Abstract:
This note develops easily applicable techniques that improve the convergence
and reduce the computational time of indirect low thrust trajectory
optimization when solving fuel- and time-optimal problems. For solving fuel
optimal (FO) problems, a positive scaling factor -- $\Gamma_{TR}$ -- is
introduced based on the energy optimal (EO) solution to establish a convenient
profile for the switching function of the FO problem. This negates the need for
random guesses to initialize the indirect optimization process. Similarly,
another scaling factor-$\beta$-, is introduced when solving the time-optimal
(TO) problem to connect the EO problem to the TO. The developed methodology for
the TO problem was crucial for the GTOC11 competition. Case studies are
conducted to validate the solution process in both TO and FO problems. For
geocentric cases, the effect of eclipses and $J_2$ perturbations were also
considered. The examples show that EO can provide a good guess for TO and FO
problems and that introducing the constants can reduce the initial residuals
and improve convergence. It is also shown that the equation for the Lagrangian
multiplier of mass and the associated boundary condition can be ignored for
both FO and TO cases without affecting optimality. This simplification reduces
the problem dimensions and improves efficiency.
