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Preliminary design of low-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. In addition, a time-history of control variables must be chosen that defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated, which can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a hybrid optimal control problem. The method is demonstrated on hypothetical missions to Mercury, the main asteroid belt, and Pluto.

Solar electric propulsion (SEP) is the dominant design option for employing low-thrust propulsion on a space mission. Spacecraft solar arrays power the SEP system but are subject to blackout periods during solar eclipse conditions. Discontinuity in power available to the spacecraft must be accounted for in trajectory optimization, but gradient-based methods require a differentiable power model. This work presents a power model that smooths the eclipse transition from total eclipse to total sunlight with a logistic function. Example trajectories are computed with differential dynamic programming, a second-order gradient-based method.

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In the companion paper, analytic methods were presented for computing the Jacobian entries for two-sided direct shooting trajectory models that utilize the bounded-impulse approximation. In this paper we discuss practical implementation considerations. Efficient computation of the mathematical components required to compute the partials is discussed and a guiding numerical example is provided for validation purposes. A solar electric power model suitable for preliminary mission design is presented, including a method for handling thruster cut-off events that result in non-smooth derivatives. The challenges associated with incorporating the SPICE ephemeris system into an optimization framework are discussed and an alternative is presented that results in smooth time partials.Application problems illustrate the benefits of employing analytic Jacobian calculations vs. using the method of finite differences. The importance of accurately modeling hardware and operational constraints at the preliminary design stage, and the benefits of using an analytic Jacobian in a solver that combines the monotonic basin hopping heuristic method with a local gradient search are also explored.

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DART, Double Asteroid Redirection Test, will be the rst mission to demonstrate and characterize the concept of a kinetic impactor for planetary defense, by impacting the smaller member of a binary asteroid system Didymos. Results of this mission will have implications for planetary defense, Near-Earth Object science, and resource utilization. This research focuses on the heliocentric transfer phase of the mission. The heliocentric trajectory is evaluated using various objective functions, including a search for the latest possible escape date, the shortest time-of-ight, and the maximum impact energy. Also included in the search is the potential to use Earth gravitational assists, which proves not to oer any useful advantages. A new way to assess the trajectory's margin for missed thrust is used, which quanties the ability of the spacecraft to recover its mission following unplanned non-thrusting events, such as safe-mode. The baseline trajectory is shown to be capable of recovering from missed thrust events lasting 14 days using only 1% of its propellant as margin. Finally, we consider contingency trajectories that attempt to impact Didymos at a subsequent perihelion.