Future missions to the Moon and beyond are likely to involve low-thrust propulsion technologies due to their propellant efficiency. However, these still present a difficult trajectory design problem, owing to the near continuous thrust, lack of control authority and chaotic dynamics. Lyapunov control laws can generate sub-optimal trajectories for such missions with minimal computational cost and are suitable for feasibility studies and as initial guesses for optimisation methods. In this work a Reinforced Lyapunov Controller is used to design optimal low-thrust transfers from geostationary transfer orbit towards lunar polar orbit. Within the reinforcement learning (RL) framework, a dual-actor network setup is used, one in each of the Earth- and Moon-centred inertial frames respectively. A key contribution of this paper is the demonstration of a forwards propagated trajectory, removing the need to define a patch point a priori. This is enabled by an adaptive patch distance and extensive initial geometry exploration during the RL training. Results for both time- and fuel-optimal transfers are presented, along with a Monte Carlo analysis of the robustness to disturbances for such transfers. Phasing is introduced where necessary to aid rendezvous with the Moon. The results demonstrate the potential for such techniques to provide a basis for the design and guidance of low-thrust lunar transfers.

Spacecraft trajectory optimization is essential for all the different phases of a space mission, from its launch to end-of-life disposal. Due to the increase in the number of satellites and future space missions beyond our planet, increasing the level of autonomy of spacecraft is a key technical challenge. In this context, traditional trajectory optimization methods, like direct and indirect methods are not suited for autonomous or on-board operations due to the lack of guaranteed convergence or the high demand for computational power. Heuristic control laws represent an alternative in terms of computational power and convergence but they usually result in sub-optimal solutions. Successive convex programming (SCVX) enables to extend the application of convex optimization to non-linear optimal control problems. The definition of a good value of the trust region size plays a key role in the convergence of SCVX algorithms, and there is no systematic procedure to define it. This work presents an improved trust region based on the information given by the nonlinearities of the constraints which is unique for each optimization variable. In addition, differential algebra is adopted to automatize the transcription process required for SCVX algorithms. This new technique is first tested on a simple 2D problem as a benchmark of its performance and then applied to solve complex astrodynamics problems while providing a comparison with indirect, direct, and standard SCVX solutions.

Heteroclinic connections represent unique opportunities for spacecraft to transfer between isoenergetic libration point orbits for zero deterministic $\mathrm{\Delta }V$ expenditure. However, methods of detecting them can be limited, typically relying on human-in-the-loop or computationally intensive processes. In this paper we present a rapid and fully systematic method of detecting heteroclinic connections between quasi-periodic invariant tori by exploiting topological invariants found in knot theory. The approach is applied to the Earth–Moon, Sun–Earth, and Jupiter–Ganymede circular restricted three-body problems to demonstrate the robustness of this method in detecting heteroclinic connections between various quasi-periodic orbit families in restricted astrodynamical problems.

A novel high-order target phase approach (TPhA) for the station-keeping of periodic orbits is proposed in this work. The key elements of the TPhA method, the phase-angle Poincaré map and high-order maneuver map, are constructed using differential algebra (DA) techniques to determine station-keeping epochs and calculate correction maneuvers. A stochastic optimization framework tailored for the TPhA-based station-keeping process is leveraged to search for fuel-optimal and error-robust TPhA parameters. Quasi-satellite orbits (QSOs) around Phobos are investigated to demonstrate the efficacy of TPhA in mutli-fidelity dynamical models. Monte Carlo simulations demonstrated that the baseline QSO of JAXA’s Martian Moons eXploration (MMX) mission could be maintained with a monthly maneuver budget of approximately 1 m/s.

Understanding the internal composition of a celestial body is fundamental for formulating theories regarding its origin. Deep knowledge of the distribution of mass under the body’s crust can be achieved by analyzing its moments of inertia and gravity field. In this regard, the two moons of the Martian system have not yet been closely studied and continue to pose questions regarding their origin to the space community; thus, they deserve further characterization. The Martian Moons eXploration mission will be the first of its kind to sample and study Phobos over a prolonged period. This study aims to demonstrate that the adoption of periodic and quasi-periodic retrograde trajectories would be beneficial for the scientific value of the mission. Here, a covariance analysis was implemented to compare the estimation of high-order gravitational field coefficients from different orbital geometries and for different sets of processed observables. It was shown that the adoption of low-altitude non-planar quasi-satellite orbits would help to refine the knowledge of the moon's libration angle and gravitational field.