Low-Thrust Trajectory Design for Tours of the Martian Moons

While the interest in the Martian moons increases, the low-thrust propulsion technology is expected to enable novel mission scenarios but is associated with unique trajectory design challenges. Accordingly, the current investigation introduces a multi-phase low-thrust design framework. The trajectory of a potential spacecraft that departs from the Earth vicinity to reach both of the Martian moons, is divided into four phases. To describe the motion of the spacecraft under the influence of gravitational bodies, the two-body problem (2BP) and the Circular-Restricted Three Body Problem (CR3BP) are employed as lower-fidelity models, from which the results are validated in a higher-fidelity ephemeris model. For the computation and optimization of low-thrust trajectories, direct collocation algorithm is introduced. Utilizing the dynamical models and the numerical scheme, the low-thrust trajectory design challenge associated each phase is located and tackled separately. For the heliocentric leg, multiple optimal control problems are formulated between the planets in heliocentric space over different departure and arrival epochs. A contour plot is then generated to illustrate the trade-off between the propellant consumption and the time of flight. For the tour of the Martian moons, the science orbits for both moons are defined. Then, a new algorithm that interfaces the Q-law guidance scheme and direct collocation algorithm is introduced to generate low-thrust transfer trajectories between the science orbits. Finally, an end-to-end trajectory is produced by merging the piece-wise solutions from each phase. The validity of the introduced multi-phase formulation is confirmed by converging the trajectories in a higher-fidelity ephemeris model.