Collision Analysis for Multiple Satellites Released from a Common Dispenser
Authors:   Cranfield University, Cranfield, United Kingdom, D'Anniballe Antonio , Felicetti Leonard , Hobbs Stephen , Harrison-Bayes Dylan 
Published: January 2024

With the increasing demand for multiple satellites released in a single launch being supported by developments in both rocketry and satellite manufacturing, risks of having collisions in the early phases of missions have become one of the key challenging aspects that new operators need to face. This is especially true when onboard propulsion capabilities are limited, and trajectory corrections are not possible over several orbits, a scenario which is common with smaller spacecraft. In addition, accurate tracking and orbit determination cannot be done accurately due to the unreliability of the TLEs when satellites are closely packed together.
In multiple satellite launches (MSLs) the high risk of collisions in the early phases of the mission arises from many factors. Whenever the uncertainty on the initial state of a satellite is high, this propagates along the nominal trajectory. If the measurements are limited, the uncertainty grows. If two satellites with high uncertainty share similar nominal trajectories, this generates many conjunction events where the probability of sharing the same position at the same time is high. If the satellite has good on-board propulsion capabilities and it is able to estimate its state accurately, it can correct its trajectory and avoid the conjunction event. This is, however, hardly the case for small satellites at the time of release, when onboard and ground-based measurements are scarce, initial uncertainties may be high, and propulsion systems may be limited or absent. Whenever this is the case, it is critical that the release system can deploy spacecraft into safe trajectories generating few or no conjunction events.
The aim of this study is to identify safe release systems and methodologies for MSLs targeting LEO. Different dispenser configurations are analysed through numerical simulations to categorize, rank, and assess their viability and safety. To be considered safe, a dispenser would need to yield a minimal amount of conjunction events, together with a low probability of collision among the released spacecraft in the short and long term. The analyses are not limited to a single dispenser or a small set of dispensers but are generalised to include all the main configurations in use while considering a broad range of parameters. Thanks to this, not only can dispenser configurations be analysed in terms of their safety, but optimal configurations and release parameters can also be found.
The effects of uncertainties and variations of parameters are evaluated through covariance analysis and unscented transform techniques and assessed through Monte Carlo analysis. Several MSL configurations are considered, such as the 4 in-line, the 4-up, the 8-up, the PSLV-C37-like, the SL_OMV-like, and Starlink-like dispensers. In addition to these, some new dispenser concepts are proposed. Parametric analyses are carried out by varying the dispenser parameters such as the total number of released satellites, the time between each release, the momentum imparted to the spacecraft, and the direction of release. For each of the selected cases, the number of possible conjunction events and the probability of collision are computed. The optimal parameters for each configuration are therefore identified, and the various configurations are ranked accordingly based on the resulting safety metrics. The obtained results might inform possible enhancements for improving the safety of future MSL systems.