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

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.