Design parameters of tethered 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 cables 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. We developed a finite element (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 are considered through the Green-Lagrange strain tensor. Cable elements are assumed to react only in tension according to a relaxed hyper-elastic constitutive law. Global damping is introduced into the model according to Rayleigh’s hypothesis. Contact with the target may be considered by introducing additional constraint equations through the method of Lagrange multipliers. The governing equations for the nonlinear dynamical problem are solved numerically by means of the Newmark method. Our mechanical model can be exploited to compare several net configurations, as well as initial conditions. In the literature, four main performance parameters have been established to evaluate the effectiveness of the deployment of the net: the maximum area of the net, the deployment time, the travelling distance, and the effective period. In this study, we focus on the evaluation of the performance parameters by simulating the threedimensional deployment of a square-mesh net. The results obtained from the simulation tool can drive the effective design of deployable cable nets for ADR missions.