Asymptotic stability for a transformed nonlinear UAV model with a suspended load via energy shaping

In this article, we present a new passivity-based controller which ensures asymptotic stability of the desired equilibrium point for a quadrotor with a cable-suspended load. Two steps compose the control synthesis procedure: the first step uses a new coordinate transformation on the position coordinates together with a partial feedback controller to tailor a new dynamical model; where the translational and rotational dynamics become coupled via a new control input. Since the new dynamical model preserves the Lagrangian structure and verifies the conditions imposed in Donaire et al. [5] and Romero et al. [13] to design energy shaping controllers, avoiding to solve a Partial Differential Equation, the second step designs a proportional-integral controller around the two cyclo-passive outputs of the new dynamical model. Using Lyapunov theory, a strict analysis to ensure asymptotic convergence to the desired equilibrium point is presented. Besides, we show that a simple modification to the proposed controller solves the problem of constant velocity tracking on the translational coordinates. The performance of the controller is evaluated using numerical simulations.