Mapping filtered forwarding-based trajectory tracking control

Forwading-based immersion and invariance approaches have been applied to control the high-order nonlinear systems, whereas it is an off-line algorithm and needs to directly compute analytic derivatives of the mappings. In our study, a new tracking control algorithm is developed by introducing a second-order filter at each step of the design. This recursive algorithm does not only overcome the problem of "explosion of complexity" to improve computational efficiency, but also suppresses the high-frequency noise arising from time derivatives of states and virtual controls. Unlike other existing control methodologies, it does not require the knowledge of a Lyapunov function in principle. The boundedness of all mappings and their analytic derivatives can be ultimately guaranteed by using the internal stability of filters. Also, this bottom-up algorithm is able to provide the modularized design of the controller, where real-time applications can be to some extent realized. In this work, a quadrotor helicopter is used to demonstrate the controller performances via various simulations.