Whilst Micro Aerial Vehicles (MAVs) possess a variety of promising capabilities, their high energy consumption severely limits applications where flight endurance is of high importance. Reducing energy usage is one of the main challenges in advancing aerial robot utility. To address this bottleneck in the development of unmanned aerial vehicle applications, this work proposes an bioinspired mechanical approach and develops an aerial robotic system for greater endurance enabled by low power station-keeping. The aerial robotic system consists of an multirotor MAV and anchoring modules capable of launching multiple tensile anchors to fixed structures in its operating envelope. The resulting tensile perch is capable of providing a mechanically stabilized mode for high accuracy operation in 3D workspace. We explore generalised geometric and static modelling of the stabilisation concept using screw theory. Following the analytical modelling of the integrated robotic system, the tensile anchoring modules employing high pressure gas actuation are designed, prototyped and then integrated to a quadrotor platform. The presented design is validated with experimental tests, demonstrating the stabilization capability even in a windy environment.