Modeling and Sliding Mode Control of a Heavy-lift Quadrotor with a Cable-suspended Payload under Wind Disturbances

We address the dynamic modeling and control of a heavy-lift quadrotor and its suspended payload operating in the presence of wind disturbances. A compact 3D model is developed in matrix form using a Lagrangian formulation. The payload is treated as a rigid cuboid; the drag forces and the gyroscopic effects of the propellers are considered. The wind disturbances are modeled as a combined mean shear and turbulent velocity field with discrete gusts. Both first order (conventional) sliding mode control (SMC) and higher order sliding mode control (HOSMC) techniques are employed to solve the trajectory tracking problem. In the case of first order SMC the coefficients of the sliding surfaces are computed via linearization and Hurwitz analysis, and the closed-loop stability is proven via Lyapunov’s Second Method. The resulting controllers require tuning of a small number of parameters. To reduce chattering, a boundary layer approach is used: the signum function is approximated with a continuous saturation function, leading to the ultimate boundedness of the errors. To improve the tracking capabilities, HOSMC based on the Modified Super-Twisting Algorithm is also proposed. In this case, the controllers ensure asymptotic tracking of the reference trajectory, while maintaining low computational demands. Finally, simulations are carried out to compare the performance of first order SMC and HOSMC with proportional integral derivative (PID) control, as the latter type of control is most often embedded in commercial aerial vehicles. Considering a simulated 72 kg cargo drone with a 25 kg payload suspended by an 18 m cable in presence of non-vanishing disturbances, the designed sliding mode controllers reduce the integral of time multiplied by absolute error by an average factor greater than 100 when compared with PID controllers.