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  1. 1. MISSION ENGINEERING AND SYSTEM ANALYSIS Code 596 GN&C Components and Hardware Systems Branch Presenters Siddhant Nanda Cornell University Liberty Shockley University of Cincinnati Mentors Alvin Yew, Ph.D. Mechanical Engineering Sean Semper, Ph.D. Aerospace Engineering ABSTRACT Star trackers are used in spacecraft missions due to their higher accuracy attitude measurements than most other sensors. However, exorbitant costs and their closed proprietary nature have drastically limited their potential for more exotic uses and configurations, especially as a component in a spacecraft’s attitude control system (ACS). This project investigates the use of core algorithms that are applicable to two innovative hardware prototypes currently under development. (1) Astrometric Alignment Sensor A unique stellar sensor that captures sky and spacecraft imagery and quickly processes images to produce vectors in orbit. (2) SSNano A compact, novel star scanning method for a “lost in space,” tumbling spacecraft that uses brightness transit signatures as opposed to traditional images to calculate attitude. The core algorithms selected were the Pyramid Star Identification and the Singular Value Decomposition (SVD), which are used in conjunction for attitude determination. For the attitude determination, different methods were explored, including the well-known TRIAD Algorithm, Markley’s Fast Quaternion and SVD methods. Ultimately, the SVD method was chosen and implemented, after considering the drastically simpler implementation, low computational time and accuracy of the results. How does this work together? SSNANO AND THE PYRAMID ALGORITHM The SSNano is a compact star scanner for spacecraft instruments that need sub-arcminute attitude information. The traditional star tracker is replaced by a sensor that uses star detection to provide accurate attitude information. As the SSNano is still in a development phase, the gathering of sensory information was simulated. Using a catalog of the 200 brightest stars, a lost in space scenario was randomly generated and visualized by placing the coordinates of these stars on a virtual sphere as shown in Figure 1 below. To generate the transit signature for this particular field, we perform a sweep across the 0 degree latitude line, and record the corresponding brightness. The key distinction of this methodology from a normal star tracker is that these images are as a function of time as opposed to space. We detect the centroid of a spike in the signature, but use temporal measurements as opposed to spatial ones to do this, and the resulting signature can be shown in Figure 4. The brightness corresponding to the centroid is then passed to our implementation of the Pyramid algorithm, the heart of star pattern recognition. The Pyramid algorithm is a highly robust method used to identify the stars observed by traditional star trackers in the lost in space scenario5. The k-vector approach allows for an efficient, search-less method to obtain cataloged stars that could possibly correspond to a particular measured pair, given an angle between two stars and a precision5. The Pyramid builds on the identification of a four-star structure and uses a smart technique to scan triangles that avoids unnecessary computation while simultaneously identifying and discarding “false stars.” The algorithm implemented is outlined below, in Figure 5. By taking a cross product to the vectors to two identified stars, the vector orthogonal to the plane of the spacecraft can be determined shown in Figure 6. Advanced Star Tracker Development for Next Generation Attitude Determination CONCLUSIONS and FUTURE RESEARCH By implementing star identification, attitude determination and control simulations, we lay the foundation for developing advance architectures that work seamlessly with in-house advance star-tracking hardware and software needed for future innovative science missions. Now that there is a functional routine for using an Astrometric Alignment Sensor for attitude determination, it can be implemented into formation flying missions, and developed further to get even more accurate results. Further investigation can be done on the sensor, to make it faster and more accurate than it is now. The goal would be to have a continuous answer for the attitude of the spacecraft. With its compact, credit-card sized design, the SSNano has the potential to be incredibly convenient to an assortment of smallsat missions. The star ID of the SSNano and the simulations developed helped to further the development process for this prototype. Optimizing the attitude will complete the star scanning process. Another venture under development involves a VR simulation environment of a star scanner to perform a hardware-in-the- loop simulation. Star sensors will be put behind the Oculus Rift optics to read star field patterns as we induce attitude perturbations to a low-friction hemispherical air bearing system. A closed loop control system will restore stability to the system based on sensor feedback and reaction wheel spin up. SINGULAR VALUE DECOMPOSITION (SVD) ALGORITHM o Learn the linear algebra and geometry behind computations involving space vehicles o Familiarize yourself with Wahba’s problem and ways to solve it o Code in Matlab the TRIAD algorithm, Markley’s Fast Quaternion Attitude Determination method, and the SVD method to determine the best method While the original attitude determination using flight data used took an 1 hour and 20 minutes to go through all the data and produce the results, the SVD algorithm takes 11 minutes, reducing runtime by 90%. This is due to the simple calculations of the SVD algorithm3, opposed to the long original that included a weighted guess and an optimization of Wahba’s Loss Function4. The new routine also searched every 5 rows and columns for bright spots (opposed to every one) to analyze the image faster without sacrificing the number of bright spots found. While these are good for efficiency, the SVD algorithm is also more accurate to the truth values of the star’s positions. Results of 19,101 data points that represent images of the night sky taken by a ICESat-2 Laser Reference System (LRS) every 0.1 seconds have less error when calculating the spacecraft’s true pointing Right Ascension and Declination. This is because, unlike the optimization routine, it does not take an initial weighted guess of where the spacecraft is looking. This plot shows how the script finds the stars (bright spots) in an image from the ICESat-2 LRS. It looks for a certain pixel value (for white) and then puts a box around the spot. From here, each star can be centroided and its location determined. This is the output of the code with the SVD algorithm. It shows the movement of the stars tracked across the FOV. This is quite accurate to the real movement. 2 1 2 The SVD method of attitude determination can also be used in formation flying missions, as pictured below. The routine will check to make sure spacecraft 2 is in the FOV of spacecraft 1, then scan the surrounding stars. Spacecraft 1’s FOV Side view of the formation of both spacecraft and Spacecraft 1’s FOV Detect Star Transit Signal Processing Take a Picture Image Processing Star ID: Pyramid Algorithm Star Catalog Star Search Bright Object Search Attitude Solution: SVD Algorithm Attitude Solution: TRIAD Algorithm* Astrometric Alignment Sensor SSNano This graphic demonstrates how the two sensors start and end with different information, but employ a common core routine. This core is shown with red boxes, and is what both of our projects worked to optimize. Image Analysis Star Movement ⍵ vector Star 1 Star 2 Fig. 1, adapted from Mackison et al (1973) Notional Operation of a Star Scanner Fig. 2, adapted from Mackison et al (1973) Star Pulses Recorded From Instrument Fig.5, adapted from M.A. Samaan (2003) Star Identification with the Pyramid Approach Fig. 3, Simulated Star Scanner Swaths Fig. 4, Star Pulses from Simulated Swath Fig. 6, Attitude Determination using Cross Product