  In this paper, a flexible tether-net system is applied to capture the space
debris and a numerical framework is established to explore its nonlinear
dynamic behaviors, which comprises four principal phases: folding, spreading,
contacting, and closing. Based on the discretization of the whole structure
into multiple nodes and connected edges, elastic force vectors and associated
Jacobian matrix are derived analytically to solve a series of equations of
motion. With a fully implicit method applied to analyze the nonlinear dynamics
of a slender rod network, the involved mechanical responses are investigated
numerically accounting for the interactions. Contact between the deformable net
and a rigid body is handled implicitly through a cost-effective modified mass
algorithm while the catenary theory is utilized to guide the folding process
(from planar configuration to origami-like pattern). The dragging and spreading
actions for the folded hexagon net could be realized by shooting six corner
mass toward a specific direction; next, the six corners would be controlled to
move along a prescribed path producing a closing gesture, when touch between
the flying net and the target body is detected, so that for the space debris
could be captured and removed successfully. We think the established discrete
model could provide a novel insight in the design of active debris removal
(ADR) techniques, and promote further development of the model-based control of
tether tugging systems.
