Dynamic modeling of a net-membrane capture system with combined deformation for space debris removal

The rapid increase in space debris poses a significant threat to the safety of in-orbit spacecraft and the utilization of valuable orbital resources. Active debris removal (ADR) has emerged as the most effective approach to mitigating debris growth. However, traditional rigid capture methods are limited by constraints such as capture distance, target adaptability, and the risk of generating secondary debris, making them inadequate for the increasingly complex space debris environment. Net-membrane capture systems integrate smart materials with controllable deployment mechanisms, offering advantages such as long-range capture, adaptability to non-cooperative targets, and reusability. However, the dynamic characteristics throughout the entire process—shooting, deployment, contact, and wrapping capture—remain insufficiently understood. The combined stretching, shearing, and bending deformations of the membrane, along with the complex contact mechanics introduced by debris spin, pose challenges for traditional modeling approaches such as the finite element method (FEM) and the absolute nodal coordinate formulation (ANCF).

In a recent study published in Space: Science & Technology, a research team from the Chinese Academy of Sciences and the University of Electronic Science and Technology of China proposed a dynamic modeling and simulation method for a net-membrane capture system that accounts for combined deformations. The study develops a dynamic model of the membrane using the multiparticle method (MPM), incorporating stretching, shearing, and bending stiffness to accurately describe combined deformations. A contact model based on continuous contact theory and Coulomb’s law is also established to simulate the interaction between the membrane and debris. Through multiple sets of numerical simulations, the study systematically analyzes the effects of shooting velocity, ejection angle, and bullet mass on membrane deployment behavior, leading to the identification of optimal shooting parameters. Simulation results demonstrate that the proposed model can effectively simulate the capture of both stationary and spinning debris with spherical or polyhedral shapes. During the capture of spinning debris, the tangential friction between the membrane and debris significantly reduces the debris’s spin rate, demonstrating excellent despinning capability. This research provides a theoretical foundation for parameter optimization and engineering design of net-membrane capture systems, contributing to the advancement of reusable and highly adaptable active debris removal technologies.

The authors focus on an innovative concept in the field of active debris removal—the net-membrane capture system—and systematically elaborate on its operational principles and technical advantages. As illustrated in Fig. 1, the system consists of a launcher mounted on a servicing satellite, tethers connected to bullets, a multilayer composite membrane structure, and layers of smart materials. Its operational workflow is divided into six key steps: after the servicing satellite approaches the target debris, it ejects bullets from the four corners at a specific velocity; the bullets pull the membrane via tethers to deploy and move toward the debris; the membrane contacts the debris and wraps around it to achieve capture; the debris is deorbited through tether control; the membrane is actively deployed and releases the debris using shape-memory smart materials; finally, the membrane is actively folded for storage, and the servicing satellite moves to the next target, enabling repeatable capture. Compared with traditional capture methods such as rigid robotic arms or harpoons, the net-membrane system offers comprehensive advantages, including long capture range, adaptability to debris of various shapes and sizes, no requirement for precise docking, high safety, and reusability. The study further points out that during deployment and capture, the membrane exhibits complex combined deformation behaviors, including stretching, shearing, and bending, along with large displacements, strong nonlinearity, and rigid-flexible coupling characteristics, posing significant challenges for dynamic modeling.

Second, the authors propose a dynamic modeling method for membrane structures based on the multiparticle method and introduce a contact–collision model to fully describe the capture process. As shown in Fig. 2, the membrane is discretized into n² square units, with the mass of each unit equally distributed to the four mass points at its vertices. Adjacent mass points are connected by massless spring–damper elements. Springs along the boundaries of the unit simulate tensile stiffness, while springs along the diagonals simulate shear stiffness. To accurately describe the bending deformation of the membrane, the study further introduces torsion spring elements, calculating the bending force generated at creases based on equivalent cantilever beam theory. The equations of motion for each mass point are established in an inertial frame, comprehensively considering tensile forces, shear forces, bending forces, contact forces, and Earth's gravity. In terms of contact dynamics, the study designs a stepwise collision detection algorithm, as shown in Fig. 3: a capture space is first defined; when debris enters this space, the Gilbert–Johnson–Keerthi algorithm is used to quickly determine the contact status between membrane mass points and the debris. The normal contact force is calculated based on the Hunt–Crossley continuous contact force model, considering penetration depth and penetration velocity; tangential friction adopts the Coulomb model, distinguishing between static and dynamic friction states according to relative velocity. This modeling framework provides a complete theoretical foundation for subsequent numerical simulations.

Finally, the authors systematically verified the membrane deployment dynamics and capture capability through multiple sets of numerical simulations and determined the optimal shooting parameters. The simulation sets the membrane material as polyimide and the debris material as aluminum. First, deployment simulations were conducted to analyze the effects of ejection angle, ejection velocity, and bullet mass on four key indicators: maximum area, deployment time, effective period, and effective distance, as shown in Fig. 4. The results show that if the ejection angle is too small (15°), the membrane fails to deploy properly; if too large (75°), the effective distance is shortened; approximately 30° is the optimal angle. Increasing the ejection velocity significantly increases the effective distance (reaching 1.66–4.23 m at 25 m/s). Increasing the bullet mass expands the maximum deployment area, but care must be taken to avoid exceeding the membrane's strength limit. In the capture simulations, three scenarios were set: stationary spherical debris, spinning spherical debris, and spinning polyhedral debris. The results show that the membrane system can successfully capture all types of debris. The maximum collision force in the capture direction reaches 3374 N (at a capture distance of 2 m), and extending the capture distance to 3 m effectively reduces the collision force. When capturing spinning debris, the friction between the membrane and debris generates continuous torque, reducing the spin angular velocity from 0.1 rad/s to 0 within 0.52 s, demonstrating significant despinning effectiveness, as shown in Fig. 5. The study validates the effectiveness of the net-membrane capture system for complex targets and provides key parameter references for engineering practice.