This paper introduces a motion planning framework to plan morphology and trajectory for morphing quadrotors under extremely constrained environments. We develop a novel obstacle avoidance cost function for nonlinear model predictive control (MPC) that enables navigation through extremely narrow gaps under limited perception from a 2D LiDAR. Classical artificial potential field-based costs typically have a high cost in narrow passages, artificially blocking the navigable path. In contrast, we propose a smooth exponential obstacle cost that preserves low traversal cost within narrow gaps while maintaining strong collision avoidance behavior. The formulation avoids hard activation thresholds and introduces a cost reduction factor to reduce the cost within narrow passages. Direct use of 2D LiDAR measurements in MPC allows navigation around arbitrarily shaped obstacles. The method is embedded within an acados-based nonlinear MPC framework. Simulation and experimental results demonstrate successful traversal of narrow corridors where typical repulsive cost functions would fail. The approach provides a computationally efficient and practical solution for navigating through tight spaces while maintaining safety from the obstacles. While we are implementing the framework on the morphing quadrotors, the cost function formulation is general-purpose for any mobile robot application, and is not limited to the morphing quadrotors. The implementation code is available at \href{https://github.com/harshjmodi1996/morphocopter_mpc}{Github Repo} and a short video is available at \href{https://zh.engr.tamu.edu/wp-content/uploads/sites/310/2026/03/MPC_MorphoCopter_video.mp4}{Video Link}.

翻译：本文提出一种用于在极端约束环境下规划变形四旋翼形态与轨迹的运动规划框架。我们针对非线性模型预测控制（MPC）开发了一种新颖的避障成本函数，使其能够在2D激光雷达有限感知条件下穿越极端狭窄间隙。传统基于人工势场的成本函数在窄通道中通常会引入高成本，人为阻碍可通行路径。相反，我们提出一种平滑指数障碍成本函数，其在保持窄间隙内低通行成本的同时，仍具有强碰撞规避能力。该公式避免了硬激活阈值，并引入成本缩减因子以降低窄通道内的成本。在MPC中直接使用2D激光雷达测量值，可实现对任意形状障碍物的导航。该方法被嵌入基于acados的非线性MPC框架中。仿真与实验结果表明，该框架能成功穿越典型斥力成本函数无法通过的狭窄通道。该方案为在保障安全性的前提下穿越狭窄空间提供了计算高效且实用的解决方案。尽管我们是在变形四旋翼平台上实现该框架，但该成本函数公式适用于任何移动机器人应用，并不局限于变形四旋翼。实现代码已开源至 \href{https://github.com/harshjmodi1996/morphocopter_mpc}{Github仓库}，相关演示视频可通过 \href{https://zh.engr.tamu.edu/wp-content/uploads/sites/310/2026/03/MPC_MorphoCopter_video.mp4}{视频链接} 查看。