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Abstract
The high-precision measurement of the six degrees-of-freedom (6DoF) relative position and pose deformation of satellites on the ground in vacuum and high-/low-temperature environments plays a critical role in ensuring the on-orbit mapping accuracy of satellites. To meet the strict measurement requirements for a satellite of a high accuracy, high stability, and a miniaturized measurement system, this paper proposes a laser measurement method for simultaneously measuring 6DoF relative position and attitude. In particular, a miniaturized measurement system was developed and a measurement model was established. The problem of error crosstalk between the 6DoF relative position and pose measurements was solved by conducting a theoretical analysis and OpticStudio software simulation, and the measurement accuracy was improved. Laboratory experiments and field tests were then conducted. The experimental results revealed that the measurement accuracy of the developed system for the relative position and relative attitude reached 0.2 µm and 0.4", within the measurement ranges of 500 mm along the X axis, ±100 µm along Y and Z axes, and ±100", and the 24-h measurement stabilities were superior to 0.5 µm and 0.5", respectively, which meets the ground measurement requirements for the satellite. The developed system was successfully applied on site, and the 6Dof relative position and pose deformation of the satellite were obtained via a thermal load test. This novel measurement method and system provides an experimental means for satellite development, in addition to a method for the high-precision measurement of the relative 6DoF position and pose between two points.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The high-precision measurement of a six degrees-of-freedom (6DoF) relative position and pose plays a critical role in multiple fields such as aerospace engineering [1], mechanical manufacturing [2], and precision assembly [3]. On December 29, 2021, a satellite was launched for scientific experimental research, land and resource surveys, and geographic information mapping, among other tasks. As the installation carrier of the satellite payloads, the satellite substrate is influenced by the temperature variation during the on-orbit operation. Moreover, the 6DoF relative position and pose deformation is implemented, which changes the relative position and pose relationship between the payloads and significantly reduces the on-orbit mapping accuracy of the satellite. The deformation law of the satellite can be obtained by measuring the 6DoF relative position and pose due to the temperature variation on the ground. In particular, it can verify the high-stability structure design of the satellite and correct the on-orbit position and pose of the payloads, thus effectively improving the on-orbit mapping accuracy of the satellite [4].
In this context, to obtain the 6DoF relative position and pose deformation of the satellite with a high precision on the ground in vacuum and high-/low-temperature environments, the following requirements are proposed. (1) In the range of ± 100 µm and ± 100", the relative position and pose measurement accuracy should be at the sub-micron and sub-arcsecond scales, respectively. (2) The measurement stability within 24-h should be at the sub-micron and sub-arcsecond scales. (3) The free space in the satellite is limited due to the compact layout of satellite payloads, the volume requirement of the two parts of the measurement system should be 100 × 100 × 100 mm3.
