Koopman Expectation for Range Safety Assurance
Conference
21st Australian International Aerospace Congress (AIAC21)
Title
Koopman Expectation for Range Safety Assurance
Abstract
With uncrewed autonomous systems gaining traction in aerial domains, their ubiquity presents a challenge in their integration into airspace management. In particular, assuring public safety in the case of a system failure poses the challenge in timely regulatory approval. Simulation of the autonomous systems across a range of failure modes is useful in determining appropriate range safety perimeters in a timely, cost-effective way. However, given the uncertainty in launch conditions and sophistication of their control systems, performing enough flight simulations of Uncrewed Aerial Vehicles (UAVs) to capture debris statistics and mitigate safety concerns may be computationally infeasible.
We investigated the use of Koopman expectation as an alternative to Monte Carlo methods, for estimating the mean location and spread of debris in the case of launch failure. This statistical technique has proven itself promising in reducing the number of range safety simulations and may provide a route for automating range safety assurance processes. To evaluate this methodology, we conducted a series of experiments on a three-dimensional aerodynamic flight model of a UAV. Uncertainty in the flight condition at failure was modelled as a normal distribution in wind vector, mass and angle of attack; failure modes considered fixed angle of attack and fixed elevator position. The experiments revealed numerical issues with the use of quadrature integration employed by the Koopman expectation code utilised, which since paper submission have been resolved. Ongoing work is underway to explore the utility of this technique in estimating other safety measure statistics, such as directly calculating the casualty risk.
Key takeaway:
- Shoal’s research found that the Koopman Expectation reduced the number of range safety simulations required over Monte Carlo analysis and, therefore, could decrease simulation costs.
Authors
Emma Comino, Modelling and Simulation Analyst, Shoal Group
John Wharington PhD, Principal System Engineer, Shoal Group
Date
Monday 24 March 2025
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About Shoal
Shoal is complex systems design company. We use Systems Engineering combined with Modelling, Simulation and Analysis to help our clients define, analyse, decide, optimise, and deliver technology-intensive projects in complex environments across Defence, Space, Transport, Energy and Infrastructure.
More: shoalgroup.com
Contact
Matthew Wylie
Chief Engineer, Shoal Group
[email protected]
