International Journal of Aerospace Engineering

Volume 2018, Article ID 9731512, 9 pages

https://doi.org/10.1155/2018/9731512

## Relative Pose and Inertia Determination of Unknown Satellite Using Monocular Vision

Miusskaya Sq.4, Keldysh Institute of Applied Mathematics RAS, Moscow 125047, Russia

Correspondence should be addressed to Danil Ivanov; moc.liamg@svonavilinad

Received 7 March 2018; Accepted 5 September 2018; Published 29 October 2018

Academic Editor: Vaios Lappas

Copyright © 2018 Danil Ivanov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The paper proposes a two-stage algorithm for autonomous relative motion determination of noncooperative and unknown object flying in space. The algorithm is based on image processing and can be applied to motion determination of space debris with unknown geometry and dynamic characteristics. The first stage of the algorithm is aimed at forming a database of possible reference points of the object during continuous observation. Tensor of inertia, initial velocity, and angular velocity of the object are also estimated. Then, these parameters are used in the second stage of the algorithm to determine the relative motion in real time. The algorithm is studied numerically and tested using the video of the Chibis-M microsatellite separation.

#### 1. Introduction

A large amount of space debris flying around the Earth prevents intensive exploration of near-Earth orbits. Space community aims to remove the most dangerous fragments and inactive satellites. Many missions were proposed in the last decade. One of the most perspective concepts is to launch the special “chaser” satellite that will collect debris and move them to the low Earth orbit, so they will be rapidly deorbited by atmospheric drag. The most crucial and complicated part of this algorithm is the debris collection [1], but for the task solving it is necessary to determine the relative motion of the debris of unknown shape and dynamic characteristics.

In recent years, relative position and attitude estimation of spacecraft have been extensively studied, and many methods have been proposed. Chaser satellite must be equipped with the onboard sensor for relative pose determination, i.e., relative attitude and relative center of mass position. The most reliable sensor type is an optical one that usually comprises a CCD camera. In the paper [2], an overview of the existing visual-based systems is presented, and in the paper [3], the state of the art of the cooperative and uncooperative satellite pose determination techniques are presented. A set of papers are devoted to the developing and flight testing of the algorithms for relative center of mass position determination of the unknown target using angles-only visual navigation [4–6]. The relative pose navigation system based on image processing was implemented in several projects; for example, PRISMA [7, 8], it is used during docking stage of the “Progress” to ISS [9] and also of the cargo spacecraft ATV [10–12]. In the paper [13], a set of the relative initial pose estimation techniques are compared. A number of papers are devoted to the developing of image-based navigation for satellites using laboratory facility [14–19]. In the papers mentioned above, the motion determination algorithms are usually based on recognition of specially designed satellites’ marks which positions are known in the target-related reference frame. Moreover, the dynamic characteristics such as tensor of inertia or position of the center of mass are used for target satellite motion prediction, i.e., the 3D model of the target is known. In the case of the unknown target before the pose determination, a prior monitoring stage should proceed and the model of the target is estimated. The well-known concept of the simultaneous localization and mapping (SLAM) can be adopted for these tasks [20]. A set of papers are devoted to the problem using images obtained by multiple cameras installed onboard of the chaser satellite [21–23]. For example, a SLAM approach based on the extended Kalman filter and inertia tensor determination using stereovision measurements is proposed in the paper [22]. A feature-based SLAM algorithm using the stereovision system is developed in [23]. There are a very few papers on the pose determination of unknown object using monocular vision measurements. In the paper [24], a purely monocular-based vision SLAM algorithm for pose tracking and shape reconstruction of an unknown target is presented; however, it is assumed that the target rotates with constant angular velocity and the target inertia tensor is not estimated. The fusion of the data obtained from the monocular camera and a range sensor is utilized in the algorithm for the pose, and shape reconstruction of a noncooperative spacecraft is considered in the paper [25]; the unscented Kalman filter is used for the estimation of variables, where is the number of the feature points. The current paper is quite similar to [25], but we divided the pose determination algorithm into two stages—the most computational power consumed determination of the reference point position and inertia tensor using least square method and the second, determination of the relative pose only based on the data obtained by the first stage. So, it is not necessary to estimate the reference points and the inertia tensor all the time since it is assumed that they are constant since the unknown satellite is considered as a rigid body.

In this paper, a noncooperative and unknown object relative motion determination algorithm based on the image processing of satellite illuminated by the Sun is considered. Initially, the target satellite has unknown geometry and mass distribution. It is assumed that the object has some features (surfaces, lines, or points) which can be recognized in the picture. The algorithm consists of two stages. First, the reference features’ positions in target satellite reference frame are estimated during continuous observation. Also, the tensor of inertia is determined using video information. During this stage, the database of observable reference features is formed. These features will be used later for relative motion estimation in real time. The pose vector of a relative state that consists of the center of mass position, linear velocity, attitude quaternion, and angular velocity vectors is estimated. The main idea of the first stage of the algorithm is to find such dynamical parameters and positions of reference points that minimize the difference between the points’ pixel coordinates on frames and the estimated by model ones.

The second stage of the algorithm is briefly described as follows. For a given initial relative state vector, the satellite reference point positions are projected to the video frame. Reference points’ projections are searched then in the neighborhood of these positions. Found reference points’ positions are inaccurate due to a noise and discrete sensing element. Least-square method (LSM) is used to minimize the sum of squared distances between the predicted and obtained reference points’ positions in the frame. In such a way, the relative position and attitude are roughly estimated. This estimation is used as the Kalman filter input to compute the state vector with higher precision. In the paper, the relative motion determination accuracy is investigated depending on the parameters of the objects. The algorithm is tested using the video of the Chibis-M microsatellite separation.

#### 2. Equations of Motion

Consider two satellites, a chaser and a target, flying along the circular LEO. Let the relative translational motion be described by well-known Clohessy-Wiltshire equations [26]: where , , and are coordinates of the target satellite with respect to the orbital reference frame , origin is placed in the chaser satellite center of mass which moves along a circular orbit of radius and with orbital angular velocity , axis is directed along chaser satellite radius-vector from the center of the Earth, is a normal vector to the orbit plane, and is the vector product of and (see Figure 1).