to adjust the mechanism. When the error is less than 0.005 °, the pointing mechanism will stop pointing，so an error elimination algorithm is necessary.
The vector

Simulation results
The simulation program of the mathematical model was compiled using MATLAB software. The parameters of the pointing mechanism are shown in Table 1. Because the accuracy of parameter b is difficult to guarantee in engineering, we set the error range of b as 5 mm in the calculation program and then calculated the workspace and pointing error of the pointing system.  Figure 9 shows the simulation result of the workspace of the mechanism and its workspace is ± 9° for two axes. The calculation results of the pointing error are shown in Figures 10 and 11. It can be seen from these figures that the uniaxial accuracy of the system is >0.0012° and the spatial synthetic pointing accuracy is >0.002°.

Figure 9
Simulation results of mechanism workspace

Verification
In order to further verify the correctness of this scheme, we manufactured a prototype, as shown in Figure   12. sensor obtains the data of the two axes of the pointing mechanism and these data are shown in Figure 13. It can be seen that the workspace of the mechanism meets the requirement of ±9° for the two axes.

Figure 13
Test results of workspace We tested the uniaxial error loaded with 0 and 110 kg, respectively, and the results are shown in Figure 14. The test results show that the uniaxial error of this pointing system is <0.004° even under the load condition. We also tested the spatial synthetic pointing error of the pointing system and the test results are shown in Figure 15. The synthetic spatial pointing error is <0.006°.
The response speed is also an important parameter to evaluate the pointing system. Generally, the mechanical system will have an adjustment process in the working position. The adjustment time is known as the pointing stability time for the high-precision pointing system and when the stability time of the system is shorter, its response characteristics are better. The researchers tested the stability time of the prototype when the control error band was set as ±0.005° and Figure 16 presents the test results. It can be seen from the data that the stability time of the prototype is <100 ms. The prototype is one of the achievements in the study.
The research objective of this project is the uniaxial error is not greater than 0.005°, the synthesis error is not greater than 0.008° and the load is not less than 100 kg. The experimental results of the prototype have reached these properties, and the prototype performs satisfactorily. The experimental results are analyzed as follows.
(1) This pointing system used a 2-DOF parallel mechanism, which has a workspace of ±9° for two axes with the parameters given in Table 1. The data also show that the mechanism has no singular positions in the workspace.
(2) The uniaxial error of the single-stage pointing system is <0.004° and its spatial synthesis error is <0.006°.
These values are higher than the simulation results. In the test, the researchers observed that the vibration will cause significant disturbance to the test and studies have also proved the impact of vibration on the pointing accuracy [25], so the vibration of the test environment may lead to this difference. The pointing error with load is higher than that without load, and the data with load is also more discrete than the simulation results, which are all due to the discreteness caused by the inertia of load.

Conclusions
The researchers put forward a scheme of high-precision pointing technology in the study, and it adopts an idea of no position floating. The researchers has developed a prototype for proving the idea, which has no floating errors of transmission, and it erased the cumulative errors. This idea can simplify the control algorithm. Even if there is the influence of clearance in the ball hinges [26], the study still achieves the research goal. The main conclusions are as follows: (1) In order to reduce the complexity of the pointing system, a single-stage high-precision pointing technology is proposed. When the prototype of this scheme is loaded with 110 kg, its synthesis error is still no more than 0.006°, its stability time is no more than 100 ms and its workspace is ±9° for two axes, so we have achieved the expected goal. experimental results proved the correctness of this scheme.
(3) In the test, it is found that the vibration has caused significant disturbance to the results; this is because there is no vibration suppression device in the prototype. If the vibration suppression technology is added to the scheme, the pointing accuracy and stability can be further improved, which has also become an important aspect for further research in the future.
(4) The high-precision pointing technology proposed in this study is a single platform and the test also proves that this scheme is correct and realizable. Therefore, the research results of this study can effectively reduce the complexity of the existing pointing technology, so as to provide a method for the compact and lightweight of the system in the future.