Contact-rich aerial manipulation remains fundamentally challenging because interaction forces are directly transmitted to the aerial platform, often leading to instability and degraded task performance. While compliant manipulators can mitigate these effects, existing aerial manipulation systems typically struggle to reconcile interaction compliance with manipulation precision. To this end, this article presents an aerial rigid-soft integrated manipulator (AeRSoM) robot that realizes embodied compliance for aerial manipulation. The proposed system integrates a fully actuated aerial platform, a rigid-soft manipulator, and variable-stiffness regulation to simultaneously achieve stable flight, compliant interaction, and precise manipulation. By distributing compliance throughout the manipulation system, the proposed design leverages distributed embodied compliance to passively absorb contact disturbances while preserving sufficient stiffness for task execution. To fully exploit the mechanical design, a composite control framework is developed for precise end-effector trajectory tracking in the presence of uncertainties and external disturbances. Extensive real-world experiments are conducted in representative contact-rich aerial manipulation tasks, including dynamic transmission-line grasping, physical interaction with a wind turbine blade, peg-in-hole, and screwing operations. The results demonstrate that the proposed rigid-soft integration significantly improves interaction robustness and task adaptability while maintaining manipulation accuracy, highlighting that embodied compliance provides a promising design paradigm for enhancing the safety, robustness, and versatility of aerial manipulation.

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