This paper presents an online trajectory and morphology planning framework for morphing quadrotors to traverse passages narrower than their unfolded width using only a 2D LiDAR for obstacle sensing. Fixed-frame vehicles cannot pass through such gaps, and classical artificial potential field (APF) based obstacle costs seal them off for planners as well, because the repulsive cost grows sharply inside a tight gap. The core enabler of our framework is a novel cost reduction factor, computed in closed form from the LiDAR data, that cancels the obstacle cost along the medial axis of a narrow passage. A true opening thus becomes a low-cost corridor, while the full repulsive cost is retained everywhere else. The cost reduction factor is embedded at every prediction node of an acados-based nonlinear MPC, which jointly plans the trajectory, yaw, and fold angle of the platform. A user-specified minimum-width limit ensures that the cost reduction factor only opens the corridors that the platform can actually pass. Gazebo/PX4 simulations and hardware experiments on the MorphoCopter demonstrate autonomous folding and unfolding through curved, inclined, and cluttered passages narrower than the unfolded width, where the standard repulsive cost fails to pass safely in most of the trials. The implementation code is available at \href{https://github.com/harshjmodi1996/morphocopter_mpc}{\textcolor{blue}{Github}} and a short video about the paper is available at \href{https://zh.engr.tamu.edu/wp-content/uploads/sites/310/2026/10/Morphocopter_planning_final.mp4}{\textcolor{blue}{\textbf{video link}}}.

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