The commonly used 6DoF relative position and pose measurement methods include laser trackers, iGPS, and visual measurements, in addition to laser interference and collimation measurements. Measurement systems such as laser trackers [5] and iGPS [6] provide the advantages of a large measurement range and high measurement accuracy. However, it is necessary to obtain the coordinates of each measuring point, and the measurement efficiency is low. The visual measurement method is convenient, exhibits a simple structure, flexible installation, and has been widely used [7–9]. However, this method is mainly used for the low-precision measurement of position and pose. Its position accuracy is generally at the millimeter or sub-millimeter scales, and the attitude measurement accuracy is generally less than 0.1°, which does not meet the measurement accuracy requirements for the satellite. To improve the measurement accuracy and efficiency of the 6DoF relative position and pose, multiple researchers conducted long-term research and proposed various 6DoF relative position and pose measurement methods based on laser interference and collimation, which are generally used to measure the 6DoF geometric error (three position errors: positioning error, horizontal and vertical straightness, and three angular errors: yaw, pitch, and roll) of the linear guide. Lou et al. [10] used the Michelson interference method to measure the positioning error and vertical straightness, the pitch and yaw were obtained by the analysis of interference fringes, and the horizontal straightness and roll were measured using the collimation method. Fan et al. [11] used four sets of dual-frequency laser interferometers to measure the 6DoF geometric error of an XY platform. Gillmer et al. [12] combined the differential wavefront sensing method [13] and heterodyne interferometry to realize 6DoF geometric error simultaneous measurements. It provides the advantages of less optical components and a simple structure; however, the roll measurement accuracy was 9.45". Lee et al. [14] obtained the positioning error by the four-step phase-shifting method [15] using a one-dimensional grating. The vertical straightness and other four errors were obtained by collimation and decoupling, respectively. The measurement resolution of the positioning error, straightness, and three angular errors were 0.4 nm, 20 nm, and 0.03", respectively. Yu et al. [16] proposed a dual-channel grating encoder to measure the 6DoF motion of two adjacent sub-components of synthetic-aperture optics, and achieved a high resolution superior to 0.1 nm and 0.02" with respect to the displacement and angle measurements. Renishaw developed a commercial laser multi-beam interferometer, namely XM-60 [17], where the volumes of the transmitter and receiver were 161.2 × 82 × 82 mm3 and 25.5 × 124.1 × 86 mm3. It uses three-channel interferometry to measure the length, pitch, and yaw. The straightness and roll were measured based on the principles of collimation and polarization [18], respectively. The measurement accuracies of the positioning error, straightness, pitch, yaw, and roll were ± 0.5 µm/m, ± 0.01A ± 1 µm, ± 0.004A ± (0.5 µrad + 0.11 M µrad), and ± 0.01A ± 6.3 µrad (where A is the displayed reading, M is the measurement distance). Although the above mentioned methods based on laser interference and collimation demonstrate high measurement accuracies, these methods and systems are mainly used in normal temperature and pressure environments, and the measurement system is bulky, which cannot meet the requirements for vacuum and high-/low-temperature environments, in addition to the miniaturization of measurement systems, as required for the satellite.
We conducted long-term research on the simultaneous measurement of the 6DoF geometric error of the linear guide and proposed various measurement methods combining laser interference and collimation [19–21]. The positioning error, straightness, pitch and yaw, and roll measurement resolution were 1 nm, 50 nm, 0.05", and 0.1" in the normal temperature and pressure environments. Accordingly, this paper proposes a simultaneous measurement method of the 6DoF relative position and pose based on laser heterodyne interferometry and laser collimation to meet the high-precision measurement requirements for a satellite. According to the measurement requirements for vacuum and high-/low-temperature environments, a miniaturized measurement system was designed and developed. Moreover, the error crosstalk between the 6DoF relative position and pose measurements was comprehensively analyzed, and the error compensation model was established and verified by conducting an OpticStudio simulation. The developed measurement system was successfully applied to the satellite, and the 6DoF relative position and pose deformation of the satellite substrate were obtained, which supports satellite development and provides a novel method for the high-precision measurement of the 6DoF relative position and pose between two points. Due to the limitations of the length, there is no detailed description of the specialized design and experimental test of the measurement system in vacuum and high-/low-temperature environments.
2. Measurement method and error crosstalk analysis
2.1 Optical configuration
The proposed measurement method comprises a fiber-coupled laser, Sensors A and B, as shown in Fig. 1. Sensors A and B are fixed at Points A and B during measurement, which are used to measure the 6DoF relative position and pose change between Points A and B. Moreover, Lx, Ly, and Lz are the relative displacements between Points A and B along the X, Y, and Z axes respectively; and Rx, Ry, and Rz are the relative poses around the X, Y, and Z axes, respectively.
Fig. 1. Simultaneous measurement method of the 6DoF relative position and pose based on laser heterodyne interferometry and collimation.
