Collocation Method and Model Predictive Control for Accurate Landing of a Mars EDL vehicle

This thesis aims at investigating numerical methods through which the accuracy in landing of a Mars entry-descent-landing (EDL) vehicle can be improved. The methods investigated include the collocation method and model predictive control (MPC). The primary control variable utilized in this study is the bank angle of the spacecraft, which is the angle between the lift vector and the vertical direction. Modulating this vector affects the equations of system of equations and the seven state variables, namely altitude, velocity, latitude, longitude, flight path angle, heading angle and total time taken. An optimizer is implemented which utilizes the collocation method, through which the optimal bank angle is found at every discretized state along the trajectory which are equally separated through a definite timestep, which is a function of the end time state. A 3-sigma wind disturbance model is introduced to the system, as a function of the altitude, which introduces uncertainties to the system, resulting in a final state deviating from the targeted location. The trajectory is split into two parts, for better control of the vehicle during the end stages of flight. The MPC aims at reducing the end state deviation, through the implementation of a predictor-corrector algorithm that propagates the trajectory for a certain number of timesteps, followed by running the optimizer from the current disturbed state to the desired target location. At the end of this analysis, a new set of optimal bank angle are found, which account for the wind disturbances and navigates the EDL vehicle to the desired location.