Optimization of Minimum-Time Low-Thrust Transfers Using Convex Programming

Abstract

In this paper, a convex optimization method for the numerical solution of the minimum-time low-thrust orbit transfer problem is presented. The main contribution is the transformation of the free-final-time low-thrust trajectory optimization problem into a sequence of convex optimization problems. First, a new independent variable is introduced to rewrite the equations of motion, and a nonlinear optimal control problem is obtained. Then, the nonlinearity in the dynamics is reduced through a change of variables. By applying a lossless convexification technique, the nonconvex control constraints are convexified, and an equivalent problem is formed. The equivalence of the relaxation and the existence of the solution to the relaxed problem are proved. Based on the linearization of the dynamics, a successive convex approach is developed, and in each iteration, a second-order cone programming problem is solved efficiently by state-of-the-art interior-point methods. The effectiveness of the proposed method is verified through numerical simulations of an Earth-to-Mars low-thrust transfer problem. Furthermore, the performance of this convex approach is demonstrated by comparing with a general-purpose optimal control solver for transfers with multiple revolutions.