Fast Passive Safety Checks Using General Ellipse Constraints

This paper presents a fast technique that shows promise for real-time checking of one-orbit passive safety during ballistic near-circular relative motion. By leveraging geometric insights from relative orbital elements (ROEs), the technique establishes envelope models to accurately represent both the keep-out volume (KOV) and the relative trajectory projected onto the radial/cross-track plane. An ROE-based passive safety criterion is then formulated to ensure short-term passive safety based on these envelopes and the ROE formulation. The authors conduct a comprehensive analysis of ellipse–ellipse intersection techniques to verify one of the conditions, ultimately selecting a robust technique with an average runtime of 0.15 ms. In a preliminary analysis using a Monte Carlo simulation, the technique demonstrated an overall accuracy of 98.2% using binary classification under realistic perturbations. This motivated the addition of the technique with a binary search algorithm to quantify passive safety as a percentage of KOV radii. Testing against challenging cases identified in the Monte Carlo simulation showed an improved quantification of error while achieving an average runtime of 0.82 ms under a sufficient binary search tolerance. Finally, this approach allows for the use of flexible safety constraints, which effectively mitigate the issues encountered with nominal breach cases in the preliminary studies.