Linear and Nonlinear Model Predictive Control applied to a lunar drone

The focus of the thesis’ work is the development of an optimal control algorithm applied to a lunar flying drone, LuNaDrone, which is an autonomous UAV with propulsion actuators designed to perform reconnaissance and, eventually, last mile delivery activities on the lunar surface. Model Predictive Control (MPC) was chosen as one of the possible candidates for controlling the system’s dynamics. Two different MPC formulations were used to study the implementation of the control algorithm: Nonlinear (NL) MPC and Linear Time Varying (LTV) MPC. The standard MPC algorithm requires the minimization of a suitable cost function that penalizes different parameters such as the deviation of the drone from a reference trajectory or an excessive consumption of propellant mass. This formulation allows the designer to tune and personalize the controller to achieve the most efficient behavior for the desired application. The first MPC formulation analyzed in the thesis uses a nonlinear model of the drone to evolve the system’s dynamics over the prediction horizon which is then used to create the cost function, whose minimization becomes a nonlinear programming (NLP) problem. The CasADi symbolic environment is used to create the solver’s function in multiple shooting, which is then exported and compiled as a MEX file needed to run simulations in Simulink. The LTV formulation was later tested to improve the computational cost and the speed of the controller, which are fundamental requirements for a fast system such as a UAV. In this case, the linearization of the system is performed using the standard Jacobian approach around a given state and input reference, fundamental to ensure that the prediction performed by the MPC is accurate enough to guarantee a sufficiently small positioning error. Particular attention was paid to the linearization of the quaternion dynamics, performed using the small angles approximation, to ensure a mathematically correct result. The thesis focuses on the possible integration of the two control methodologies rather than a strict comparison, since the results of the nonlinear MPC simulation can be later used as reference for the LTV controller; this procedure will allow, in a real case scenario, to compute the optimal state and input sequences offline that will be used to ensure the proper online tracking via the linear algorithm. Finally, the results obtained by means of both MPC formulations are analyzed together, with a particular focus on the deviation from the trajectory provided. In addition, a further analysis is carried out with the aim of assessing the controller's ability to handle any events that weren’t modelled beforehand, such as an incorrect positioning at the start of the mission or parameters uncertainties in the model.