A mesh refinement method for low‐thrust orbit transfer problems

Abstract

This paper researches the fuel-optimal geocentric orbit transfer problem using a low-thrust, electric propulsion. First, the transfer trajectory is divided into N burn-coast arcs via introducing (N−1) intermediate orbits between the initial and the target orbits. By restricting the time duration of each burn, the changes in orbital states caused by one time of ignition can be represented by a discrete velocity impulse; therefore, a considerable large N, a great many optimization variables, and a months and revolutions long trajectory will be calculated to solve the optimization problem. By proposing a new transfer coordinate system, the performance index is analytically calculated, and strict constraints derived from the continuous condition between adjacent orbits are removed from the mathematical optimization model. Meanwhile, an improved particle swarm optimization (PSO) method and a mesh refinement method are proposed to address the optimization problem. The mesh refinement algorithm begins with a simple bi-impulse transfer problem, automatically increases/decreases N, and finally converges to the optimal solution. Numerical simulation shows the efficiency of the method with some classical and representative scenarios.