TIME-FREE TARGETING FOR DIRECT TRAJECTORY OPTIMIZATION

A bounded, time transformation, based on vercosine of the change in eccentric anomaly, is introduced. This transformation, coupled with the F and G functions, explicitly defines the velocity vectors for a pair of position vectors. Using this property, a discretization strategy is formulated where continuous or impulsive thrusting arcs are represented by set of impulses, implicitly realized by maintaining spatial continuity. Time discontinuity is propagated forward and removed at the last grid point either via explicit constraints or a Lambert arc. The trajectory is transformed into a NLP which is solved using existing solvers. Algorithm performance is studied and compared to JPL's Mission Analysis Low-Thrust Optimizer(MALTO).