Differentiable Rendering for Pose Estimation in Proximity Operations

Differentiable rendering aims to compute the derivative of the image rendering function with respect to the rendering parameters. This paper presents a novel algorithm for 6-DoF pose estimation through gradient-based optimization using a differentiable rendering pipeline. We emphasize two key contributions: (1) instead of solving the conventional 2D to 3D correspondence problem and computing reprojection errors, images (rendered using the 3D model) are compared only in the 2D feature space via sparse 2D feature correspondences. (2) Instead of an analytical image formation model, we compute an approximate local gradient of the rendering process through online learning. The learning data consists of image features extracted from multi-viewpoint renders at small perturbations in the pose neighborhood. The gradients are propagated through the rendering pipeline for the 6-DoF pose estimation using nonlinear least squares. This gradient-based optimization regresses directly upon the pose parameters by aligning the 3D model to reproduce a reference image shape. Using representative experiments, we demonstrate the application of our approach to pose estimation in proximity operations.Comment: AIAA SciTech Forum 2023, 13 pages, 9 figure

NaRPA: Navigation and Rendering Pipeline for Astronautics

This paper presents Navigation and Rendering Pipeline for Astronautics (NaRPA) - a novel ray-tracing-based computer graphics engine to model and simulate light transport for space-borne imaging. NaRPA incorporates lighting models with attention to atmospheric and shading effects for the synthesis of space-to-space and ground-to-space virtual observations. In addition to image rendering, the engine also possesses point cloud, depth, and contour map generation capabilities to simulate passive and active vision-based sensors and to facilitate the designing, testing, or verification of visual navigation algorithms. Physically based rendering capabilities of NaRPA and the efficacy of the proposed rendering algorithm are demonstrated using applications in representative space-based environments. A key demonstration includes NaRPA as a tool for generating stereo imagery and application in 3D coordinate estimation using triangulation. Another prominent application of NaRPA includes a novel differentiable rendering approach for image-based attitude estimation is proposed to highlight the efficacy of the NaRPA engine for simulating vision-based navigation and guidance operations.Comment: 49 pages, 22 figure

Averaged Solar Radiation Pressure Modeling for High Area-to-Mass Ratio Objects in Geostationary Space

Space Situational Awareness is aimed at providing timely and accurate information of the space environment. This was originally done by maintaining a catalog of space objects states (position and velocity). Traditionally, a cannonball model would be used to propagate the dynamics. This can be acceptable for an active satellite since its attitude motion can be stabilized. However, for non-functional space debris, the cannonball model would disappoint because it is attitude independent and the debris is prone to tumbling. Furthermore, high area-to-mass ratio objects are sensitive to very small changes in perturbations, particularly those of the non-conservative kind. This renders the cannonball model imprecise in propagating the orbital motion of such objects. With the ever-increasing population of man-made space debris, in-orbit explosions, collisions and potential impacts of near Earth objects, it has become imperative to modify the traditional approach to a more predictive, tactical and exact rendition. Hence, a more precise orbit propagation model needs to be developed which warrants a better understanding of the perturbations in the near Earth space. The attitude dependency of some perturbations renders the orbit-attitude motion to be coupled. In this work, a coupled orbit-attitude model is developed taking both conservative and non-conservative forces and torques into account. A high area-to-mass ratio multi-layer insulation in geostationary space is simulated using the coupled dynamics model. However, the high fidelity model developed is computationally expensive. This work aims at developing a model to average the short-term solar radiation pressure force to perform computationally better than the cannonball model and concurrently have a comparable fidelity to the coupled orbit-attitude model