The fiber-coupled laser is mainly composed of a He-Ne dual-frequency laser, which outputs two orthogonal linearly polarized beams. The two beams are coupled into a polarization maintaining fiber (PMF) by a coupler, and propagated to Sensor A. The half wave plate (HWP1) is adjusted to align the laser polarization direction with the fiber optical axis. The main advantages of using a fiber-to-coupler laser are as follows: (1) Beam drift caused by the thermal deformation of the laser device only influences the laser coupling efficiency and has a slight influence on the beam direction emitted from the fiber, thus improving the measurement accuracy. (2) The volume and weight of Sensor A can be significantly reduced, and the heat generated by the laser source is removed from Sensor A by a fiber connection, thus improving the thermal stability of the measurement system.
The measurement system comprises two measurement beams (Beams 1 and 2). Beam 1 is the measurement beam of three relative displacements. The orthogonal linearly polarized light emitted by the PMF is split by the beam splitter (BS1) after passing through a collimator (C). The transmitted beam of BS1 is then re-split by BS2, and the reflected beam passes through the polarizer (P1) to induce heterodyne interference. Thereafter, P1 is adjusted to cause its optical axis and the laser polarization direction to be 45°, to improve the interference signal intensity. This signal is considered as the reference signal for measuring Lx, and is detected by a photodiode (D). The laser polarization direction is aligned with the optical axis of the polarization beam splitter (PBS1) by adjusting HWP2. The transmitted beam of BS2 is divided into two beams by PBS1. The reflected beam and transmitted beam are returned by two corner cube prisms (CCR1 and CCR2), respectively, and generate heterodyne interference after passing through P2. Thereafter, it is detected by QD1. This interference signal is as a measurement signal for measuring Lx. Both heterodyne interference signals are then inputted to a phase meter to obtain Lx. Moreover, QD1 can measure the beam spot position returned from CCR2 in the Y and Z directions with high precision. Thus, Ly and Lz can be obtained simultaneously based on the collimation measurement principle.
Beam 2 is the measurement beam of Ry, Rz, Ly, and Lz. The reflected beam of BS1 is rotated by 90° using a penta prism, wherein the p-polarized light is transformed into circularly polarized light after passing through PBS2 and a quarter-wave plate (QWP). Thereafter, it is split by BS3. The transmitted beam of BS3 is detected by QD2 for the simultaneous measurement of Ly and Lz. The return beam of BS3 is converted into s-polarized light after passing through QWP for a second time, and is fully reflected by PBS2 and focused by the lens. It is detected by a position sensitive detector (PSD). Moreover, Ry and Rz are obtained based on the autocollimation measurement principle.
The penta prism causes Beams 1 and 2 to be accurately parallel, and the two beams are considered as the measurement reference of Rx. If Rx changes, the spot position in the Z direction on QD1 and QD2 are changed. According to the geometric relationship, Rx can be calculated.
2.2 Measurement principle of 6DoF relative position and pose
In the 6DoF geometric error simultaneous measurement system of the linear guide, the system is mainly composed of a stationary part and a moving part [22]. The stationary part generally remains still, and the moving part moves with the linear guide and is used as the error sensitive element. In this case, the beam emitted by the fixed part is considered as the measurement datum. In the 6DoF relative position and pose measurement, Sensors A and B are installed at Points A and B, respectively. Both points exhibit position and attitude changes; thus, there is no measurement datum. A comprehensive analysis is therefore required, and a measurement model should be established. In this study, the ray tracing method was used to analyze changes in the detector readings due to the independent motions of Sensors A and B, and then the simultaneous motion of both were considered and analyzed. Finally, a 6DoF relative position and pose measurement model was established and the crosstalk error was separated.
