Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Minimum-Fuel Planar Earth-to-Mars Low-Thrust Trajectories Using Bang-Bang Control

Version 1 : Received: 11 September 2021 / Approved: 14 September 2021 / Online: 14 September 2021 (09:48:25 CEST)

How to cite: Lee, D. Minimum-Fuel Planar Earth-to-Mars Low-Thrust Trajectories Using Bang-Bang Control. Preprints 2021, 2021090226 (doi: 10.20944/preprints202109.0226.v1). Lee, D. Minimum-Fuel Planar Earth-to-Mars Low-Thrust Trajectories Using Bang-Bang Control. Preprints 2021, 2021090226 (doi: 10.20944/preprints202109.0226.v1).

Abstract

Recent advance in electric propulsion systems have demonstrated that these engines can be used for for long-duration interplanetary voyages. Constant specific impulse engine described as a thrust-limited engine is an example of this type of engine, processing the ability to operate at a constant level of impulse. The determination of minimum-fuel, planar heliocentric Earth-to-Mars low-thrust trajectories of spacecraft using a constant specific impulse is discussed considering the first-order necessary conditions derived from Lawden’s primer vector theory. The minimum-fuel low-thrust Earth-to-Mars optimization problem is then solved in two-dimensional, heliocentric frame using both indirect and direct methods. In the indirect method, two-point-boundary-value problems are derived to solve boundary value problems for ordinary differential equations. In the direct method, a general-purpose optimal control software called GPOPS-II is adopted to solve these optimal control problems. Numerical examples using two different optimization methods are presented to demonstrate the characteristics of minimum-fuel planar low-thrust trajectories with on-off-on thrust sequences at three chosen flight times and available maximum powers. The results are useful for broad trajectory search in the preliminary phase of mission designs.

Keywords

Low-thrust trajectories; bang-bang control; electric propulsion; constant specific impulse; indirect method; direct method

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