A time-regularized, multiple gravity-assist low-thrust, bounded-impulse model for trajectory optimization

The multiple gravity-assist low-thrust (MGALT) trajectory model is a computationally efficient preliminary design algorithm, and provides an accurate estimation of the total mass budget that will be required by the flight-suitable integrated trajectory. However, it suffers from one major drawback, namely its temporal spacing of the control nodes. We introduce a variant of the MGALT transcription that utilizes either the generalized anomaly from the universal formulation of Kepler's equation or the true anomaly as a decision variable in addition to the trajectory phase propagation time. This results in two improvements over the traditional model. The first is that the maneuver locations are now at regular intervals of the chosen anomaly, rather than at locations separated by equal propagation times. The second is that the Kepler propagator now has as its independent variable the generalized anomaly, instead of time and thus becomes an iteration-free propagation method. The new algorithm is outlined, including the impact that this has on the computation of Jacobian entries for numerical optimization, and a motivating application problem is presented that illustrates the improvements that this model has over the original MGALT transcription.