Quantifying Uncertainty in Space Debris Capture with Active Tether-Net Systems Caused by Noisy Observations

Active tether-net systems are a promising solution for capturing large non-cooperative targets, such as space debris, by deploying a flexible net manipulated by maneuverable units (MUs). However, concurrent systematic explorations of design and control choices of the tether-net system to understand its full potential remain limited, partly due to the complex, constrained, nonlinear optimization problem that it presents -- one that involves a mixture of continuous, integer and categorical variables, with the latter two arising from net connectivity and component choices, respectively. Classical binary encoding methods are often ineffective for solving highly nonlinear and multimodal Mixed Combinatorial Nonlinear Programmings (MCNLPs) in engineering design, while integer coding approaches can introduce spurious relations among combinations. Given the graph-structured characteristics of the combinatorial space, this paper adopts and extends a new graph-learning-aided optimization approach to solve this MCNLP problem. Here, a Graph Neural Network (GNN) is trained to score (as output) and thereof recommend candidate combinations represented as nodes in a graph, with the continuous variable vector portion of a candidate design given as input. As a result, the MCNLP optimization reduces to an NLP, which can be solved using standard solvers. While this reduction approach is agnostic to the choice of the NLP solver, here a state-of-the-art Particle Swarm Optimization (PSO) algorithm with gradient-based fine-tuning is used as the solver. Demonstrated on the problem of concurrently designing the morphology of the net, choice of mass and thrusters in the MUs and aiming points used by the controller of the tether-net system, the GNN-based recommender is shown to provide significantly faster convergence to similar optimal solutions, compared to direct solution of the MCNLP problem.

Quadrotors offer the agility needed to rapidly transport suspended payloads during time-critical applications, including search-and-rescue and medical delivery. While suspended-payload transport and traversal for these missions are well studied, the highly dynamic targeted release of the payload remains comparatively underexplored. State-of-the-art approaches typically rely on model-based trajectory optimization and tracking; however, these methods often yield sub-optimal performance due to conservative feasibility constraints, tracking errors, and the inherent difficulty of analytically modeling flexible rope dynamics. To overcome these limitations, we propose a hybrid simulation framework that couples a high-fidelity analytical quadrotor model with a physics solver for complex rope and payload interactions. By exchanging forces between the two domains at every step, we obtain a physically accurate simulation of the suspended-payload system. Leveraging this environment, we train a deep reinforcement learning (RL) policy that executes agile, accurate payload throws to designated targets. Deployed zero-shot on hardware, our RL policy pushes the boundary of the agility-accuracy trade-off, outperforming the model-based baseline by reducing the landing error by up to 50% and the throw duration by up to 30%. Ablation studies confirm that the coupled simulation is the key enabler of these gains. We further show that the same pipeline trains a policy driven by visual observations rather than an explicit state estimate, achieving accuracy comparable to that of the state-based policy. To accelerate future research in dynamic aerial manipulation, we open-source the simulator to the community upon acceptance.

Modeling tethered space systems is critical for advanced orbital operations. Flexible components such as tethers and space nets are integral to these systems but present significant control challenges due to their high dimensional, strongly coupled, and nonlinear dynamics. While data driven methods offer alternative modeling approaches, they frequently struggle with long term predictive stability and spatial generalization. To address this, we propose the Koopman Graph Dynamics (KGD) framework to learn the structural dynamics by integrating the global linear evolution of the Koopman operator with the local topological priors of Graph Neural Networks. Building upon this representation, we develop a KGD based Model Predictive Control strategy for tethered space systems. Subsequently, the ground experiments on flexible tether and space net demonstrate the high precision modeling capabilities of the proposed method. Crucially, the framework exhibits exceptional capacity for spatial transfer without retraining. Models trained exclusively on small configurations successfully predict and control significantly larger, unseen physical scales. Furthermore, the orbit simulations within a physics engine verify the effectiveness of the proposed approach for tethered space systems.