Research on Relative Orbit and Attitude Estimation for Asteroid Exploration Using Stereo Cameras = 스테레오 카메라를 이용한 소행성 탐사 시 상대 궤도 및 자세 추정 연구

다국어 초록 (Multilingual Abstract)

Asteroids preserve relatively unaltered records of the early solar system, making them highly valuable targets for both scientific exploration and strategic technological development. However, their irregular shapes, heterogeneous mass distributions, and the severe communication latency inherent to deep-space environments render ground-based real-time control infeasible. As a result, autonomous navigation systems are essential. In particular, relative pose estimation for unknown and non-cooperative targets plays a critical role not only in future scientific missions but also in space security applications such as active debris removal and adversarial satellite tracking.
In this study, the asteroid proximity navigation problem is formulated as a static Simultaneous Localization and Mapping (SLAM) problem. To solve it, an Extended Kalman Filter (EKF)-based state estimation framework is developed. Feature points are detected and matched from stereo images captured by an onboard stereo camera using the SIFT algorithm, enabling simultaneous estimation of the asteroid’s relative pose and surface geometry. Simulations utilize synthetic stereo images generated in Blender and a realistic shape model of asteroid Itokawa, based on radar-derived data from NASA PDS. The camera is assumed to follow an orbital trajectory in the Hill frame, constantly oriented toward the asteroid.
RMSE analysis of the 3D feature points reconstructed via stereo triangulation shows larger errors in the depth direction, consistent with the limitations of disparity-based depth estimation. When estimating the asteroid centroid from these features, both arithmetic mean and spherical center methods exhibited opposite directional biases. A combined approach demonstrated improved neutrality and stability in centroid estimation.
For EKF-SLAM implementation, constant translational and rotational motion is assumed, and the estimation begins without any prior knowledge of the target's shape. A modified EKF-SLAM framework is proposed, incorporating iterative linearization and correction to mitigate linearization errors and improve numerical stability over long-term operations.
Numerical simulations confirm that the proposed modified EKF-SLAM outperforms the standard approach in terms of attitude and position estimation accuracy, and significantly improves surface mapping precision. These improvements are attributed to the iterative correction mechanism that compensates for modeling and observation errors, particularly under conditions of dynamic uncertainty. Moreover, the proposed method exhibits reduced error accumulation over time, indicating enhanced robustness against environmental variations.

국문 초록 (Abstract)

소행성은 태양계 형성 초기의 정보를 비교적 온전히 보존하고 있어 과학적·전략적 가치가 높다. 그러나 형상이 불규칙하고 질량 분포가 비균질한 데다, 통신 지연이 심한 심우주 환경에서는 지상 기반 실시간 제어가 불가능하므로, 자율 항법 기술이 필수적이다. 특히 사전 정보가 없는 비협조(non-cooperative) 천체에 대한 상대 포즈 추정 기술은 미래의 과학 탐사뿐 아니라 우주 안보 분야에서도 핵심적인 역할을 수행한다.
본 연구에서는 소행성 근접 항법 문제를 정적 SLAM(Simultaneous Localization and Mapping) 문제로 정의하고, 이를 해결하기 위한 EKF 기반 상태 추정 프레임워크를 설계하였다. 스테레오 카메라로부터 획득한 영상에서 SIFT 기반 특징점을 검출하고 매칭하여, 상대 포즈와 지형을 동시에 추정하였다. 시뮬레이션에는 Blender로 생성한 가상의 스테레오 이미지와 Itokawa의 실측 형상 모델을 사용하였고, Hill 좌표계에서 궤도 운동하는 카메라를 가정하였다.
스테레오 삼각측량을 통해 추출된 3차원 특징점의 RMSE 분석 결과, 깊이 방향에서 더 큰 오차가 나타났으며, 이는 시차 기반 깊이 추정의 특성에 기인한 것이다. 특징점들로부터 소행성 중심을 추정할 때 단순 평균과 구면 중심 방식 각각의 편향이 확인되었고, 두 방식을 결합함으로써 보다 안정적인 중심 추정이 가능함을 확인하였다.
EKF-SLAM 구현 시에는 소행성의 등속·등각속도 운동을 가정하고, 초기 형상이 주어지지 않은 상태에서 형상 및 상대 포즈 추정을 시작하였다. 본 연구에서는 반복 선형화 및 보정 기법을 도입하여 기존 EKF-SLAM의 구조를 개선하였고, 이는 선형화 오차를 줄이고 장기 운용 시 수치적 안정성과 정확도를 동시에 확보하는 데 효과적이었다.
수치 시뮬레이션 결과, 제안된 modified EKF-SLAM은 자세 및 위치 추정 정확도에서 기존 기법 대비 성능 향상을 보였고, 특히 지형 매핑 정확도에서 높은 오차 감소를 달성하였다. 이러한 성능 향상은 반복 보정 과정에 기반한 오차 보상 덕분이며, 동역학 불확실성이 존재할 때 더욱 효과적인 것으로 나타났다. 또한 시간 경과에 따른 오차 누적도 상대적으로 작아, 환경 변화에 대한 강인성도 향상되었음을 확인하였다.

