Asteroids have been a subject of interest for many years. They hold information on the early stages of the Solar System and planetary formation, they likely contain many rare minerals, and have been closely monitored to detect possible collisions with Earth. Many satellite missio
...
Asteroids have been a subject of interest for many years. They hold information on the early stages of the Solar System and planetary formation, they likely contain many rare minerals, and have been closely monitored to detect possible collisions with Earth. Many satellite missions to asteroid have been successfully completed over the years and more are planned for the future. However, a challenge for any asteroid mission is the irregular shape of these bodies. These irregular shapes can lead to highly irregular gravity fields that exert significant perturbations on any spacecraft that has to investigate these asteroids closely. These perturbations make navigation around asteroids challenging. So far, missions relied on human interference during orbiting phases, to correct for the perturbations experienced by the spacecraft. However, there are delays in communication that worsen with increasing distance to the spacecraft. These delays pose a threat as it could take minutes to correct any unexpected perturbations, possibly leading to a catastrophic end of the mission.
To make spacecraft more robust against these perturbations, a new autonomous navigation method was developed to include the gravity field of the asteroid in the position estimate. Several design iterations of the navigation filter have been completed before this study. A Unscented Kalman Filter has been used to estimate the spherical harmonic coefficients of the gravity fields, which was then extended to include a formation of small satellites to estimate the coefficients. A mass concentrated gravity field model was evaluated to estimate the gravity field below the Brillouin sphere, and a convolutional neural network was implemented to automate landmark tracking during navigation. These studies were all completed using numerical models, with limited error sources in the navigation measurements. There have been several studies that found benefits in the use of experimental measurements and integrated tests with flight hardware. Due to limits in numerical models, physical experiments can evaluate robustness in performance better. To further evaluate and develop the performance of the autonomous navigation, an experiment was designed to gather experimental measurements that might be used to further the development of the autonomous navigation filter.
The experiment simulated an orbit around the asteroid 433 Eros. A camera was placed in the position of the satellite to gather navigation images of a 3D printed scale model. The 10:1·106 scale model of the asteroid 433 Eros was created using stereolithography printing. The model was adapted to be hollow, with an internal grid structure for strength. Furthermore, as the model had to be printed in two pieces, the openings were strengthened with stringer sheets to avoid warping. It was found that a significant drying time was needed to fully dry the model before it could be cured and that the model had to be cured at room temperature to keep the dimensions as close to required as possible. The two halves were joined with alignment pins and epoxy putty, after which they were coloured using spray paint. By creating thin layers of spray paint, the surface obtained a rough surface that was more similar to the surface of 433 Eros than the bare plastic.
The 3D printed model was placed in an experimental set-up, that recreated an equatorial orbit around Eros at orbital radii of 30 km, 100 km and 200 km. A stationary camera placed at the spacecraft position at 10:1·106 scale, was used to capture optical navigation images of the surface of the asteroid and the asteroid was rotated to simulate an orbit with a series of image captures. The experiment was lit from above using Sun-like diodes in a dark room to further increase the realism of the experiment. A second set of numerical measurements was created using the 3D modelling software Blender, to act as a benchmark for the experimental measurements created in the test set-up. Several limitations of the experiment were found; the focal length of the camera had to be adjusted which made it an unknown, the distance measurements for the orbits were off by 1 cm, and the exact positions of the asteroid and the camera during the experiment were not recorded for later use. The first limitation could be solved by using a camera with a fixed focal length and the laboratory has since been fitted with a motion capture system which could be used for the latter two problems.
In total 5 datasets were created with 181 measurements each (one image every 2 degrees for a full rotation). The camera had a pixel size of 3.45 μm, a resolution of 1440×1080 pixels and a focal length of 8.6 mm. To evaluate the experimental dataset, the surface landmarks seen in the images were used to estimate the position of the camera. The location of the landmarks was known and the difference in the position estimate between the experimental and numerical datasets was used to evaluate the accuracy of the dataset and thus the experiment. The position estimate was calculated by finding the intersection of the vectors between the camera and the landmarks, solving the linear system with an ordinary least squares. A bias correction was applied to adjust a misalignment in the position of the experiment camera and a sensitivity analysis was performed to find the effect of each component, namely the Cartesian position of the landmarks and the focal length of the camera, on the position estimate. It was found that the position error of the camera in the experimental dataset was in the range of 3000-4600 m for the lower orbits and up to 12000 m for the 200 km orbit radius. It was more than one order of magnitude larger than the numerical dataset, which had an error in the range of 80-450 m for the lower orbits and up to 5000 m for the 200 km orbit. The main causes to this were hypothesized to be uncertainty in the exact camera position, the landmark location with respect to the camera and the focal length. These were all direct results of the experiment set-up. Additionally, the ordinary least squares method used was not sensitive to outliers, which limited the insight into the error contribution of the individual landmarks in the position estimate.
There is still merit in using experimental images over numerical simulations. By completing an experiment, direct sensor inputs could be used in the navigation filter and hardware integration could be tested as well. By using motion capture and robotics to more accurately position all the components of the experiment, the results would become much more reliable. Even if some errors remain inherent in the experiment, it would prove robustness of the navigation filter if it functions under those conditions.