Recent research at the University of Auckland has advanced techniques for low-thrust trajectory optimisation in support of electric propulsion missions. This work began with Darcey Graham’s PhD thesis (2022), which addressed the challenge of planning low-thrust interplanetary transfers from non-traditional launch conditions, such as lunar rideshare deployments. Low-thrust propulsion systems, while highly efficient, produce complex equations of motion that require numerical integration and careful trajectory design across multiple gravitational regimes.

Graham developed a multi-fidelity optimisation framework based on the Sims–Flanagan transcription, where low-fidelity methods provide robust initial guesses for high-fidelity solvers. Unlike traditional approaches that patch together different segments (e.g., Earth-centred to Sun-centred), her method solves for the entire trajectory in a unified problem. This approach supports trajectory designs incorporating gravity assists, such as from the Moon, and was demonstrated in a high-fidelity solution for a small spacecraft trajectory from lunar orbit to weak capture at Venus. The work highlighted limitations in gravity assist modelling near the Moon due to its large sphere of influence relative to cislunar distances, prompting refinement of assist formulations for perturbed multi-body environments.

Building on this, PhD student William Zhou is developing a hybrid optimisation framework aimed at low-thrust exploration of main-belt asteroids. His research integrates global and local optimisation strategies with machine learning. Global search is achieved using kinodynamic-RRT* algorithms that accommodate dynamic constraints such as thrust and mass depletion, enabling the efficient exploration of high-dimensional asteroid visitation sequences. For local optimisation, Zhou applies the Sims–Flanagan method to refine low-thrust transfers, and augments this with Physics-Informed Neural Networks (PiNNs) trained on a high-quality dataset of perturbed Lambert transfers. These PiNNs embed physical constraints directly into their loss functions, enabling fast and physically consistent trajectory predictions. His work also focuses on real-time adaptability and computational scalability, which are critical for autonomous onboard planning.

Complementing these projects, MSc student Henry Senturia is investigating low-thrust transfers from Earth orbit to Halo orbits around Earth-Moon libration points, particularly in the context of rideshare launches. His work explores the use of multiple-arc Sims–Flanagan optimisation to efficiently connect impulsive transfers in the Earth-centred regime with low-thrust propagation into the cislunar region. The study assesses the effects of varying thrust duration, initial conditions, and targeting criteria to understand how best to position a spacecraft for insertion into a periodic Halo orbit with minimal propellant use. This effort contributes to current interest in cost-effective access to near-rectilinear halo orbits (NRHO) and other libration point orbits for communication relays, staging platforms, or exploration missions.

Together, these studies form a coherent body of research aimed at enabling efficient low-thrust missions launched from cislunar space or targeting interplanetary destinations. By integrating trajectory optimisation, electric propulsion modelling, and AI-based prediction tools, the work supports the design of next-generation deep-space missions with minimal mass and high operational flexibility.

Graham, Darcey, Low-Thrust Gravity Assist Trajectories at Low and High Fidelity, PhD Physics The University of Auckland 2022.

Darcey R. Graham, Jacob A. Englander, Nicholas J. Rattenbury, and John E. Cater, Low-Thrust Trajectory Design from Lunar Rideshare to Venus Capture, Journal of Spacecraft and Rockets 2022 59:6, 2070-2083

Graham, D. R., Englander, J. A., Rattenbury, N. J., & Cater, J. E. (2020, August). Low-Thrust Transfer to Interplanetary Trajectories from Lunar Trajectories with Rideshare. In AAS/AIAA Astrodynamics Specialist Conference.