Low-thrust trajectory design with constrained particle swarm optimization

In this paper, combined with the direct approach, particle swarm optimization (PSO) is applied to low-thrust trajectory optimization problems. A double-loop trajectory optimization algorithm is developed. The outer loop of this algorithm is a modified PSO optimizer, which can deal with constrained optimization problems and avoid premature convergence. The function of the outer loop is generating a series of time histories of control, called particles, and driving the particles toward the optimal solution. The direct approach (fourth-order Runge–Kutta shooting/parallel shooting method) is adopted as the inner loop algorithm, whose main task is to correct the particles provided by the outer loop and ensure that all the constraints are satisfied. This algorithm has the global search feature of the PSO and the relative large radius of convergence of the direct approach. Its efficiency is substantiated by solving a fixed-time fuel-optimal transfer problem from an asteroid to the Earth. Furthermore, this algorithm can be considered to be a universal low-thrust optimizer, and it can easily be used to solve more complex trajectory optimization problems such as multi-swingby problem and multidisciplinary design optimization (MDO) problems.