목차 (Table of Contents)

• ListofTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
• ListofFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
• Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
• Chapter1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
• 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
• 1.2 ResearchObjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
• 1.3 ResearchMethodologyandDocumentOutline . . . . . . . . . . . . . . . . . . . . 7
• Chapter2: Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
• 2.1 ReferenceFrames. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
• 2.1.1 Inertialframe,ℐ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
• 2.1.2 Hillframe,ℋ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
• 2.1.3 Asteroid-Centered,Asteroid-Fixed(ACAF)Frame,𝒜. . . . . . . . . . . . . 11
• 2.1.4 SpacecraftBody-Fixed(SBF)frame,ℬ . . . . . . . . . . . . . . . . . . . . . 12
• 2.1.5 Camera-ReferenceFrame(CRF),𝒞 . . . . . . . . . . . . . . . . . . . . . . . 13
• i
• 2.1.6 ImageFrame(IMF),𝒟 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
• 2.1.7 Rotationmatrixandquarternion . . . . . . . . . . . . . . . . . . . . . . . . 14
• 2.2 ProblemandStateDefinitionforRelativeAsteroidPoseEstimation . . . . . . . . 15
• 2.2.1 OpticalNavigationandCameraParameters . . . . . . . . . . . . . . . . . . 15
• 2.2.2 ProblemDefinitionforRelativeAsteroidPoseEstimation . . . . . . . . . . 17
• 2.2.3 StateDefinitionforRelativeAsteroidPoseEstimation . . . . . . . . . . . . 19
• 2.3 ArchitectureofRecursiveFilter-basedEstimation . . . . . . . . . . . . . . . . . . 22
• 2.3.1 BayesianFilter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
• 2.3.2 KalmanFilter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
• 2.3.3 ExtendedKalmanFilter(EKF) . . . . . . . . . . . . . . . . . . . . . . . . . . 24
• Chapter3: ReconstructionofAsteroidSurfaceFeaturesAcquiredfromStereo
• Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
• 3.1 Imagepre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
• 3.2 AsteroidFeatureDetectionUsingSIFTDetector . . . . . . . . . . . . . . . . . . . . 29
• 3.3 ReconstructionofDetectedFeaturesintheCameraFramefromStereoImages . . 31
• 3.4 AsteroidFeaturematchingandindexing. . . . . . . . . . . . . . . . . . . . . . . . 33
• 3.5 AsteroidCentroidEstimationthroughShapeEstimation . . . . . . . . . . . . . . . 33
• Chapter4: Feature-basedRelativeAsteroidPoseEstimation . . . . . . . . . . . . 38
• 4.1 ArchitectureofFeature-basedRelativeAsteroidPoseEstimation . . . . . . . . . . 38
• 4.1.1 VisualSimultaneousLocalizationAndMapping(vSLAM) . . . . . . . . . . 38
• ii
• 4.1.2 ExtendedKalmanFilter-basedSimultaneousLocalizationandMapping(EKF
• SLAM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
• 4.1.3 ModificationofEKF-SLAM. . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
• 4.2 DynamicPredictionModelfortheRelativePoseoftheAsteroid. . . . . . . . . . . 48
• 4.3 Feature-basedObservationModel . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
• 4.3.1 StereoCameraObservationModelBasedon3DPointFeatures . . . . . . . 52
• 4.3.2 InverseObservationModelforStereoCameraMeasurements . . . . . . . . 56
• 4.3.3 SensitivityJacobianModelofObservationModel . . . . . . . . . . . . . . . 57
• 4.4 AugmentedStateEstimationfortheIncorporationofNewFeatures . . . . . . . . 58
• 4.5 ObservationCorrection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
• Chapter5: NumericalValidationviaMonteCarloSimulation . . . . . . . . . . . . 64
• Chapter6: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
• References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
• 국문초록. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83