Augmented Lagrangian methods for handling terminal constraints in spacecraft trajectory optimization

Abstract Augmented Lagrangian methods are well-established for terminal constraint-handling but implementation varies significantly in practice. A new system-level algorithm is developed using combinations of first- versus second-order Lagrange multiplier (LM) updates, fixed versus variable LM step sizes, inner- versus outer-loop schemes for LM updates, penalty-only versus split versus concurrent LM and penalty multiplier updates, and exact versus inexact convergence criteria. Each component is combined to create twenty-two submethods that are applied to ten diverse spacecraft trajectory optimization problems with up to ten revolutions and both bang-bang and smooth thrusting profiles. Performance results indicate all submethods can be successful with varying degrees of tuning, but differ in ideal applications. Second-order inner-loop methods with step size management perform the best, but outer-loop methods with step size management and inexact convergence are more robust to tuning parameters.