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Improved geometric positioning method with constellation configuration screening
Journal of Tsinghua University (Science and Technology) 2024, 64(11): 1979-1986
Published: 15 November 2024
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Objective

As the number of low earth orbit(LEO) satellites increases, the applicability of optical navigation technology, which uses these satellites as optical information sources, is continually improving. When three or more satellites are simultaneously observed within the optical field of view, the perspective-n-point (PnP) positioning method can be used for pose estimation and positioning. The PnP problem was initially used primarily for camera calibration. Currently the applications of the PnP problem have expanded to various engineering tasks, including simultaneous visual localization and mapping, spatial noncooperative target pose estimation, and the critical stages of rendezvous and docking. However, the PnP algorithm struggles with low positioning accuracy over long distances. Therefore, it is necessary to study the spatial geometric positioning problem when observing satellites at relative distances exceeding hundreds of kilometers.

Methods

This study begins by selecting positioning data sources and statistically investigating the impact of constellation configuration within the optical field of view on positioning errors. The relationships between the constellation area and positioning errors, the geometric angle and positioning errors, and the relationship between the orbit height distribution and positioning errors are analyzed. Through this analysis, the primary influencing indicators are identified as the area, angle, and distance indicators. The distance indicator, in particular, represents the three-dimensional information of the configuration, which cannot be characterized by position dilution of precision (PDOP). To unify the measurement space of each indicator, the indicators are normalized, and the entropy weight method is used to calculate the weight of each indicator. An evaluation function for the constellation configuration is established to assess the configuration availability. The availability distribution is statistically analyzed to determine the evaluation criteria. Finally, using the calculated availability, configurations that are less affected by image noise are selected for the PnP pose calculation. In addition, the difference between the PDOP and positioning error is presented, and the PnP pose is estimated after the configuration is evaluated.

Results

Taking the P3P problem as an example, the positioning error was smaller when the distribution area of the three satellites was larger and more dispersed. According to the proposed screening method, positioning accuracy was improved by more than 50% compared with the situation without screening. Additionally, the configuration positioning accuracy was improved by approximately 37% compared with that of the PDOP-optimized configuration.

Conclusions

Constellation satellites enhance space navigation information sources. Configuration screening effectively improves the accuracy of PnP geometric positioning over long distances, thereby introducing a new concept for long-distance optical navigation.

Research Article Issue
A comparative assessment of gravitational field modeling methods for binary asteroid landing
Astrodynamics 2024, 8(3): 417-435
Published: 13 March 2024
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The tradeoff between accuracy and efficiency in gravitational field modeling for binary asteroid landing is one of the challenges in dynamical analyses. Four representative gravitational modeling methods are employed and compared in this study. These are the sphere–sphere model, ellipsoid–sphere model, inertia integral-polyhedron method, and finite element method. This study considers the differences between these four models, particularly their effects on the landing dynamics of a lander. A framework to simulate the coupled orbit–attitude motion of a lander in a binary system is first established. Numerical simulations are then performed on the natural landings on the second primary of the (66391) Moshup–Squannit system. The results show significant differences in the final landing dispersions, settling time, and sliding distance when applying the simplified models. On the basis of the modeling accuracy and computational efficiency, the finite element method should be chosen for future missions.

Research Article Issue
Attitude-adjusting dynamical behavior of cubic rover on low-gravity testbed
Astrodynamics 2024, 8(1): 149-159
Published: 08 February 2024
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Cubic rovers that traverse by hopping systems are promising in low-gravity environments. Although several analyses of the control methods and mobility of the cubic rover are available, investigations of its attitude-adjusting behavior are still limited. This study derives the dynamic equations of the two attitude-adjusting modes of the cubic rover, referred to as walking and twisting. The relationships between the speed threshold and rotation angle of the cubic rover were investigated in both rigid and regolith environments using a self-designed low-gravity testbed. Comparative studies were conducted by considering the experimental and simulated outputs. The results of this study can be interesting for roving mission planning when exploring planetary moons and small celestial bodies.

Open Access EditorialNotes Issue
Message from the Guest Editors of the Special Issue on Entry, Descent, and Landing of Tianwen-1—China's First Mission to Mars
Astrodynamics 2022, 6(1): 1
Published: 04 January 2022
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Downloads:105
Editorial Issue
Message from the Guest Editors of the Special Issue on Astrodynamics and Engineering Aspects of Hayabusa2—Sample Return Mission to the Asteroid Ryugu
Astrodynamics 2020, 4(2): 87
Published: 30 June 2020
Abstract PDF (186.5 KB) Collect
Downloads:78

Editorial Issue
Message from the Guest Editors of the Special Issue on Solar-Photon Space Sailing
Astrodynamics 2019, 3(3): 205
Published: 07 September 2019
Abstract PDF (72 KB) Collect
Downloads:57

Review Article Issue
Solar sail 𝑯-reversal trajectory: A review of its advances and applications
Astrodynamics 2019, 3(1): 1-15
Published: 14 December 2018
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The set of the orbital angular-momentum reversal, or H-reversal, sailcraft trajectory was born as a type of unconventional precursor interstellar mission trajectory by using high-performance solar sails. Starting from an outline of the H-reversal sail trajectory, this paper mainly focuses on the 2D reversal-mode solution to the general solar-photon sail motion equations. The feasible region for H-reversal trajectories in fixed sail attitude angles is illustrated. Some interesting applications of the H-reversal trajectory are presented in detail to show its advantages. As a special case, a precursor interstellar probe can be delivered with a constant sail orientation in the H-reversal trajectory to be compared with the direct-motion sail flyby of the Sun. Of importance are the heliocentric periodic orbits in double H-reversal modes, obtained via both fixed and time-varying sail attitude angles. Two more applications involving H-reversal trajectories are discussed in terms of asteroid deflection and transfer trajectory to rectilinear orbits. Finally, some items of the mathematics behind the 3D motion-reversal trajectories are summarized.

Research Article Issue
Periodic orbits in the Chermnykh problem
Astrodynamics 2017, 1(1): 41-55
Published: 08 September 2017
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Periodic orbits in irregular gravitational fields are significant for an understanding of dynamical behaviors around asteroids as well as the engineering aspect for deep space explorations. The rotating mass dipole, referred to as the Chermnykh problem, is a good alternative model to study qualitative dynamical environments near elongated asteroids, like the asteroid 1620 Geographos, 216 Kleopatra, or 25143 Itokawa. In this paper a global searching method is adopted to search for periodic orbits around the dipole model based on the concept of Poincaré section of surface. Representative families of periodic orbits are illustrated with respect to all three topological cases of the dipole model. Topological transitions of orbits during iso-energetic continuations are also presented as well as identification of new types of periodic orbits.

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