Finite-time geometric control for underactuated aerial manipulators with unknown disturbances

In this article, the finite-time geometric control for underactuated aerial manipulators is investigated. The dynamics of the aerial manipulator with unknown disturbances is analyzed first. The dynamics of the system is decomposed into the locked subsystem and shape subsystem. The finite-time controller for the aerial manipulator is then designed based on the analyzed dynamics. In the controller, the attitude tracking error of the aircraft base is expressed from the rotation matrix, which makes the controller continuous and almost globally stable on SO(3). A continuous adaptive term is added in the controller to compensate for the unknown disturbances. Finite-time filters are designed to ensure the smoothness of the commands on each loop. The convergence of the entire controlled system is strictly proved using Lyapunov theory and the definition of finite-time stability. The results show that the tracking error and the disturbance bound estimation error of the entire system are finite-time bounded near origin. Finally, comparative simulation results are presented to show the performance of the proposed controller.