In this work, we present a model-based optimal boundary control design for an aerial robotic system composed of a quadrotor carrying a flexible cable. The whole system is modeled by partial differential equations (PDEs) combined with boundary conditions described by ordinary differential equations (ODEs). The proper orthogonal decomposition (POD) method is adopted to project the original infinite-dimensional system on a subspace spanned by orthogonal basis functions. Based on the reduced order model, nonlinear model predictive control (NMPC) is implemented online to realize shape trajectory tracking of the flexible cable in an optimal predictive fashion. The proposed reduced modeling and optimal control paradigms are numerically verified against an accurate high-dimensional FDM-based model in different scenarios and the controller's superior performance is shown compared to an optimally tuned PID controller.

翻译：本文提出了一种基于模型的最优边界控制设计，用于由四旋翼飞行器携带柔性缆绳组成的空中机器人系统。整个系统通过偏微分方程（PDEs）建模，并结合由常微分方程（ODEs）描述的边界条件。采用本征正交分解（POD）方法将原始无限维系统投影到由正交基函数张成的子空间上。基于降阶模型，在线实现非线性模型预测控制（NMPC），以最优预测方式实现柔性缆绳的形态轨迹跟踪。所提出的降阶建模与最优控制范式在不同场景下通过与基于有限差分法（FDM）的高精度高维模型进行数值验证，并展示了相较于优化调参的PID控制器的优越性能。