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Tethered net systems are considered one of the most effective solutions for addressing the problem of space debris. However, it is crucial to study the robustness of net-based debris capture in the presence of a wide range of possible activation and environmental uncertainties. The aim of this study was to analyze the limitations and operational envelope of tethered net systems in capturing space debris, with a particular focus on robustness and safety. The success of capture in nonnominal conditions was investigated, with errors considered in the target position, angular velocity, and parameters concerning the ejection of the net. In the sensitivity study, a capture quality index and mission safety factor were used to evaluate the success or failure of capture in an automated way. The quantitative relationships between relative parameter errors and capture evaluation metrics are also presented. The results of the sensitivity studies are promising and suggest that the target capture is robust to inaccuracies in the mission parameters beyond what is expected in reality. 

Tether-nets deployed from a chaser spacecraft are a promising solution to capturing space debris. The success of the one-shot capture process depends on the net’s structural dynamic properties, attributed to its physical design, and on the ability to perform an optimal launch and closure subject to sensing and actuation uncertainties. Hence, this paper presents a reliability-based optimization framework to simultaneously optimize the net design and its launch and closing actions to minimize the system mass (case 1) or closing time (case 2) while preserving a specified probability of capture success. Success is assessed in terms of a capture quality index and the number of locked node pairs. Gaussian noise is used to model the uncertainties in the dynamics, state estimation, and actuation of the tether-net, which is propagated via Monte Carlo sampling. To account for uncertainties and ensure computational efficiency, given the cost of simulating the tether-net dynamics, Bayesian optimization is used to solve this problem. Optimization results show that the mission success rate in the presence of uncertainties has increased from 75% to over 98%, while the capture completion time has almost halved. 

One of the most promising solutions to the issue of the increasing amount of space debris orbiting the Earth is net-based Active Debris Removal. For accurate contact detection of thin target geometries with lumped-parameter modeled nets in simulations, many nodes (possibly 10 or more) must be introduced along threads. However, such introduction significantly increases the computational cost of simulations. This work proposes a modeling approach that introduces additional nodes during the deployment phase of the simulation rather than at the beginning to reduce such costs. The approach conserves the net’s total linear momentum and adheres to the work-energy principle when employed mid-simulation. Through both quantitative and qualitative comparisons of nets with and without model switching, this work demonstrates that the methodology does not alter the overall dynamics of the net flight toward the target in a significant way. Capture simulations of a scaled-down Envisat satellite model are performed, where the introduction of model switching results in approx. 2.45 times faster simulation without compromising accuracy in the representation of capture. 

Tethered capture of space debris is a promising method of Active Debris Removal, but has numerous well-known challenges in the post-capture phase. Control of the system in this phase is complicated by nonlinear dynamics with the potential of chaotic motion, unknown debris parameters, and debris tumbling. The inherent uncertainty present in the system and the need for control often necessitate the estimation of debris states and parameters such that the post-capture system can remain controlled. To this end, a relative distance Proportional-Integral-Derivative control and an Unscented Kalman Filter are implemented during the post-capture phase of an ADR mission. It is assumed that some debris (target) states and properties are unknown to the chaser, requiring the estimation of the attitude, angular rates, and principal moments of inertia of the target. For estimating these states, the UKF uses measurements of the tether tension magnitude and pixel coordinates of feature points on the target provided by a camera mounted on the chaser. Both estimation and control are done simultaneously, simulating online estimation and control of an ADR mission. The PID control was found to maintain safe conditions when using the estimated states in two separate Monte-Carlo simulations, differing in the measurement frequency of the pixel coordinates, while the estimation of the principal moments of inertia of the debris was satisfactory. 

This work validates lumped-parameter models and cable-based models for nets against data from a parabolic flight experiment. The capabilities of a simulator based in Vortex Studio, a multibody dynamics simulation framework, are expanded by introducing i) a lumped-parameter model of the net with lumped masses placed along the threads and ii) a flexible-cable-based model, both of which enable collision detection with thin bodies. An experimental scenario is recreated in simulation, and the deployment and capture phases are analyzed. Good agreement with experiments is observed in both phases, although with differences primarily due to imperfect knowledge of experimental initial conditions. It is demonstrated that both a lumped-parameter model with inner nodes and a cable-based model can enable the detection of collisions between the net and thin geometries of the target. While both models improve notably capture realism compared to a lumped parameter model with no inner nodes, the cable-based model is found to be most computationally efficient. The effect of modeling thread-to-thread collisions (i.e., collisions among parts of the net) is analyzed and determined to be negligible during deployment and initial target wrapping. The results of this work validate the models and increase the confidence in the practicality of this simulator as a tool for research on net-based capture of debris. A cable-based model is validated for the first time in the literature. 

The earth’s orbit is becoming increasingly crowded with debris that poses significant safety risks to the operation of existing and new spacecraft and satellites. The active tether-net system, which consists of a flexible net with maneuverable corner nodes, launched from a small autonomous spacecraft, is a promising solution to capturing and disposing of such space debris. The requirement of autonomous operation and the need to generalize over debris scenarios in terms of different rotational rates makes the capture process significantly challenging. The space debris could rotate about multiple axes, which along with sensing/estimation and actuation uncertainties, call for a robust, generalizable approach to guiding the net launch and flight – one that can guarantee robust capture. This paper proposes a decentralized actuation system combined with reinforcement learning based on prior work in designing and controlling this tether-net system. In this new system, four microsatellites with thrusters act as the corner nodes of the net, and can thus help control the flight of the net after launch. The microsatellites pull the net to complete the task of approaching and capturing the space debris. The proposed method uses a reinforcement learning framework that integrates a proximal policy optimization to find the optimal solution based on the dynamics simulation of the net and the MUs in Vortex Studio. The reinforcement learning framework finds the optimal trajectory that is both energy-efficient and ensures a desired level of capture quality