Star sensors are high-precision spatial attitude measurement devices that use the starry sky as a reference frame of motion and stars as observation objects. By observing stars at different positions in the starry sky, star sensors can calculate their rotation angle relative to the celestial sphere, providing accurate spatial attitude information for various aerospace vehicles, which has great application value. Compared with other attitude measurement devices, such as sun sensors, gyroscopes, magnetometers, etc., star sensors are particularly outstanding in terms of high accuracy and no drift. Their attitude measurement accuracy can reach the angular second level or even the sub angular second level.
The star sensor is equivalent to an electronic camera connected to a microcomputer, and its imaging components include a front optical lens and an image sensor located at the focal plane behind the lens. The selection of image sensors is currently dominated by CMOS APS. The attitude calculation process of star sensors can be decomposed into multiple steps, and any one of these steps may introduce errors in the attitude calculation results. This article mainly focuses on the spatial pose parameters of the star sensor APS, analyzes their impact on the attitude calculation process, and proposes a method to control and calibrate these parameters during the assembly process, and completes the development of the corresponding assembly calibration system.
There are numerous stars distributed in the vast starry sky, and stars that meet a certain magnitude and field of view angle can be captured by star sensors, forming circular bright spots on the APS receiving surface (image plane). Although there may be many differences between different star sensors, their basic composition and structure are common, as shown in Figure 1.
Fig.1 Common structure of star sensor
The star sensor components mainly involved in this article include the APS, reference lens, and optical lens shown in Figure 1. The star sensor takes the image of a star as the input signal and outputs attitude data after a series of calculations. The attitude calculation process involves three coordinate systems, which are:
1) Image coordinate system O-xyz. The origin is set to the center of the image plane, with the horizontal and vertical axes along the row and column directions of the pixel array, and the vertical axis pointing towards the normal direction of the image plane. For circular bright spot images on the image plane: firstly, it is necessary to identify their corresponding stars through pattern recognition; Secondly, in order to obtain their precise coordinates in the coordinate system, it is necessary to use some sub pixel algorithms to calculate the centroid coordinates. Due to the requirement of subpixel algorithm that the coverage range of circular bright spot images exceeds one pixel, the image surface needs to have a certain degree of defocus.
2) Star sensitive coordinate system. The origin is set as the intersection point of the lens optical axis and the image plane, and the coordinate axis points to the reference mirror provided by the star sensor. The optical lens of a star sensor is usually equivalent to a pinhole. In the coordinate system, the line connecting the centroid of a circular bright spot image and the equivalent pinhole points to the corresponding star, and the unit vector where this line is located is called the observation vector.
3) Inertial coordinate system. It is the reference coordinate system, namely the celestial coordinate system.
The observation vector of a star in an inertial coordinate system is a known quantity. By using the observation vectors of at least two stars in the star sensitive coordinate system and the inertial coordinate system, the rotation angle of the star sensitive coordinate system relative to the inertial coordinate system can be calculated, which is the attitude of the star sensor. There are many methods for representing posture, including attitude matrix, Euler angle, quaternion, rotation vector, etc.
The calculation methods for attitude are divided into static deterministic algorithms and dynamic state estimation algorithms. The former includes TRIAD algorithm, MLS algorithm, QUEST algorithm, etc., while the latter generally uses Kalman filtering method and its improvements. In the assembly process of star sensors, controlling the spatial pose of APS is very important. As shown in Figure 2, in an ideal state, it is required that the image plane and the star sensitive coordinate system completely coincide;
However, in practical situations, as shown in Figure 3, due to the APS having six degrees of freedom of motion, the image plane coordinate system may deviate from the star sensitive coordinate system at these six degrees of freedom.
The spatial pose of APS mainly affects the calculation accuracy of the observation vector, which in turn affects the final attitude calculation accuracy of the star sensor. The spatial pose parameters of APS include tilt, roll, eccentricity, and defocus. In APS assembly, except for defocusing which cannot be too small due to special requirements, other parameters should be minimized as much as possible. In cases where it cannot be reduced, these parameters should be calibrated with the highest possible accuracy
The calibration of APS spatial pose parameters can be carried out after the assembly of the star sensor is completed using a star simulator and imaging methods. However, the assembly calibration system proposed in this article can calibrate multiple spatial pose parameters during the assembly phase of APS, and the specific content is as follows:
1) Tilt. Tilting represents the deviation in the direction of the vertical axis, which is essentially the normal deviation between the APS receiving surface and the surface of the reference mirror. This deviation can be measured using an autocollimator. When measuring tilt, the star sensor is in a lensless state.
