ESTCUBE-1 ATTITUDE DETERMINATION: IN-FLIGHT EXPERIENCE Andris Slavinskis(1,2), Hendrik Ehrpais(2), Henri Kuuste(1,2), Indrek Sünter(1,2), Erik Kulu(1,2), Jaan Viru(2), Johan Kütt(1), Robert Valner(2), Kristo Tammeoja(3), Pavel Drozdov(2), Mart Noorma(1,2) Tartu Observatory, Observatooriumi 1, 61602 Tõravere, Estonia, +372 696 2510, [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] (2) University of Tartu, Institute of Physics, Tähe 4-111, 51010 Tartu, Estonia +372 737 6524, [email protected], [email protected], [email protected], [email protected] (3) CGI Estonia, Sõbra 54, 50106 Tartu, Estonia, +372 737 0700, [email protected] (1)

ABSTRACT This paper presents in-orbit operations and validation of the ESTCube-1 attitude determination system (ADS). ESTCube-1 is a 1-unit CubeSat launched on May 7, 2013 on board the Vega VV02 rocket. Its primary mission is to perform the first in-orbit experiment of electric solar wind sail (Esail) technology by measuring changes in the spin rate caused by an ionospheric plasma stream on a charged tether. ESTCube-1 will deploy a 10 m long tether using centrifugal force which is provided by spinning up the satellite to 360 deg/s. In order to spin-up the satellite and to estimate the E-sail effect, a precise ADS has been developed. The system is required to estimate the attitude with an accuracy better than 3°. The ADS uses three-axis magnetometers, three-axis gyroscopic sensors and two-axis Sun sensors, a Sun sensor on each side of the satellite. The attitude of the satellite is estimated on-board using an Unscented Kalman filter (UKF). Attitude estimation is validated by comparing on-board images with images from the Systems Tool Kit (STK). 1

INTRODUCTION

ESTCube-1 primary mission is to measure the Coulomb drag force exerted by an ionospheric plasma stream on a charged tether and, therefore, to perform the proof of concept measurement and technology demonstration of electric solar wind sail (E-sail) technology [1, 2]. The E-sail is a propellantless propulsion system concept that uses thin charged electrostatic tethers for turning the momentum flux of a natural plasma stream such as the solar wind into spacecraft propulsion. An attitude determination system (ADS) has been developed to provide the satellite orientation and the angular velocity during the following phases [3, 4]. 1. Satellite spin-up with controlled spin axis alignment required for tether deployment. 2. Tether deployment during which the spin rate should be monitored. 3. The experiment during which the tether is charged synchronously with the satellite spin and changes in the satellite spin rate are measured. Before the launch, the ADS was characterised in the laboratory and with simulations [5, 6]. Both methods showed a feasibility to fulfil the following mission requirements. 1. Spin-up the satellite to 360 deg/s with the spin axis aligned to the Earth polar axis with a pointing error less than 3°. 2. Estimate the attitude with an accuracy better than 3° in parts of the orbit where the E-sail experiment will be performed. 3. Estimate the angular velocity with an accuracy better than 0.4 deg/s in parts of the orbit where E-sail experiment will be performed.

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Due to the fact that there is only a single chance to deploy the tether, the ADS has been thoroughly tested and characterised in-orbit to minimise the risk of mission failure. The ESTCube-1 ADS uses two three-axis magnetometers, four three-axis gyroscopic sensors and two-axis Sun sensors, a Sun sensor on each side of the satellite. An Unscented Kalman Filter (UKF) is used for attitude estimation [7]. The attitude is defined as an orientation of the satellite’s body frame in the Earth centred inertial frame. In this paper, we present in-orbit operations and validation of the ESTCube-1 ADS. The system is validated by comparing on-board images with images from the Systems Tool Kit (STK)1 that are acquired by identifying the satellite and setting the camera’s field of view, as well as by providing the attitude and the time when images were taken. 2

IN-ORBIT OPERATIONS

Since the satellite is in the orbit, software of the electrical power system, the command and data handling system (CDHS) and the camera has been updated regularly. While ADS has its own sensor board, the UKF and other calculations (pre-processing and corrections of sensor readings, the rotation model of the Earth, the magnetic field model of the Earth and the Sun model) are run on the CDHS. Therefore the ADS software is updated together with CDHS software. The ADS has been updated iteratively. 1. The satellite was launched with a functionality to demand sensor readings from the ground station. 2. A major CDHS update provided a functionality of logging and scheduling sensor data. 3. Pre-processing of sensor readings allowed to smoothen signals and replace faulty signals based on historical records. 4. Correction of measurements allowed to take calibration curves, zero-offsets and temperature influence into account. 5. Ultimately, attitude estimation has been successfully tested on-board. For each update multiple steps were performed to ensure that software will work successfully onboard. 1. Development of algorithms has been performed in Matlab and C using in-orbit measurements as test cases. 2. Attitude estimation has been performed in Simulink. Results were validated by comparing magnetic field and Sun sensor measurements with respective model outputs which were transformed to the satellite’s body frame using the estimated attitude. 3. Functionality and optimisation tests have been performed on the engineering model. 4. On-board attitude estimation have been validated using on-board images (see Section 3). 3

VALIDATION

In order to validate on-board attitude estimation of ESTCube-1, we compare on-board images with images acquired from the STK. The following steps are performed to estimate attitude determination error (fist two steps are performed on-board, others in post-processing). 1. Estimate attitude on-board the satellite. 2. Take an image of the Earth while performing the first step. 3. Slerp (spherical linear interpolation) is used to acquire the attitude at the time instance when the on-board image was taken.

