Contact dynamic models for active debris capturing using a net are presented and analyzed using numerical simulations. The contact dynamics are based on two methods: the penalty-based method and the impulse-based method. Both methods apply contact detection algorithms based on the Axis-Aligned Bounding Box. The impulse-based method is, for the first time, being used in a net capturing scenario. Strengths and weaknesses of both models are compared and discussed. Moreover, the results from numerical simulations of target capturing are presented and analyzed to evaluate the effectiveness of the contact dynamic models. It is found that the average difference of bullet trajectories obtained by two models can be restricted within 6% when it compares with the dimension of the net.

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This paper presents an innovative approach combining a fuzzy controller and a control allocation method applied to the control problem of allocating actuators’ efforts in an over-actuated system. The controller is applied to a space debris removal mission using a deployable net on-board a 3U CubeSat. The controller calculates the necessary effort of each thruster on-board the spacecraft to compensate the disturbances generated by the firing of the bullets attached to the borders of the net. Two cases with four and six thrusters are tested in a simulation scenario with experimental data. The simulation also covers the non-nominal situation of failure in one of the thrusters. A Monte Carlo simulation is performed in order to assess different scenarios. Results show that the proposed approach successfully recovers the stability of the satellite within a reasonable time. A comparison against a traditional control allocation method is done to assess the performance of the proposed approach specially in terms of computational time. Results with both methods are similar in terms of stabilization time and computational time.

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Space debris poses a big threat to operational satellites which form a crucial infrastructure for society. According to the main source of information on space debris, the U.S. Space SurveillanceNetwork (SSN), more than 17 500 objects larger than 10 cmhave been catalogued as of February 2017. Among the total number of objects in orbit, only 1875 spacecraft are active, i.e., around 10% of the objects are operating in an environment where 90% of the other objects are space debris. Even more serious, space debris is a threat to astronauts. In March 2009, a five inch space debris object passed particularly close to the International Space Station (ISS). Fortunately, the alarmwas cleared 10 minutes later. Moreover, the collision of the satellites Cosmos 2251 and Iridium 33 in 2009 highlighted the threat by space debris, since it signaled a trend that the future space environment will be dominated by fragmentation debris generated via similar collisions, instead of explosions of rocket upper stages, which had formed the majority of space debris objects in the past. To mitigate the risk of collision and stabilize the space environment, active debris removal (ADR) is of great relevance. According to an analysis by NASA, five space debris objects need to be removed each year to stabilize the space environment starting from the year 2020. The objective of this research is to investigate the net capturing method for active space debris removal. To remove a debris object from its orbit, many capturing and removal methods have been proposed, such as using a robotic arm, a tethered space robot, or a harpoon system. Among the existing ADR methods, net capturing is regarded as one of the most promising capturing methods due to its multiple advantages. For example, it allows a large distance between a chaser satellite and a target, so that close rendezvous and docking are not mandatory. It is furthermore compatible to different sizes, shapes and orbits of space debris. Additionally, it is flexible, lightweight and cost efficient. Even though some research on net capturing has been performed, the dynamics of net deployment and debris capturing and the feasibility and reliability of capturing a tumbling target using a net are not fully understood. Based on the relevance of this problem and a review of the state-of-the-art of the scientific literature, the following research questions were formulated. These research questions are answered in this thesis. RQ1. Which levels of non-cooperativeness of space debris exist? Which are their associated capturing and/or removal methods and what is the role the net capturing method plays among all those methods? RQ2. What are the dynamic characteristics of the net capturing method? RQ3. How to reliably capture a tumbling and non-cooperative debris object using the net capturing method? To characterize the net capturing method among existing ADR methods and to address the strengths and weaknesses of the net capturing method, matrices with the advantages and drawbacks of the most relevant capturing and removal methods are developed. Space debris objects were divided into three main categories based on their properties, namely, non-operational satellites, rocket upper stages and fragments from collision or explosion. A tailored associated capturing and removal method for each category of space debris objects is provided to facilitate decision-making through these ADR methods. A comparison of the most relevant ADR methods concludes that net capturing is considered as a promising method among others due to its multiple advantages. It is also found that capturing a tumbling space debris object with unknown physical properties is still facing many technological challenges. Therefore, capturing of tumbling targets using a net needs to be further investigated. The net capture mechanism consists of four flying weights in each corner of a net. The flying weights, named "bullets", are shot by a spring system, named "net gun". These four bullets expand the large net thus wrapping the target that will be transported by the tether connecting the chaser and the net. This thesis starts with the analysis of the deployment dynamics of a net. The deployment dynamic characteristics of a net folded in a pattern proposed in this research called "inwards-folding scheme" are investigated based on the mass-spring model and the absolute nodal coordinates formulation (ANCF) model. Deployment dynamics of a net based on the ANCF model are, for the first time, modeled, analysed and discussed in-depth. Besides, four critical parameters describing the deployment dynamic characteristics of the net, namely, the maximum area, the deployment time, the travelling distance and the effective period are defined. A sensitivity analysis of the initial input parameters, such as the initial bullet velocity, the shooting angle and the bullet mass with respect to the four critical parameters are performed. Simulations based on the ANCF model are performed and compared with the conventional mass-spring model. The results from both methods show a good agreement on changes of the four critical parameters. Furthermore, the ANCF model is more capable of describing the flexibility of the net with fewer nodes than the conventional mass-spring model. However, it is more computationally expensive. To investigate the contact dynamics between a net and a target, two contact modeling methods: the penalty-based and the impulse-based method are compared and analyzed. The theoretical solutions of the single contact and the multiple contacts dynamics based on the impulse-based method are derived. To our knowledge, the impulse-based method is, for the first time, being used in a net capturing scenario. Numerical simulations of targets with basic shapes, i.e., a cube, a ball and a cylinder, are performed to cross-verify the two contact models. It is concluded that the impulse-based method is superior to the penalty-based method with respect to the penetration avoidance and computational robustness. Moreover, the modeling of the flexibility of a net is addressed and discussed for the first time. To investigate the influence of the flexibility modeling on the net dynamics, simulations of capturing of a ball- and a cube-shaped target using themass-spring model and the ANCF model are performed and compared, respectively. However, it is found that the modeling of the flexibility of a net for capturing a space debris object has little influence on net deployment and contact dynamics. The dynamics of the net deployment and contact with the target have to be experimentally validated. A parabolic flight experiment performed under ESA contract allows to compare the experimental results with the simulations of the net deployment and the capturing phase. In the net deployment phase, simulation results based on both net modelling methods, the mass-spring model and the ANCF model, are compared with the experimental results. From the analysis of the absolute and the average relative residuals between the simulations and results of the parabolic flight experiment, it is concluded that both models are able to describe the motion of the bullets and the net along the traveling direction with an average relative residual error up to 15%. In the net capturing phase, both contact models, the penalty-based method and the impulse-based method, are validated by the parabolic flight experiment of the capturing of an Envisat mockup. The comparison shows that the average difference between the two models is limited to 7% when comparing with the travelling distance of the net. With the validated net deployment and contact dynamic models, net capturing of free-floating targets and tumbling targets is investigated for the first time. The net’s compatibility to handle different sizes and shapes of targets is demonstrated by simulation results of the capturing of three types of targets varying in size and shape, namely, a 3-unit Cubesat without appendages, the simplified representation of the second upper stage of the Zenit-2 rocket and the Envisat satellite. Simulation results show that for free-floating targets the net is able to capture and surround the targets without pushing them away. For tumbling targets, the net without a closing mechanism is able to capture the targets when their tumbling rates are within a certain range: 0-1.5 rad/s for the Cubesat and 0-0.7 rad/s for the rocket upper stage. Simulations of the tumbling Envisat, which has appendages such as a solar panel and a radar antenna, indicates that the net capturing method is more robust to irregularly shaped targets than regularly shaped targets. Finally, a novel concept of a closing mechanism is designed and its effectiveness is demonstrated to ensure a successful capturing of the targets evenwith a higher tumbling rate.@en

