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In cluttered spaces, such as forests, drone picking up a payload via an abseil claw is an open challenge, as the cable is likely tangled and blocked by the branches and obstacles. To address such a challenge, in this work, a cooperative aerial system is proposed, which consists of a payload drone and a dexterous rappelling end droid. The two ends are linked via a Kevlar tether cable. The end droid is actuated by four propellers, which enable mid-air dexterous adjustment of clawing angle and guidance of cable movement. To avoid tanglement and rappelling obstacles, a trajectory optimization method that integrates cable length constraints and dynamic feasibility is developed, which guarantees safe pickup. A tether cable dynamic model is established to evaluate real-time cable status, considering both taut and sagging conditions. Simulation and real-world experiments are conducted to demonstrate that the proposed system is capable of picking up payload in cluttered spaces. As a result, the end droid can reach the target point successfully under cable constraints and achieve passive retrieval during the lifting phase without propulsion, which enables effective and efficient aerial manipulation.