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http://www.agi.com/

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4. The ESTCube-1 identifier, the field of view of the on-board camera, the timestamp and the attitude is provided to the STK to acquire an image taken by an emulated camera. 5. On-board image is corrected for the lens distortion. 6. On both images, five landmarks are chosen preferably that they are spread on the image – four near corners and one near the middle. 7. For each landmark, we perform pixel counting – for how many pixels on-board image should be shifted for the landmark to match the same landmark on the STK image. Each pixel represents a rotation error of 262 arcseconds [7]. 8. We average errors of all landmarks to estimate the attitude determination error of the sample. To achieve statistically reliable results, ten samples were processed and results are presented in Table 1. Nº of sample

Table 1. All samples that are used to estimate the attitude determination error Attitude Time in GMT On-board image STK image Error, deg quaternion

1

23.01.2014 07:30:20.362

2

23.01.2014 09:09:29.503

3

25.01.2014 08:28:59.089

4

25.01.2014 08:32:23.143

5

03.02.2014 09:52:02.795

6

03.02.2014 09:52:10.201

7

08.02.2014 09:09:13.647

8

08.02.2014 09:09:15.053

9

08.02.2014 09:09:16.456

0.4985 0.4365 [ ] −0.0638 0.7462 −0.2936 0.3967 [ ] −0.1383 0.857 −0.6802 0.3987 [ ] −0.0468 0.6134 −0.4845 0.3849 [ ] −0.0472 0.7841 0.3357 −0.2441 [ ] 0.2918 −0.8617 0.5404 −0.3921 [ ] −0.073 −0.7409 −0.5521 0.3092 [ ] −0.0885 0.7692 −0.5807 0.3427 [ ] −0.0216 0.7382 −0.6072 0.3735 [ ] 0.0481 0.6996

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2.863026

1.942947

5.09544

1.383918

3.213748

1.062565

2.599918

2.599492

3.297889

3

10

08.02.2014 09:09:17.859

−0.6278 0.4021 [ ] 0.1129 0.6568

3.262681

An average error from all samples is 2.7321624°. The on-board image and the STK image from the sample with the highest error (third sample) are shown in Figures 1 and 2, respectively.

Figure 1. On-board image from the sample with the highest error. Landmarks are marked with circles.

Figure 2. STK image from the sample with the highest error. Landmarks are marked with circles.

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CONCLUSIONS

In this paper, we presented requirements set to ESTCube-1 ADS, in-orbit operations and validation of the system. The system is able to estimate the attitude on-board with an error less than required 3°. The method of comparing on-board images with STK images to estimate the error is simple and can be used for validation of ADS but it cannot be used to fully characterise the system because the method does not provide an error in three dimensions. For further research to fully characterise the ADS, authors suggest to compare the attitude estimated on-board with attitude estimated from onboard images. 5

ACKNOWLEDGEMENTS

We are grateful to all ESTCube-1 team members. The research by Andris Slavinskis was supported by the European Social Fund's Doctoral Studies and the Internationalisation Programme DoRa. 6

REFERENCES

[1] Janhunen, P. and Sandroos, A. Simulation study of solar wind push on a charged wire: basis of solar wind electric sail propulsion, Ann. Geophys., 25, 755–767, 2007. [2] Janhunen, P., Toivanen, P.K., Polkko, J., Merikallio, S., Salminen, P., Haeggström, E. et al. Electric solar wind sail: Toward test missions, Rev. Sci. Instrum, 81, 111301:1–11, 2010. [3] Kulu, E., Slavinskis, A., Kvell, U., Pajusalu, M., Kuuste, H., Sünter, I, et al. ESTCube-1 nanosatellite for electric solar wind sail demonstration in low Earth orbit, presented in IAC 2013, Beijing. [4] Slavinskis, A., Kvell, U., Kulu, E., Sünter, I., Kuuste, H., Lätt, S. et al. High spin rate magnetic controller for nanosatellites, Acta Astronautica, 95, 218–226, 2014. [5] Slavinkis, A., Kulu, E., Viru, J., Valner, R., Ehrpais, H., Uiboupin, T. et al. Attitude determination and control for centrifugal tether deployment on ESTCube-1 nanosatellite, accepted for publishing in Proc. Est. Acad. Sci., 2014. [6] Vinther, K., Jensen, K.F., Larsen, J.A., Wiśniewski, R. Inexpensive CubeSat Attitude Estimation Using Quaternions and Unscented Kalman Filtering, Online journal Automatic Control in Aerospace, 2011. [7] Kuuste, H., Eenmäe, T., Allik, V., Agu, A., Vendt, R., Ansko, I et al. Imaging system for nanosatellite proximity operations, accepted for publishing in Proc. Est. Acad. Sci., 2014.

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