Equivalent Control of a 2D Crane and a 2D Drone Using Exact Linearization Based on Differential Flatness

This paper presents the exact linearizing trajectory tracking control of two underactuated mechatronic systems, namely a 2D crane and a 2D quadcopter. This method is based on differential flatness, and it is shown that in the case of these two systems the controller structure is extremely similar down to a coordinate transformation. The flat outputs are the coordinates of the load and the coordinates of the center of mass of the body for the crane and quadcopter respectively. The resulting controllers both have two internal states, meaning that exact linearization is only achievable by dynamic state feedback. The reference trajectories need to be sufficiently smooth meaning that they have to be four times differentiable w.r.t. time. This intuitively means that the load of the crane can be thought of as a drone moving in the 2D plane. The force form the rope is equivalent to the thrust force generated by the propellers of the quadcopter. The same can be said about the rope angle and the orientation of the drone body. The presented control algorithm is validated using simulations, where the equivalence between the trajectories of the two systems is well observable.