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University of Auckland researcher Henry Senturia is developing a planning tool for small low-thrust satellite trajectories in the Saturnian system.
CubeSats, small, standardised satellites that are mass-produced and cost-effective, have made space more accessible than ever. Most are currently used in Earth’s orbit, but CubeSats also hold great promise for deep-space exploration, with the additional challenge that their small fuel reserves make the traditional short-burn rocket motors impractical.
Low-thrust propulsion systems such as ion engines can solve this issue, trading high thrust for greatly increased efficiency. A low-thrust spacecraft gradually accelerates over long periods of time rather than performing short burns to change its trajectory.
These propulsion systems are often combined with gravity assists, flybys that “borrow” momentum from planets or moons to modify a spacecraft’s velocity. While this technique can save significant fuel, the manoeuvres are complex to plan.
To address this, a University of Auckland researcher at the time, Dr Darcey Graham, developed the Tool for Initial Low-Thrust Design (TILTD), a MATLAB-based program that models continuous-thrust trajectories. TILTD uses a method called monotonic basin hopping (MBH). First, a nonlinear solver is used to find an optimal path, before making a random “hop” to a different starting point, and searching again. Over many loops, this maps out the most promising routes through the complex landscape of possible trajectories.
Earlier this year, University of Auckland Masters student Henry Senturia contacted our support team seeking help to further develop TILTD as a planning tool for small low-thrust satellite trajectories in the Saturnian system.
Saturn-lit Tethys, Cassini Orbiter, NASA/JPL-Caltech/Space Science Institute, 2017.
On a personal laptop, a simple trajectory undergoing 100 MBH iterations took nearly a full day, limiting the scope of missions that could be tested.
The code also offered opportunities for improvement, from usability, to code clarity and maintainability.
Though a Consultancy project, Researcher Support Team members at REANNZ worked with Henry to make TILTD faster, easier to use, and simpler to maintain. Originally, the input data was hard coded into the program itself, which made making changes difficult. By separating code and inputs and using GitHub for version control, Henry and his team could now track changes and work together seamlessly.
To ensure reliability, a testing framework was created to check the results after every change. With that safety net in place, we streamlined the code, cutting out duplication and making it easier to adapt for exploring a wide range of low-thrust trajectories.
The main challenge was speeding up TILTD through parallelisation, getting different parts of the program to run on multiple CPUs at once. Because MBH builds on the best result so far, the CPUs couldn’t just work independently. Instead, we designed a system where each CPU could “check out” the current best result, try to improve it, and only update the shared result if it found something better.
Provided the ratio of MBH loops to CPUs was high, the results remained accurate. However, this added a complication to the random number generation used for generating new trajectories, running in parallel risked making the sequence of numbers unpredictable. To solve this, a long sequence of random numbers was generated at the start and assigned each CPU its own slice, based on position rather than order of retrieval.
Together, these improvements have made TILTD a faster and more robust trajectory planning tool.
The parallelisation of the MBH function achieved up to an 88% reduction in execution time for a 100 loop MBH run when running on 10 cpus. This opens up the possibility of solving more complex trajectories.
The ability to queue multiple simultaneous runs in a job array on an HPC platform allows for a much more comprehensive exploration of possible trajectory solutions.
Using the REANNZ advanced computing platform, Henry is able to complete 40 complex trajectories through 100 loops in less time than a single run on a personal laptop.
Modularisation of the code base and use of version control will make collaborating on this project easier, especially over the long term.
Thanks to this Consultancy, Henry and his colleagues are now better positioned to support New Zealand efforts in shaping the future of deep space exploration.
Satellite trajectory with multiple gravity assists, MATLAB, Henry Senturia, 2025.
I want to especially highlight the improved time to solution. Parallelisation implemented by Callum Walley reduced runtimes from days to hours, an 88% reduction in the best case. This has enabled a much wider exploration of parameters that would have previously been impractical to run. Thank you Callum!
Henry Senturia, Faculty of Science, University of Auckland
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