Periodic Reporting for period 2 - THOR (Towards Higher Levels of Autonomy and Robustness in Space Operations through Uncertainty Management and Quantification)
Berichtszeitraum: 2023-05-01 bis 2024-04-30
The THOR project has explored gravity field modeling and the gravimetry problem around asteroids. These celestial bodies have irregular shapes and heterogeneous density distributions that create a very complex gravity field. It is well-known that satellite orbits in these gravity fields can divert into escape or collision trajectories. In astrodynamics, gravity field modeling beyond the point mass is usually done with the spherical harmonics series expansion. However, spherical harmonics are not a valid approximation within the celestial body's circumscribing sphere, which is relatively large for elongated asteroids. There are several alternatives to spherical harmonics, such as polyhedron, mascon, and various neural network approaches. The THOR project mainly focuses on the discretized mascon approach and its fusion with physics-informed neural networks. Additionally, it also offers perspectives on how to determine the asteroid gravity field while on orbit (namely gravimetry).
From a societal perspective, THOR is mainly involved in advancing deep space exploration. In particular, it focuses on asteroids, which are of great scientific interest since they are remnants of the early Solar System period. Moreover, certain types of asteroids contain valuable resources such as water, metals, and minerals. These resources could be mined and utilised in space exploration endeavours, potentially enabling long-duration space missions through resource utilisation. The THOR project contributes to these areas by developing methods to characterize gravity around asteroids while in flight. Asteroid details are hardly observable by Earth-based sensors; thus, they have to be characterised in situ.
THOR project objectives can be succinctly resumed in:
I. How can we solve the asteroid gravimetry problem using on-board optical navigation measurements?.
II. How can we fuse physics-founded gravity models with neural network models?.
From a societal perspective, THOR is mainly involved in advancing deep space exploration. In particular, it focuses on asteroids, which are of great scientific interest since they are remnants of the early Solar System period. Moreover, certain types of asteroids contain valuable resources such as water, metals, and minerals. These resources could be mined and utilised in space exploration endeavours, potentially enabling long-duration space missions through resource utilisation. The THOR project contributes to these areas by developing methods to characterize gravity around asteroids while in flight. Asteroid details are hardly observable by Earth-based sensors; thus, they have to be characterised in situ.
THOR project objectives can be succinctly resumed in:
I. How can we solve the asteroid gravimetry problem using on-board optical navigation measurements?.
II. How can we fuse physics-founded gravity models with neural network models?.
During the outgoing phase at CU Boulder, the THOR project has concentrated on addressing the on-orbit gravimetry problem. The objective is to utilize optical navigation measurements for determining the asteroid's gravity field. To achieve this, we have integrated a dynamical model-compensated unscented Kalman filter (DMC-UKF) with a mascon gravity optimizer. The primary achievement is the capability to conduct gravimetry using on-board measurements around an asteroid.
Subsequently, during the return phase at U. Sevilla, THOR aimed to refine the previously optimized mascon gravity models by integrating them with neural networks. This approach amalgamates the strengths of a physics-founded model, which extrapolates effectively in data-sparse regions, with the high accuracy provided by neural networks within the dataset area. The outcome is a highly accurate yet lightweight fused gravity model tailored for asteroids.
THOR research outputs are:
J.C. Sanchez, H. Schaub, "Simultaneous navigation and mascon gravity estimation around small bodies," Acta Astronautica, vol. 213, pp. 725-740, 2023.
J.C. Sanchez, J.R. Martin, "Investigating the fusion of mascon and neural network gravity models", submitted to AAS/AIAA Astrodynamics Specialist Conference, 2024.
J.C. Sanchez, H. Schaub, " Small body navigation and gravity estimation using Kalman filter and least-squares fitting", 33rd AAS/AIAA Space Flight Mechanics Meeting, Austin, USA, 2023.
J.C. Sanchez, H. Schaub, "Semi-autonomous navigation and gravity estimation around small bodies", 2nd International Stardust Conference, Noordwijk, The Netherlands, 2022.
THOR dissemination comprises:
https://cafeconciencia.fundaciondescubre.es/noticias/estudiantes-de-bachillerato-se-toman-un-cafe-con-ciencia-aeroespacial-para-celebrar-la-semana-del-espacio/
https://lanochedelosinvestigadores.fundaciondescubre.es/investigador/julio-cesar-sanchez-merino/
https://www.us.es/actualidad-de-la-us/11-investigaciones-de-la-us-reciben-ayudas-marie-curie
Subsequently, during the return phase at U. Sevilla, THOR aimed to refine the previously optimized mascon gravity models by integrating them with neural networks. This approach amalgamates the strengths of a physics-founded model, which extrapolates effectively in data-sparse regions, with the high accuracy provided by neural networks within the dataset area. The outcome is a highly accurate yet lightweight fused gravity model tailored for asteroids.
THOR research outputs are:
J.C. Sanchez, H. Schaub, "Simultaneous navigation and mascon gravity estimation around small bodies," Acta Astronautica, vol. 213, pp. 725-740, 2023.
