Dr Xiaoyu Fu

Quasi-satellite orbits (QSOs) have been under the research spotlight due to their linear stability and close proximity to the secondary body in a restricted three-body system. In this research, the numerical continuation and stationkeeping method of quasi-periodic QSOs is investigated based on the Poincaré section. By means of Differential Algebra (DA) techniques, a DA-enhanced numerical method to compute quasi-periodic orbits is proposed. This method is formulated to solve for the invariant curve on a Poincaré section of a quasi-periodic orbit. An enhanced Poincaré map, which is established with DA techniques, effectively reduce the problem dimensionality and promote computation efficiency. A family of quasi-periodic QSOs around Phobos are continued to validate the proposed method. A subsequent stationkeeping approach adapted from the Target Phase Approach (TPhA) is tailored for the maintenance of generated quasi-periodic QSOs. A stochastic optimization scheme for the adapted TPhA method is formulated in search for fuel-optimal and error-robust stationkeeping parameters. Stationkeeping simulations for the achieved quasi-periodic QSO family are provided to showcase the effectiveness of the adapted TPhA method.

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 Poincare 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.

To maintain the periodic orbits in a three-body regime, a high-order Target Phase Approach (TPhA) is proposed in this work. Two types of polynomial maps, the phase-angle Poincaré map and high-order maneuver map, are established respectively for the determination of stationkeeping epochs and calculation of correction maneuvers. A stochastic optimization framework tailored for the TPhA-based stationkeeping process is leveraged in search of fuel-optimal and error-robust TPhA parameters. Quasi-Satellite Orbits (QSOs) around Phobos are investigated to demonstrate the efficacy of this approach in both low-and high-fidelity models. Monte-Carlo simulations demonstrate that the baseline QSO of JAXA's Martian Moons eXploration (MMX) mission can be maintained with a monthly manuever budget of around 1.13m/s.

Space exploration has often benefitted from the qualitative analyses of non integrable problems enabled by numerical continuation procedures. Yet, standard approaches based on Newton’s method typically end with discrete representations of family branches that may be subject to misinterpretation and overlook important dynamical features. In this research, we introduce novel continuation procedures based on the differential algebra of Taylor polynomials. Our algorithms aim at generating dense family branches as an atlas of polynomial charts that are locally valid for a range of system and continuation parameters. Examples of particular solutions will be shown within the framework of the Circular Restricted Three-Body Problem, along with fold and period-doubling bifurcations that are efficiently detected using automatic domain splitting and map inversion techniques.

CubeSat missions that take advantage of ride-sharing opportunities to the Moon are typically limited by a small v budget. In this paper, a patching point method is applied to design a low-energy lunar transfer for a spacecraft initially placed into a circumlunar free-return trajectory. Initial conditions generated within weak stability boundaries further guarantee ballistic lunar capture upon arrival. A large number of optimised trajectories are produced, with a minimum mission v cost of 32.51 m/s. Additionally, the B-plane values of the spacecraft during its initial flyby of the Moon are investigated. A relationship between the initial position of the Sun in the synodic frame and the B-plane values is observed, in which successful trajectories appear to favour entering into certain orbital resonances with the Moon.

Near Rectilinear Halo Orbits (NRHOs) are orbits of great interest for the upcom-ing lunar missions. To maintain NRHOs in a three-body regime, a stationkeeping strategy based on a high-order Target Point Approach (TPA) is proposed, where fuel-optimal and error-robust TPA parameters are acquired from stochastic global optimization. Accurate TPA manevuers are calculated in a high-order fashion enabled by Differential Algebra (DA) techniques. Stochasticity is handled by incorporating Monte Carlo simulations in the process of optimization and the evaluation of high-order ODE expansions is employed to supplant the time-consuming numerical integration. Multiple candidate NRHOs with different stability properties are investigated.

Water ice and other volatile compounds found in permanently shadowed regions near the lunar poles have attracted the interests of space agencies and private companies due to their great potential for in-situ resource utilization and scientific breakthroughs. This paper presents the mission design and trade-off analyses of the Volatile Mineralogy Mapping Orbiter, a 12U CubeSat to be launched in 2023 with the goal of understanding the composition and distribution of water ice near the lunar South pole. Spacecraft configurations based on chemical and electric propulsion systems are investigated and compared for different candidate science orbits and rideshare opportunities.

Periodic orbits in the Restricted Three-Body Problem are widely adopted as nominal trajectories by di↵erent missions. To maintain periodic orbits in a three-body regime, a stationkeeping strategy based on a high-order Target Point Approach (TPA) is proposed, where fuel-optimal and error-robust TPA parameters are acquired from stochastic global optimization. Accurate TPA maneuvers are calculated in a high-order fashion enabled by Di↵erential Algebra techniques. Orbit determination epoch is selected using a sensitivity analysis based on the convergence radius of a stroboscopic map. Stochasticity is handled by incorporating Monte Carlo simulations in the process of optimization and the evaluation of high-order ODE expansions is employed to supplant the time-consuming numerical integration. Two specific types of periodic orbits, Near Rectilinear Halo Orbits and Quasi-Satellite Orbits, are investigated to demonstrate the validity and eciency of the strategy.

Despite the advantages of very-low altitude retrograde orbits around Phobos, questions remain about the efficacy of conventional station-keeping strategies in preventing spacecraft such as the Martian Moons eXploration from escaping or impacting against the surface of the small irregular moon. This paper introduces new high-fidelity simulations in which the output of a sequential Square-Root Information Filter is combined with recently developed orbit maintenance strategies based on differential algebra and convex optimization methods. The position and velocity vector of the spacecraft are first estimated using range, range-rate, and additional onboard data types such as LIDAR and camera images. This information is later processed to assess the necessity of an orbit maintenance maneuver based on the estimated relative altitude of MMX about Phobos. If a maneuver is deemed necessary, the state of the spacecraft is fed to either a successive convex optimization procedure or a high-order target phase approach capable of providing sub-optimal station-keeping maneuvers. The performance of the two orbit maintenance approaches is assessed via Monte Carlo simulations and compared against work in the literature so as to identify points of strength and weaknesses.