The autonomous maneuverable space net, which consists of a flexible net and several maneuverable units, is a promising solution for the active removal of space debris. A novel dynamics model and a corresponding controller are proposed in this paper to resolve the approach control problem. Given that the net tethers cannot be elongated, interval functions and corresponding constraint forces are exploited to model the unilaterally constrained tethers. The proposed approach dynamics model, which is based on the Hamilton principle, includes distinctive velocity jump phenomena. A dual-loop control scheme with double optimization pseudo-dynamics inversion and sliding mode control is also established. Simulation results validate the feasibility of the proposed control scheme. The net can fly along the expected trajectory without suffering unexpected net deformation or orbital radial movement.