Minimum-Fuel Low-Thrust Transfers for Spacecraft: A Convex Approach

Abstract

This paper presents a convex approach to the numerical solution of the minimum-fuel low-thrust orbit transfer problem. The main contribution is the transformation of the original nonlinear optimal control problem into a sequence of convex optimization problems. First, the control is decoupled from the states through a change of variables. Then, by introducing a lossless convexification technique, the control constraints are convexified, and the original problem is relaxed into a sequence of second-order cone programming problems. The resulting subproblems can be solved in real time by efficient interior-point methods. Finally, the effectiveness of the proposed methodology is demonstrated through numerical simulations of the three-dimensional minimum-fuel Earth-to-Mars low-thrust transfer problem.