2.2.1 Relative displacement along X axis
As shown in Fig. 1, the relative displacement along the X axis between Sensors A and B is obtained by laser heterodyne interferometry [20]. The measurement datum is the laser wavelength, and Lx can be obtained as follows:
where n is the refractive index of air, λ is the laser wavelength, and Δφ is the phase difference between the reference and measurement interference signals.2.2.2 Relative displacements along Y and Z axes
Ly and Lz are measured simultaneously by the collimation principle, Ly is considered as an example. Irrelevant optical elements are omitted for clarity, and the optical elements and beams after moving are represented by dotted lines. As shown in Fig. 2(a), if Sensor B generates a displacement Ly-B along the Y axis, the returned beam by CCR2 moves forward by 2Ly-B along the Y axis, thus resulting in a spot position change of 2Ly-B in the Y direction of QD1. Moreover, QD2 moves forward by Ly-B along the Y axis, thus resulting in a spot position change of -Ly-B in the Y direction of QD2. Therefore, the spot position change of QD1 is twice that of QD2, and the sign is opposite. Given that Rx leads to the same sign of the spot position change on the two detectors (with reference to Section 2.2.4), to reduce the measurement crosstalk of Rx to Lz, the spot position changes of the two detectors are subtracted:
Fig. 2. Measurement principle of displacement along Y axis. (a) and (b) indicate Sensors B and A generate displacements Ly-B and Ly-A, respectively.
As shown in Fig. 2(b), if Sensor A generates a displacement Ly-A along the Y axis, the spot position changes of QD1 and QD2 are -2Ly-A and Ly-A, respectively. Thus, the following can be obtained:
In practice, Sensors A and B produce displacement motions simultaneously. Finally, the spot position changes of QD1 (ΔYQD1 and ΔZQD1) and QD2 (ΔYQD2 and ΔZQD2) are the comprehensive results due to the simultaneous motions of Sensors A and sensor B; thus, Formula (4) can simplified as follows:
2.2.3 Relative angles around Y and Z axes
Ry and Rz are measured simultaneously by the autocollimation principle, and Rz is considered as an example. As shown in Fig. 3(a), if Sensor B generates an angle Rz-B around the Z axis, the beam direction reflected by BS3 changes by 2Rz-B. This beam is then focused by the lens and the spot position of the PSD in the X direction changes by 2fRz-B, where f is the focal length of lens. Therefore, the following can be obtained:
Fig. 3. Measurement principle of angle around Z axis. (a) and (b) indicate Sensors B and A generate angles Rz-B and Rz-A, respectively.
Similarly, if Sensor A produces an angle Rz-A around the Z axis shown in Fig. 3(b), the spot position change of the PSD is -2fRz-A, and the following can then be obtained:
2.2.4 Relative angle around X axis
As shown in Fig. 4(a), Beam 1 is parallel to Beam 2, which is the measurement datum for Rx. If Sensor B produces an angle Rx-B around X axis, the beam spot positions in the Z direction on QD1 and QD2 change by 2(h1 + h3)Rx-B and (h2-h3)Rx-B, respectively, as shown in Fig. 4(b); and h1, h2, and h3 are the distances from the return beam of CCR2 to the mid-perpendicular of CCR2, Beam 2, and the angular rotation axis of Rx-B, respectively. The sum of h1 and h2 is the distance h. Given that Lz causes the sign of the spot position change on the two detectors to be opposite, to eliminate the measurement crosstalk of Lz on Rx-B, the spot position changes of two detectors are added to obtain the following:
As shown in Fig. 4(c), if Sensor A generates an angle Rx-A around the X axis, the spot position change of QD1 along the Z direction consists of two parts: (1) the displacement -(2h1 + h3)Rx-A generated by Beam 1 in the Z direction; and (2) the displacement -h3Rx-A of QD1 in the Z direction. Therefore, the spot position change of QD1 in the Z direction is -2(h1 + h3)Rx-A, and the spot position change of QD2 in the Z direction is -(h2-h3)Rx-A. The following can then be obtained:
Fig. 4. Principle of angle measurement around the X axis. (a) is optical path for Rx measurement, (b) and (c) indicate Sensors B and A produce angles Rx-B and Rx-A, respectively.
