This paper shows that the dynamics of a general class of aerial manipulators, consist of an underactuated multi-rotor base with an arbitrary k-linked articulated manipulator, are differentially flat. Methods of Lagrangian Reduction under broken symmetries produce reduced equations of motion whose key variables: center-of-mass linear momentum, vehicle yaw angle, and manipulator relative joint angles become the flat outputs. Utilizing flatness theory and a second-order dynamic extension of the thrust input, we transform the mechanics of aerial manipulators to their equivalent trivial form with a valid relative degree. Using this flatness transformation, a quadratic programming-based controller is proposed within a Control Lyapunov Function (CLF-QP) framework, and its performance is verified in simulation.

翻译：本文显示,一般类别的空中操纵器的动态由作用不足的多色操纵器基地组成,并配有任意的K-连线的分解操纵器,其动态有差异的平坦。在断裂的对称下减少拉格朗加平方程式的方法产生减少运动方程式的关键变量:中质量线动量、车辆斜角和操纵者相对合角成为平坦输出。我们利用平坦理论和推进的二阶动态延伸,将空中操纵器的机械转换为等同的微小形式,并具有有效的相对程度。使用这种平坦性变形,在控制 Lyapunov 函数(CLF-QP) 框架内提议一个基于等式编程控制器,并在模拟中验证其性能。