Deployable Cable Nets for the Active Removal of Space Debris

Derelict satellites and spent rockets are the largest non-cooperative objects which gather most of the mass of the debris around the Earth. Also, they represent the main sources of small debris (primarily fragments) in the long period. The derelict spacecraft still orbiting in the most valuable commercial regions constitute a threat for current and future space activities. Clearly, the end-of-life disposal required by the space debris mitigation guidelines has not been thoroughly fulfilled for them. Eventually, remediation activities will have to be set out for their disposal to contain risks for functional satellites. For active debris removal (ADR), the development of an effective capturing mechanism is still one of the most problematic aspects of the mission architecture. Tethered cable nets have been considered as a promising concept for the capture of derelict non-cooperative vehicles. Their employment would simplify the approaching manoeuvres to the target and the capture process, with respect to the main alternative solution offered by robotic arms. The mechanical modelling, analysis, and design of tethered nets still results in a non-trivial task. In fact, the net is a kinematically indeterminate, flexible structure undergoing both large displacements and large deformation. The threads have different responses to tensile and compressive forces. The tumbling target constitutes a rheonomic constraint for the net, with which multiple unilateral contacts should be expected. The development of accurate and effective simulation tools is crucial for the design of deployable nets for the active removal of space debris. In the literature, several theoretical models have been proposed to describe deployment and capture processes. Cable nets are comprised of threads knotted and twisted into a grid-like, flexible structure. This configuration is well suited for adopting a discretisation procedure which distinguishes the mechanical responses of threads and knots. In a simple and effective approach, each thread may correspond to one finite element, while knots correspond to nodes in model. We developed a FE model for the cable net, adopting the nodal positions as the main unknowns of the problem in line with the position-based finite element formulation (PFEF). Large displacements and finite deformations were considered through the Green-Lagrange strain tensor. The cable elements were assumed to react only in tension according to a relaxed hyper-elastic constitutive law. Global damping was introduced into the model according to Rayleigh's hypothesis. Contact with the target was considered by introducing additional constraint equations through the method of Lagrange multipliers. In particular, the case of a steady obstacle of spherical shape was considered to obtain the complete differential set governing the problem. The governing equations for the nonlinear dynamical problem were solved numerically by means of a predictor--corrector algorithm implementing the Newmark method. As a case study, several simulations of the same planar, square-mesh net were performed, analysing at first the in-plane deployment, with and without damping, and then the three-dimensional deployment. Our mechanical model can be exploited to compare several net configurations, as well as initial conditions. Also, it may a useful tool to evaluate several performance parameters introduced in the literature.