Similarly, Angle Rx of Point B relative to Point A can be obtained by subtracting Formula (10) from Formula (9):
2.3 Crosstalk analysis of relative position and pose measurement
During the 6DoF relative position and pose measurements, there is measurement crosstalk between the six parameters, which leads to coupling in the measurement results and a significant reduction in the measurement accuracy. Thus, the measurement model was established to compensate the crosstalk error and improve the measurement accuracy.
According to the measurement principle of Rz and Ry, BS3 and the lens are only sensitive to these two angles, and in theory, the other four parameters do not cause crosstalk. However, if Sensor A generates angles Rz-A and Ry-A, it changes the direction of Beams 1 and 2. Generally, there is a distance between Sensors A and B, which directly influences the measurement results of the three relative displacements, in addition to Rx, as shown in Fig. 5.
For the Lx measurement, the crosstalk caused by Rz-A is generally referred to as a cosine error, Rz-A is generally less than 100", and the crosstalk error ΔLx after approximation is as follows:
For the measurement of Ly, Lz, and Rx, if Sensor A generates an angle Rz-A, the spot positions of QD1 and QD2 in the Y direction are changed by -(l1-1 + l1-2 + l1-3)Rz-A and l2Rz-A, respectively; where l1-1∼l1-3 are the transmission distances of Beam 1 from Sensor A to CCR2, from the incident point of CCR2 to exit point, and from CCR2 to QD1, respectively, and the sum is l1. Moreover, l2 is the transmission distance of Beam 2 from Sensor A to QD2. Substituting the changes in the abovementioned QD spot position into Formulas (5) and (11), the crosstalk error can be expressed as follows:
The results reveal that Rz-A and Ry-A are related to the propagation distance l1 and l2. It is helpful to improve the compensation accuracy of crosstalk error by increasing the difference between l2 and 0.5l1.
In summary, Ry and Rz measurements are not influenced by the crosstalk in theory. The other four relative position and pose measurements are mainly influenced by the crosstalk of Rz-A and Ry-A. These two angles can be calculated using Formula (14), the crosstalk errors are obtained using Formulas (12) and (13), and the error compensation is carried out to improve the measurement accuracy of the 6DoF relative position and pose. The measurement model after compensating crosstalk error is expressed as follows:
2.4 OpticStudio simulation
As shown in Fig. 6(a), OpticStudio software was used to model the optical path in Fig. 1. Considering the actual simulation requirements, the parameters of the optical elements are set, and the optical path is established by the non-sequence mode. The relationship between the spot positions on the QDs and PSD and the relative position and pose changes were simulated when Sensors A and B moved independently. The simulation results are shown in Figs. 6(b) and 6(c), which reveal that the direction and size of the spot position change on the detector were consistent with the analysis above, which verifies the correctness of the relative position and pose measurement principle and crosstalk analysis.
Fig. 6. Simulations and results using OpticStudio. (a) is the simulation model, (b) and (c) are simulation results of Sensors A and B motions, respectively.
3. Experiments and results
Based on the proposed measurement method, a miniaturized measurement system was developed accordingly. The laser source was a He-Ne dual-frequency laser (LH2000, Leice) with a frequency difference of 6 MHz and laser power of 1.0 mW. Sensors A and B were designed with volumes of 100 × 100 × 62 mm3 and 78 × 85 × 87 mm3, respectively, were small-sized, and met the requirements for the satellite. To improve the thermal stability of the measurement system, the optical components were made of fused silica, and the mechanical structure was made of invar alloy. The thermal expansion coefficients of the two materials were 0.55 × 10−6/°C and 0.30 × 10−6/°C, respectively. The thermal expansion coefficient was significantly small, which improved the thermal stability of the system. A photodiode (LSSPD-3.2, Lightsensing) and QD (QP50, First Sensor) were used to detect the heterodyne interference signal, and a phase meter (PT-1313B, Pretios) with a displacement measurement resolution of 1 nm was used for the phase subdivision and result output. Two QDs (QP50, First Sensor, resolution: 50 nm) and a PSD (DL100, First Sensor, resolution: 0.5 µm) were used to detect the spot position.
