Numerical simulation and behavior prediction of a space net system throughout the capture process: Spread, contact, and close

Abstract

In this paper, we develop an exhaustive numerical simulator for the dynamic visualization and behavior prediction of the tether-net system during the whole space debris capture phases, including spread, contact, and close. First of all, to perform its geometrically nonlinear deformation, discrete different geometry theory is applied to model the mechanical response of a flexible net. Based on the discretization of the whole structure into multiple vertexes and lines, the internal force and associated Hession are derived in a closed form to solve a series of nonlinear dynamic equations of motion. The spread and deployment of a packaged net can be realized using this well-established net solver. Next, a multidimensional incremental potential formulation is selected to achieve the intersection-free boundary nonlinear contact and collision between the deformable net and rigid debris. Finally, for the closing mechanism analysis, a log-like barrier functional is derived to achieve the nondeviation condition between the ring–rod linkage system. The $C^2$ continuous log barrier functionals constructed for both the contact model and the linkage system are smooth and differentiable, and, therefore, the nonlinear net capture dynamic system can be efficiently solved through a fully implicit time integrator. Overall, as a demonstration, the whole capture process of a defunct satellite using a hexagon net is simulated through our well-established numerical framework. We believe that our comprehensive numerical methods could provide new insight into the optimal design of active debris removal systems and promote further development of the online control of tether tugging systems.