2) Roll. Roll represents the angle between the corresponding horizontal or vertical axis, which is essentially the angle between the APS receiving surface and the corresponding edge line on the surface of the reference mirror. This angle can be measured using an image measurement system. When measuring the roll, the star sensor is also in a lensless state.
3) Eccentricity. Eccentricity represents the origin deviation, which is essentially the deviation between the intersection point of the lens optical axis and the APS receiving surface and the center of the APS receiving surface. When other deviations are small, it is approximately the deviation between the lens center and the APS receiving surface center. This deviation can also be measured using an image measurement system. After the tilt and roll have been measured, install the lens for the star sensor, ensuring that the other components of the star sensor are stationary relative to the assembly calibration system. Align the image measurement system with the end face of the lens and create a clear image. Take ten points on the circumference of the outer circle and least squares fit to obtain the center coordinates of the circle. Calculate the center coordinates of the four vertex coordinates of the APS receiving surface obtained from roll measurement
Figure 6 shows the composition and structure of the assembly calibration system. The core components of this system are an autocollimator and an image measurement system (which in turn consists of a positioning mechanism and an optoelectronic camera). The system also includes a lifting mechanism, an angle adjustment mechanism, and a computer as a control software carrier.
Fig.6 Components of the system
Figure 7 shows a physical model of the assembly calibration system.
Fig.7 Model of the system
When constructing an image measurement system, the positioning mechanism is at the bottom and the photoelectric camera is at the top. The optical axis of the photoelectric camera should be perpendicular to the measurement surface, and the distance from the photoelectric camera to the measurement surface should comply with the working distance. By connecting a rotating tilt table to the positioning mechanism, it is possible to adjust the three-dimensional angle to meet the requirement of measuring the surface perpendicular to the optical axis of the photoelectric camera. By connecting the photoelectric camera to the electrically controlled lifting platform, the height can be adjusted to meet the requirements of the working distance. There are two autocollimators in total, which can measure the normal deviation of the plane from top to bottom and from right to left. They are called vertical autocollimators (which share the same electronic lifting platform with the photoelectric camera) and lateral autocollimators (which are separately connected to another electronic lifting platform)
The electrically controlled lifting platform, which is connected to a photoelectric camera and a vertical autocollimator, is fixed directly above the positioning mechanism with a gantry support frame. The support frame, along with the components on it, will inevitably undergo certain deformation under the action of gravity. When measuring with a vertical autocollimator, the electrically controlled lifting table remains stationary, and this deformation can be offset by adjusting the angle of the rotating tilt table. When measuring with an image measurement system, the position of the electrically controlled lifting platform often needs to be changed. Before the position of the electric control lifting table changes, this deformation can still be offset by adjusting the angle of the rotating tilt table. However, after the position of the electrically controlled lifting table was changed, the rotating tilt table had been locked, so the resulting deformation cannot be offset and must be controlled within a small range. After continuously improving the structure of the gantry support frame, ANSYS simulation (taking six evenly distributed positions of the electric control lifting platform) showed that the deformation was controlled at the micrometer level, while the deformation modification variable was controlled at the submicron level, as shown in Figure 8.
Fig.8 Static deformation simulation of the support structure
This article introduces the attitude calculation process of star sensors, and focuses on analyzing the influence of the spatial pose parameters of APS on the calculation of observation vectors. On this basis, a method for controlling and calibrating APS spatial pose parameters during the assembly process was proposed, and a corresponding assembly calibration system was developed. The test data shows that the calibration repeatability errors of the system for the two tilted components are ± 1.05 “and ± 1.09”, respectively. The calibration repeatability errors for the rolling components are ± 9.4 “, and the calibration repeatability errors for the two eccentric components are ± 0.53”, respectively μ M and ± 0.55 μ M. This system is also suitable for the assembly and calibration of image sensors in other precision optoelectronic imaging systems
Send us a message,we will answer your email shortly!
TY-Space Technology (Beijing) Ltd. is professional focusing on advanced attitude optical sensors, especially Star Trackers for space industry.