3.1 Calibration experiment
Lx and Ly were calibrated using a laser interferometer (XL-80, Renishaw) with a linear resolution of 1 nm. During Lx calibration, Sensor B and the moving mirror of laser interferometer were mounted on the workbench of an air-bearing linear stage (ABL2000-0500, Aerotech), and the beams emitted from the two systems were coincident, as shown in Fig. 7(a). The linear stage moved along the X direction within a range of 500 mm at intervals of 50 mm, and the measurement results of the two systems were recorded simultaneously. The results are shown in Fig. 7(b). During Ly calibration, the measurement optical paths of the two systems were arranged in a 90° layout, and Sensor B and the moving mirror were installed on a linear guide (ANT130L-110, Aerotech), as shown in Fig. 7(c). The linear guide moved in the Y direction within a range of ±100 µm at intervals of 20 µm. The Ly measurement results of the two systems are shown in Fig. 7(d).
Fig. 7. Calibration experiments and results. (a), (c), (e), and (g) are calibration diagrams of Lx, Ly, Rz, and Rx, respectively; (b), (d), (f), and (h) are calibration results of Lx, Ly, Rz, and Rx, respectively.
Moreover, Rz and Rx were calibrated using a photoelectric autocollimator (Collapex STD-3032) with a resolution of 0.01" and accuracy of 0.15". During Rz calibration, a mirror was bonded behind Sensor B, which was considered as the target of the autocollimator. Sensor B was fixed on a rotary table (ANT95R-360, Aerotech), as shown in Fig. 7(e). The table rotated around the Z axis with a rotation range of ± 100" at intervals of 15". The Rz measurement results of the two systems are shown in Fig. 7(f). During Rx calibration, the developed measurement system and the autocollimator were arranged in a 90° layout, and Sensor B was installed on a tilt stage shown in Fig. 7(g). Sensor B generated an angular motion around the X axis by manual adjustment within a range of ± 100" at intervals of 20". The Rx measurement results are shown in Fig. 7(h).
The experimental results revealed that the maximum compared residual for Lx obtained by the developed measurement system and the laser interferometer was 0.16 µm and the standard deviation was 0.06 µm within a range of 500 mm. Within the range of ± 100 µm, the maximum compared residual was 0.18 µm, and the standard deviation was 0.12 µm. In the measurement range of ± 100", the maximum compared residuals of Rz and Rx obtained by the developed measurement system and the autocollimator were 0.24" and 0.39", and the standard deviations were 0.12" and 0.20", respectively. These results revealed that the measurement accuracy of the developed system was high, and satisfied the measurement accuracy requirements for the satellite.
3.2 Long-term stability experiment in laboratory
As shown in Figs. 8 (a) and 8(b), Sensors A and B were fixed to an invar base plate with an interval of approximately 100 mm. The thermal expansion coefficient of this plate was approximately 0.3 × 10−6/°C. The coefficient was significantly small; thus, the deformation of the plate in the laboratory environment was significantly small, which can be used to verify the measurement stability of the development system. During the stability experiment, the optical path was sealed to reduce the influence of atmospheric disturbance and external stray light on the measurement. The experiment was conducted for 24 hours, and the results are shown in Figs. 8(c) and 8(d).
Fig. 8. Stability experiment and results. (a) and (b) are stability experiment diagram and photos, respectively; (c) and (d) are stability results of relative position and relative pose, respectively.
The results reveal that the ambient temperature changed by 2.0 °C during the 24-h experiment. Within this time-period, the maximum changes of Lx, Ly, and Lz were 0.44 µm, 0.29 µm, and 0.17 µm, and the standard deviations were 0.14 µm, 0.08 µm, and 0.05µm, respectively. The maximum changes of Rx, Ry, and Rz were 0.32", 0.47", and 0.32", and the standard deviations were 0.07", 0.14", and 0.08", respectively. The results reveal that the measurement stability of the developed system is high and meets the measurement stability requirements for the satellite.
