尾崎 直哉

Asteroid exploration has been attracting more attention in recent years. Nevertheless, we have just visited tens of asteroids, whereas we have discovered more than 1 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. Because one of the bottlenecks of machine learning approaches is the heavy 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 Japan Aerospace Exploration Agency’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.

Recent low-thrust space missions have highlighted the importance of designing trajectories that are robust against uncertainties. In its complete form, this process is formulated as a nonlinear constrained stochastic optimal control problem. This problem is among the most complex in control theory, and no practically applicable method to low-thrust trajectory optimization problems has been proposed to date. This paper presents a new algorithm to solve stochastic optimal control problems with nonlinear systems and constraints. The proposed algorithm uses the unscented transform to convert a stochastic optimal control problem into a deterministic problem, which is then solved by trajectory optimization methods such as differential dynamic programming. Two numerical examples, one of which applies the proposed method to low-thrust trajectory design, illustrate that it automatically introduces margins that improve robustness. Finally, Monte Carlo simulations are used to evaluate the robustness and optimality of the solution.

This paper presents the trajectory design for EQUilibriUm Lunar-Earth point 6U Spacecraft (EQUULEUS), which aims to demonstrate orbit control capability of CubeSats in the cislunar space. The mission plans to observe the far side of the Moon from an Earth-Moon L2 (EML2) libration point orbit. The EQUULEUS trajectory design needs to react to uncertainties of mission design parameters such as the launch conditions, errors, and thrust levels. The main challenge is to quickly design science orbits at EML2 and low-energy transfers from the post-deployment trajectory to the science orbits within the CubeSat's limited propulsion capabilities. To overcome this challenge, we develop a systematic trajectory design approach that 1) designs over 13,000 EML2 quasi-halo orbits in a full-ephemeris model with a statistical stationkeeping cost evaluation, and 2) identifies families of low-energy transfers to the science orbits using lunar flybys and solar perturbations. The approach is successfully applied for the trajectory design of EQUULEUS.

Low-thrust propulsion is a key technology for space exploration, and much work in astrodynamics has focused on the mathematical modeling and the optimization of low-thrust trajectories. Typically, a nominal trajectory is designed in a deterministic system. To account for model and execution errors, mission designers heuristically add margins, for example, by reducing the thrust and specific impulse or by computing penalties for specific failures. These conventional methods are time-consuming, done by hand by experts, and lead to conservative margins. This paper introduces a new method to compute nominal trajectories, taking into account disturbances. The method is based on stochastic differential dynamic programming, which has been used in the field of reinforcement learning but not yet in astrodynamics. A modified version of stochastic differential dynamic programming is proposed, where the stochastic dynamical system is modeled as the deterministic dynamical system with random state perturbations, the perturbed trajectories are corrected by linear feedback control policies, and the expected value is computed with the unscented transform method, which enables solving trajectory design problems. Finally, numerical examples are presented, where the solutions of the proposed method are more robust to errors and require fewer penalties than those computed with traditional approaches, when uncertainties are introduced.

Earth observation satellites can improve the flexibility of observation sites by having “maneuverability,” and low-thrust obtained by ion thruster will be a promising method for orbital change for micro-satellites. Designing low-thrust trajectories for these satellites is a multi-revolution and multi-objective (time/fuel-optimal) optimization problem, which usually requires high computational cost to solve numerically. This paper derives an analytical and approximate optimal orbit change strategy between two circular orbits with the same semi-major axis and different local time of ascending node, and proposes a graph-based method to optimize the multi-objective criteria. The optimal control problem results in a problem to search a switching point on the proposed graph, and mission designers can design an approximate switching point on this graph, by using two heuristic and reasonable assumptions that 1) the optimal thrust direction should be tangential to orbit and 2) the optimal thrust magnitude should be bang-bang control with an intermediate coast. Finally, numerical simulation with feedback control algorithm taking thrust margin demonstrates that the proposed method can be applicable in the presence of deterministic and stochastic fluctuation of aerodynamic disturbances.