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DESTINY+ is an upcoming JAXA Epsilon medium-class mission to fly by the Geminids meteor shower parent body (3200) Phaethon. It will be the world's first spacecraft to escape from a near-geostationary transfer orbit into deep space using a low-thrust propulsion system. In doing so, DESTINY+ will demonstrate a number of technologies that include a highly efficient ion engine system, lightweight solar array panels, and advanced asteroid flyby observation instruments. These demonstrations will pave the way for JAXA's envisioned low-cost, high-frequency space exploration plans. Following the Phaethon flyby observation, DESTINY+ will visit additional asteroids as its extended mission. The mission design is divided into three phases: a spiral-shaped apogee-raising phase, a multi-lunar-flyby phase to escape Earth, and an interplanetary and asteroids flyby phase. The main challenges include the optimization of the many-revolution low-thrust spiral phase under operational constraints; the design of a multi-lunar-flyby sequence in a multi-body environment; and the design of multiple asteroid flybys connected via Earth gravity assists. This paper shows a novel, practical approach to tackle these complex problems, and presents feasible solutions found within the mass budget and mission constraints. Among them, the baseline solution is shown and discussed in depth; DESTINY+ will spend two years raising its apogee with ion engines, followed by four lunar gravity assists, and a flyby of asteroids (3200) Phaethon and (155140) 2005 UD. Finally, the flight operations plan for the spiral phase and the asteroid flyby phase are presented in detail.

Asteroid exploration has been attracting more attention in recent years. Nevertheless, we have just visited tens of asteroids while we have discovered more than one million bodies. As our current observation and knowledge should be biased, it is essential to explore multiple asteroids directly to better understand the remains of planetary building materials. One of the mission design solutions is utilizing asteroid flyby cycler trajectories with multiple Earth gravity assists. An asteroid flyby cycler trajectory design problem is a subclass of global trajectory optimization problems with multiple flybys, involving a trajectory optimization problem for a given flyby sequence and a combinatorial optimization problem to decide the sequence of the flybys. As the number of flyby bodies grows, the computation time of this optimization problem expands maliciously. This paper presents a new method to design asteroid flyby cycler trajectories utilizing a surrogate model constructed by deep neural networks approximating trajectory optimization results. Since one of the bottlenecks of machine learning approaches is the computation time to generate massive trajectory databases, we propose an efficient database generation strategy by introducing pseudo-asteroids satisfying the Karush-Kuhn-Tucker conditions. The numerical result applied to JAXA's DESTINY+ mission shows that the proposed method is practically applicable to space mission design and can significantly reduce the computational time for searching asteroid flyby sequences.