Comparison of control regularization techniques for minimum-fuel low-thrust trajectory design using indirect methods

TL;DR

This paper compares hyperbolic-tangent and L2-norm smoothing techniques for control regularization in solving minimum-fuel low-thrust trajectory problems, analyzing their impact on convergence and sensitivity calculations.

Contribution

It introduces a novel L2-norm smoothing method and evaluates its performance against traditional hyperbolic-tangent smoothing in indirect trajectory optimization methods.

Findings

L2-norm smoothing improves convergence in certain scenarios.

Both methods are effective when using the State Transition Matrix for sensitivities.

Implementation simplicity is achieved by applying smoothing directly at the control level.

Abstract

Minimum-fuel low-thrust trajectories typically consist of a finite, yet unknown number of switches in the thrust magnitude profile. This optimality-driven characteristic of minimum-fuel trajectories poses a challenge to the numerical methods that are typically used for solving the resulting Hamiltonian boundary-value problems (BVPs). In this paper, we compare the impact of the popular hyperbolic-tangent-based smoothing with a novel L2-norm-based smoothing on the convergence performance of quasi-Newton gradient-based methods. Both smoothing methods are applied directly at the level of control, which offer a significant implementation simplicity. We also investigate the application of each method in scenarios where the State Transition Matrix (STM) is used for accurate calculation of the sensitivities of the residual vector of the resulting BVPs with respect to the unknown initial costate values. The effectiveness of each control smoothing method is assessed across several benchmark minimum-fuel low-thrust trajectory optimization problems.