This study explores modeling and control for quadrotor acrobatics, focusing on executing flip maneuvers. Flips are an elegant way to deliver sensor probes into no-fly or hazardous zones, like volcanic vents. Successful flips require feasible trajectories and precise control, influenced by rotor dynamics, thrust allocation, and control methodologies. The research introduces a novel approach using Model Predictive Control (MPC) for real-time trajectory planning. The MPC considers dynamic constraints and environmental variables, ensuring system stability during maneuvers. The proposed methodology's effectiveness is examined through simulation studies in ROS and Gazebo, providing insights into quadrotor behavior, response time, and trajectory accuracy. Real-time flight experiments on a custom agile quadrotor using PixHawk 4 and Hardkernel Odroid validate MPC-designed controllers. Experiments confirm successful execution and adaptability to real-world scenarios. Outcomes contribute to autonomous aerial robotics, especially aerial acrobatics, enhancing mission capabilities. MPC controllers find applications in probe throws and optimal image capture views through efficient flight paths, e.g., full roll maneuvers. This research paves the way for quadrotors in demanding scenarios, showcasing groundbreaking applications. Video Link: \url{ https://www.youtube.com/watch?v=UzR0PWjy9W4}

翻译：本研究探索了四旋翼特技飞行的建模与控制，重点研究执行翻转机动。翻转是一种将传感器探头投送到禁飞区或危险区域（如火山口）的优雅方式。成功的翻转需要可行的轨迹与精确的控制，这受到旋翼动力学、推力分配及控制方法的影响。本文提出了一种基于模型预测控制（MPC）的实时轨迹规划新方法。该MPC考虑了动态约束与环境变量，确保机动过程中的系统稳定性。通过ROS和Gazebo中的仿真研究验证了所提方法的有效性，提供了对四旋翼行为、响应时间和轨迹精度的深入理解。在采用PixHawk 4和Hardkernel Odroid的定制敏捷四旋翼上进行的实时飞行实验，验证了MPC设计控制器的性能。实验证实了其成功执行及对现实场景的适应性。研究成果有助于自主空中机器人领域，尤其是空中特技飞行，提升任务能力。MPC控制器在探头投送和通过高效飞行路径（如全滚转机动）获取最佳图像视角等应用中具有潜力。本研究为四旋翼在严苛场景中的应用铺平了道路，展示了突破性的应用前景。视频链接：\url{ https://www.youtube.com/watch?v=UzR0PWjy9W4}