A low computation saturated controller for a quadcopter position tracking with stability and convoluted input constraints guarantees

In the class of differentially flat systems, nonlinear dynamics can be transformed into an equivalent linear representation via a coordinate change and an input mapping. Despite this beneficial linearization, one significant hindrance is that the system constraints have a convoluted form in the new space (the flat output space), which is usually disregarded in the literature or bypassed via conservative approximation of the feasible domain. In this paper, based on a pre-stabilization design and a novel input saturation component, the nonlinear input constraints are particularly handled for the position tracking problem of quadcopters in the flat output space. While the system's stability is shown to hold by Lyapunov arguments, the practical viability of the method is validated both in simulation and experiments over a nano-drone platform. Moreover, with the explicit solution introduced for the proposed saturation function, this flatness-based saturated controller not only ensures stability and constraints satisfaction, but also requires low computational effort, allowing possible embedded implementations.