3.3 On-site thermal load test
To obtain the structural thermal stability of a satellite, a thermal load test was carried out in the field using the developed measurement system. As shown in Fig. 9, Sensors A and B were mounted at Points A and B of the satellite substrate using two L-shaped adapter plates with a spacing of approximately 2.1 m. A shield was used to close the measurement beam and minimize the influences of atmospheric disturbance and external stray light on the measurement results. The satellite substrate exhibited a honeycomb sandwich structure with a thickness of 26 mm. During the test, an infrared lamp array was used to heat the satellite. The heating time was 60 min and the cooling time after heating was 30 min. A total of 5 cycles were performed, and the measurement results are shown in Fig. 10.
Fig. 9. Thermal load test of a satellite. (a) is thermal load test diagram of satellite substrate; (b) and (c) are installation photos of Sensors A and B, respectively.
Fig. 10. Thermal load test results of a satellite. (a) and (b) are deformation results of relative position and attitude, respectively.
The results reveal that the average temperature of the satellite substrate increased by approximately 0.28 °C after 60 min of heating, and the temperature generally recovered after cooling for 30 min. During this time-period, the 6DoF relative position and pose measurement results of the system were correlated with the temperature. Table 1 lists the experimental results of Cycles 2–4. When the temperature increased by 0.28 °C, the maximum deformations of Lx, Ly, and Lz were 1.77 µm, 8.18 µm, and 7.08µm, and the measurement repeatability errors were ± 0.32 µm, ± 0.66 µm, and ± 1.70 µm, respectively. The maximum deformations of Rz, Ry and Rx were 4.17", -7.79", and -4.56", respectively, and the measurement repeatability errors were ± 0.09", ± 1.04", and ± 0.39", respectively. The results reveal a small deformation of the satellite substrate, which is consistent with the design. Among these results, the measurement repeatability errors of Lz and Ry were relatively large due to the following. First, due to the limitations of the field experimental conditions, Sensors A and B were hoisted on the substrate using L-shaped adapter plates, resulting to form a cantilever structure. The structure was not stable, and mechanical structural drifts due to gravity and vibration could be readily generated. Second, the infrared lamp array only irradiated one side of the satellite, and there was a temperature gradient field of approximately 3 °C in the inner space of the satellite. After a cooling time of 30 min, the satellite structure did not reach a stable state.
Table 1. Thermal load test results of the satellite
4 Conclusions
To meet the strict measurement requirements of a high precision, high stability, and miniaturized measurement system for a satellite, this paper presents a simultaneous measurement method of the 6DoF relative position and pose based on laser heterodyne interferometry and collimation. In particular, a miniaturized measurement system was developed. The measurement principles of the 6DoF relative posititon and pose were comprehensively analyzed. A theoretical analysis and OpticStudio simulation were carried out to solve the measurement crosstalk problem, and an error compensation model was established to improve the measurement accuracy. A series of measurement experiments were carried out. The experimental results revealed that the maximum compared residual between the developed system and laser interferometer was less than 0.2 µm within the displacement measurement range of 500 mm along the X axis, and a measurement range of ± 100 µm along Y and Z axes. For pose measurement, in the measurement range of ± 100", the maximum compared residual between the developed system and the autocollimator was less than 0.4". In the 24-h stability experiment, the maximum changes of relative displacement and relative attitude were less than 0.5 µm and 0.5", respectively. Thus, the developed measurement system demonstrates a high measurement accuracy and stability, which meets the ground measurement requirements for the satellite. Finally, the 6DoF relative position and pose deformation of the satellite was obtained using the developed system, which guarantees the development quality of the satellite and provides a novel method for the high-precision measurement of the 6DoF relative pose between two points.
Funding
Science and Technology Innovation Project of Xiong’an New Area (2022XAGG0200); National Natural Science Foundation of the China-Major Program (51527806); Fundamental Research Funds for the Central Universities (2022XKRC000).
Disclosures
The authors declare that there are no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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