Development of optimal and robust predictive guidance technique for Mars aerocapture

Abstract

The paper discusses a predictive guidance technique for the optimal aerocapture maneuver accomplished by a high-mass Mars orbiter to achieve the targeted circular parking orbit with minimal fuel consumption. Unlike the majority of investigated algorithms of the “predictor–corrector” family with a time-invariant control, the guidance algorithm considered in the paper computes a time-dependent control function which, being a reference profile of the angle of attack, provides a minimum to the post-aerocapture propulsive ΔV at the apoapsis of a transfer ellipse. Initially, the two-parametric bounded linear control function has been used, and the algorithm developed found an optimal solution directly by “descending” in a control parameters space. The simulation has shown that an optimum is achieved when the slope of the linear function tends to infinity, i.e., the bounded linear control is being transformed into a one-parametric step function. Such a result proved to be in conformity with the earlier “indirect” optimal solution, namely, derived from Pontryaginʼs maximum principle for a slightly simplified motion model. Thus, the final version of algorithm providing “direct” optimization by solving a nonlinear eigenvalue problem needs to determine only one parameter – switching time of angle of attack. The solution obtained satisfies the terminal condition – a target apoapsis, as well as it is close to optimum. Another issue the paper focuses on is an improvement of robustness of the algorithm under unpredictable model disturbances, especially variations of atmospheric density. The new model adaptation algorithm is developed, which estimates density errors and updates the density profile during the descent phase to be used for control corrections in the ascent phase. Testing the example simulation model with angular motion has shown the runtime effectiveness and high targeting accuracy provided by the proposed predictive technique.