Efficient motion planning for Aerial Manipulators (AMs) is essential for tackling complex manipulation tasks, yet achieving coupled trajectory planning remains challenging. In this work, we propose, to the best of our knowledge, the first whole-body integrated motion planning framework for aerial manipulators, which is facilitated by an improved Safe Flight Corridor (SFC) generation strategy and high-dimensional collision-free trajectory planning. In particular, we formulate an optimization problem to generate feasible trajectories for both the quadrotor and manipulator while ensuring collision avoidance, dynamic feasibility, kinematic feasibility, and waypoint constraints. To achieve collision avoidance, we introduce a variable geometry approximation method, which dynamically models the changing collision volume induced by different manipulator configurations. Moreover, waypoint constraints in our framework are defined in $\mathrm{SE(3)\times\mathbb{R}^3}$, allowing the aerial manipulator to traverse specified positions while maintaining desired attitudes and end-effector states. The effectiveness of our framework is validated through comprehensive simulations and real-world experiments across various environments.

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