Nonlinear Optimal and Multi-Loop Flatness-Based Control for Dual-UAV Cooperative Load Transportation

Cooperative payload transportation by UAVs can be beneficial for transferring to remote areas ammunition, supplies and equipment. It can find use in construction works taking place in distant and difficult to access regions (for instance mountains or islands), in defense tasks and in the management of physical disasters. So-far such tasks were performed mostly by tandem helicopters (coaxial bicopters). The use of cooperative UAVs offers a new perspective and alternative technical means for accomplishing efficiently the above-noted tasks. In this article, the nonlinear control problem of quadrotor UAVs which perform cooperative transportation of payloads is treated with the use of nonlinear optimal and multi-loop flatness-based control methods. The load is suspended with a link from a cart which is turn is connected through cables with two quadrotors. The aim is to compute the flight path and the control inputs of the quadrotors that will allow them to lift the load and move it to any desirable final position. First, the dynamic model of the cable-suspended load is obtained through Euler-Lagrange analysis. Despite underactuation, the associated nonlinear optimal control problem is solved, thus allowing to compute the lift forces of the cables that enable the load to move on the vertical plane until it reaches the targeted position. These forces are also applied with opposite sign to the quadrotors' side through joints at the other end of the cables. Thus, the dynamic model of the quadrotors is updated by including in it additional drag forces which are due to the tension of the cables. The flight paths for the two quadrotors that enable to bring the suspended load to its final position are also computed. Next, for each quadrotor the nonlinear control and path following problem is solved, taking into account the cable-induced drag forces effects. To this end, a multi-loop flatness-based control approach is applied to each quadrotor. The whole control method is implemented in two successive loops and its global stability properties are also proven through Lyapunov stability analysis.