J.C. Sanchez, J.R. Martin, "Investigating the fusion of mascon and neural network gravity models", submitted to AAS/AIAA Astrodynamics Specialist Conference, 2024.
J.C. Sanchez, H. Schaub, " Small body navigation and gravity estimation using Kalman filter and least-squares fitting", 33rd AAS/AIAA Space Flight Mechanics Meeting, Austin, USA, 2023.
J.C. Sanchez, H. Schaub, "Semi-autonomous navigation and gravity estimation around small bodies", 2nd International Stardust Conference, Noordwijk, The Netherlands, 2022.
THOR dissemination comprises:
https://cafeconciencia.fundaciondescubre.es/noticias/estudiantes-de-bachillerato-se-toman-un-cafe-con-ciencia-aeroespacial-para-celebrar-la-semana-del-espacio/
https://lanochedelosinvestigadores.fundaciondescubre.es/investigador/julio-cesar-sanchez-merino/
https://www.us.es/actualidad-de-la-us/11-investigaciones-de-la-us-reciben-ayudas-marie-curie
In the field of in-situ gravimetry around asteroids, previous works have extensively utilised spherical harmonics gravity models. These models offer advantages because they are parameterised in terms of coefficients that can be incorporated into the estimation state of a filter. In line with this approach, there have been efforts to re-examine the gravity determination of the pioneer NEAR mission on asteroid 433 Eros. However, these models often prove inadequate within the body's circumscribing sphere, compromising their suitability for low-altitude operations such as descent and landing. Alternative models (e.g. mascon) that avoid accuracy losses within the circumscribing sphere present challenges when integrating into a filter-based approach. This is primarily due to the large number of parameters or the physical constraints associated with these alternative models. THOR proposes leveraging the concept of dynamical model compensation to estimate unmodeled empirical accelerations along the spacecraft trajectory. This process yields an on-orbit position-acceleration dataset that can be utilised to determine the parameters of a gravity model. Specifically, we have developed an optimised mascon model with physical consistency. This is specially relevant in scenarios where data is sparse and addressing physical constraints directly becomes imperative to ensure robust extrapolation in data less regions. In THOR, we have developed a novel optimiser that employs Adam gradient descent with constraints projection to ensure that masses remain positive and confined within the asteroid shape.
Regarding the topic of gravity field modeling, THOR has explored the concept of integrating robust physical models with data-driven neural networks. Researchers have devoted extensive efforts, with ongoing progress, to develop accurate yet lightweight gravity models for on-board autonomy. In THOR, pre-trained mascon models have been combined with physics-informed neural networks (PINNs). Mascon models offer a precise initial approximation to the asteroid's gravity field and effectively extrapolate the high-altitude profile where data is lacking. However, their learning capacity is constrained by the finite number of masses used, and errors may arise from mass placement near the surface. Recent advancements in PINN gravity models, demonstrated by J. Martin and H. Schaub, have showcased their capability to approximate highly complex patterns, such as surface gravity. Nonetheless, these authors observed neural networks' limitations in extrapolating patterns beyond data bounds, prompting the inclusion of low-fidelity analytical models (e.g. point mass) to prevent divergence. THOR proposes to enhance the low-fidelity analytic component with pre-trained mascon models, which exhibit accuracy except in areas very close to the surface. This approach enables continued learning of complex patterns by the PINN through the introduction of new basis functions. Currently, these models have been implemented in the open-source Basilisk astrodynamics framework to benefit the broader astrodynamics community. Preliminary results indicate a one-order-of-magnitude decrease in 1-day propagation errors for orbits around asteroid Eros with the fused model. We anticipate completing and submitting a journal version of this work after summer 2024.
Regarding the topic of gravity field modeling, THOR has explored the concept of integrating robust physical models with data-driven neural networks. Researchers have devoted extensive efforts, with ongoing progress, to develop accurate yet lightweight gravity models for on-board autonomy. In THOR, pre-trained mascon models have been combined with physics-informed neural networks (PINNs). Mascon models offer a precise initial approximation to the asteroid's gravity field and effectively extrapolate the high-altitude profile where data is lacking. However, their learning capacity is constrained by the finite number of masses used, and errors may arise from mass placement near the surface. Recent advancements in PINN gravity models, demonstrated by J. Martin and H. Schaub, have showcased their capability to approximate highly complex patterns, such as surface gravity. Nonetheless, these authors observed neural networks' limitations in extrapolating patterns beyond data bounds, prompting the inclusion of low-fidelity analytical models (e.g. point mass) to prevent divergence. THOR proposes to enhance the low-fidelity analytic component with pre-trained mascon models, which exhibit accuracy except in areas very close to the surface. This approach enables continued learning of complex patterns by the PINN through the introduction of new basis functions. Currently, these models have been implemented in the open-source Basilisk astrodynamics framework to benefit the broader astrodynamics community. Preliminary results indicate a one-order-of-magnitude decrease in 1-day propagation errors for orbits around asteroid Eros with the fused model. We anticipate completing and submitting a journal version of this work after summer 2024.