A tethered-net is a promising method for space debris capturing. However, its deployment dynamics is complex because of the flexibility, and its dependency of the deployment parameters is insufficiently understood. To investigate the deployment dynamics of tethered-net, four critical deployment parameters, namely maximum net area, deployment time, traveling distance and effective period are identified in this paper, and the influence of initial deployment conditions on these four parameters is investigated. Besides, a comprehensive study on a model for the tethered-net based on absolute nodal coordinates formulation (ANCF) is provided. Simulations show that the results based on the ANCF modeling method present a good agreement with that based on the conventional mass–spring modeling method. Moreover, ANCF model is capable of describing the flexibility between two nodes on the net. However, it is more computationally expensive.

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Net capturing method has been proposed to mitigate the collision risk on satellites by space debris. The mass-spring model, which is usually applied as net model, has a limitation in describing the contact between a net and a target since that the fictitious penetration of the massless spring into the target cannot be avoided. In this paper, the absolute nodal coordinates formulation (ANCF) is applied to model the net. The ANCF model is able to describe the flexibility of the net and the penetration of the cables into the target can be overcome. The analysis of the contact dynamics between the net and the space debris object based on ANCF is presented for the first time. The characteristics and benefits of ANCF are described and analysed. A drawback of the ANCF was found to be its inferior computational performance.@en

Millions of space debris are orbiting the Earth and threatening operational space missions. Tethered-Net capturing has been one of the most promising methods dealing with space debris due to its flexibility and compatibility with the unknown topology of a target. Moreover, it offers a safe capturing distance, and the capturing mechanism is lightweight and cost efficient. Several simulators have been designed for simulating the net deployment and/or capturing movement. Nevertheless, little attention has been paid on capturing a tumbling target with a tethered-net. As consequence, its capability of capturing a tumbling target is insufficiently understood since both ground-based and space-based test are difficult to be performed. In this paper, a simulator for capturing tumbling targets using a tethered-net is introduced and followed by the analysis of the simulation results. This simulator is able to simulate the entire process of space debris capturing including the net shooting, net deployment, and the contact effect between a net and a tumbling target. The flexibility of the net is modelled by a series combination of mass-spring elements. The contact dynamics are based on two methods: the penalty-based method and the constraint-based method. Strengths and drawbacks of these two contact methods are discussed. A tumbling downscaled Envisat mock-up is built as the target in the simulator. Finally, as a main contribution in this paper, criteria for a successful capturing are defined, and an available tumbling rate range is suggested based on simulation results. This analysis provides a valuable guidance for a real mission design.@en