Semi-analytical Adaptive Guidance Algorithm for Fast Retargeting Maneuvers Computation during Planetary Descent and Landing

This work focuses on an adaptive guidance algorithm for planetary landing that updates the trajectory to the surface by means of a minimum fuel optimal control problem solving. A semi-analytical approach is proposed. The trajectory is expressed in a polynomial form of minimum order to satisfy a set of boundary constraints derived from initial and final states and attitude requirements. By imposing boundary conditions, a fully determined guidance profile is obtained, function of only two parameters: time-of-flight and initial thrust magnitude. The optimal guidance computation is reduced to the determination of these parameters, according to additional path constraints due to the actual lander architecture: available thrust and control torques, visibility of the landing site, and other additional constraint not implicitly satisfied by the polynomial formulation. Solution is achieved with a simple two-stage compass search algorithm: the algorithm firstly finds a feasible solution; whenever detected, it keeps solving for the optimum; nonlinear constraints are evaluated numerically, by pseudospectral methods. Results on different scenarios for a Moon landing mission are shown and discussed to highlight the effectiveness of the proposed algorithm and its sensitivity to the navigation errors.