Visual 3D Reconstruction of a Rotating Object in Space Environment with a Least-Squares Framework

Abstract

This study focuses on a least-squares framework suitable for spacecraft onboard computing in the visual 3D reconstruction of a rotating target, such as asteroids or space debris. During a proximity mission, recognizing the motion and shape of a target is crucial to touchdown on it or seize it before starting the actual operation. The 3D reconstruction of objects from 2D images, or bundle adjustment, has been intensively studied in the field of computer vision. Most algorithms involve nonlinear optimization and are computationally expensive; therefore, they require high-performance computers on the ground to obtain a solution. However, a strong demand exists for lightweight algorithms that can be operated on onboard computers to reduce spacecraft–ground communication delays. We analyzed the 3D reconstruction problem and formulated it as an overdetermined system of linear equations. We solved these by applying least-square solutions. Linear approximation is justified under the unique circumstances of the space environment, that is, no friction exists with air or other objects, and hence the motion is considerably simple in the absence of an external force. The least-squares framework requires only matrix calculations, and its computational complexity is considerably less than that of conventional algorithms. The simulation results demonstrate the accuracy of the 3D reconstruction acquired by our method.