Semi-Analytical Adaptive Guidance Computation Based on Differential Algebra for Autonomous Planetary Landing

A novel algorithm for autonomous landing guidance computation is presented. Trajectory is expressed in polynomial form of minimum order to satisfy a set of 17 boundary constraints, depending on 2 parameters: time-of-flight and initial thrust magnitude. The consequent control acceleration is expressed in terms of differential algebraic (DA) variables, expanded around the point of the domain along the nominal trajectory followed at the retargeting epoch. The DA representation of objective and constraints give additional information about their sensitivity to variations of optimization variables, exploited to find the desired fuel minimum solution (if it exists) with a very light computational effort, avoiding less robust processes.