Journal of Aeronautics & Aerospace Engineering
Open Access

Abstract

Minimum-Fuel, Low-Thrust Trajectory Optimizations for Earth-to-Mars Orbit Transfer with Bang-Bang Control

Daero Lee

This paper presents minimum-fuel, low-thrust trajectory optimizations for Earth-to-Mars orbit transfer using a constant specific impulse engine. The problem is formulated as an optimal trajectory design with the input power and the thrust direction being the control variables in the two-dimensional polar coordinate system. The problem is solved by both direct method and indirect method, respectively. Using Pontryagin’s Minimum Principle and the primer vector theory, the thrust direction is expressed as a function of costate variables and the Bang-Bang control law is derived, respectively. The derived two-point boundary-value problem is then solved by two-point-boundary-value solver. The optimal control problem is also solved by the direct method formulation which transcribes a continuous time optimal trajectory design to a finite dimensional nonlinear programming problem which in turn is solved by a nonlinear programming solver. The two optimization methods are utilized to find optimal trajectories from Earth to Mars orbit and it is concluded that constant specific impulse thrust trajectory optimization produces Bang-Bang control responses reducing propellant consumption for a variety of trajectories. The optimization results are validated by the direct and indirect methods showing numerical matches and are also analyzed with the primer vector theory. The results are useful for broad trajectory search in the preliminary phase of mission designs

Published Date: 2025-02-14;