Fuel-Optimal Bank-Angle Control for Lunar-Return Aerocapture

Aerocapture is defined as the deceleration of a spacecraft due to drag produced on it by a planet's atmosphere such that the vehicle is captured into orbit about the planet. This is accomplished by varying the direction of the vehicle's lift vector through bank-angle modulation. This paper examines the application of four optimal-control approaches to aerocapture. The first is a minimization of a pseudo fuel cost function, which yields continuous controls. The second is bang-bang control, which minimizes the time associated with bank-angle modulation. Next, an absolute fuel function is minimized, which results in controls in the form of impulses. A fourth approach is a modification to impulsive control, where impulses are approximated by pulses of finite duration. All of the approaches are applied to a single-pass aerocapture problem. The modified impulsive-control approach is applied to a two-pass aerocapture scenario. Recommendations on the practical implementation of these control approaches in the presence of vehicle and atmospheric uncertainties are given. c E(t)

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