Net deployment and contact dynamics of capturing space debris objects

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.