Uncertainty optimization applied to the Monte Carlo analysis of planetary entry trajectories.

摘要

Future robotic missions to Mars, as well as any human missions, will require precise entries to ensure safe landings near science objectives and pre-deployed assets. Planning for these missions will depend heavily on Monte Carlo analyses to evaluate active guidance algorithms, assess the impact of off-nominal conditions, and account for uncertainty. The dependability of Monte Carlo forecasts, however, is limited by the accuracy and completeness of the assumed uncertainties. This is because Monte Carlo analysis is a forward driven problem; beginning with the input uncertainties and proceeding to the forecast output statistics. An improvement to the Monte Carlo analysis is needed that will allow the problem to be worked in reverse. In this way, the largest allowable dispersions that achieve the required mission objectives can be determined quantitatively.; This thesis proposes a methodology to optimize the uncertainties in the Monte Carlo analysis of spacecraft landing footprints. A metamodel is used to first write polynomial expressions for the size of the landing footprint as functions of the independent uncertainty extrema. The coefficients of the metamodel are determined by performing experiments. The metamodel is then used in a constrained optimization procedure to minimize a cost-tolerance function. First, a two-dimensional proof-of-concept problem was used to evaluate the feasibility of this optimization method. Next, the optimization method was further demonstrated on the Mars Surveyor Program 2001 Lander. The purpose of this example was to demonstrate that the methodology developed during the proof-of-concept could be scaled to solve larger, more complicated, “real world” problems.; This research has shown that is possible to control the size of the landing footprint and establish tolerances for mission uncertainties. A simplified metamodel was developed, which is enabling for realistic problems with more than just a few uncertainties. A confidence interval on the size of the footprint was developed, based on the assumption of a bivariate normal distribution. Because the confidence interval is a function of sample size, it may be used to determine, a priori, how many simulations must be performed to achieve a given accuracy in the size of the footprint.