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Guidance for Formation Flying and Rendezvous using Relative Orbital Elements
                                

                                            Nominal TanDEM-X configuration (credits: D'Amico)

The relative motion between co-orbiting satellites of a distributed space system, being it a formation, a rendezvous&docking mission, a swarm, or a fractionated spacecraft, needs to be parameterized and modelled in a convenient way. This is a fundamental task prior to and in conjunction with the design of an efficient and safe guidance, navigation, and control system for multi-satellite missions.
This research investigates a novel yet powerful parameterization of the relative motion based on a set of parameters called relative eccentricity and relative inclination vectors. Each of these vectors is two-dimensional and, together with the relative semi-major axis and the relative mean argument of latitude, constitute a set of 6 parameters called Relative Orbital Elements (ROEs). Describing the relative motion using ROEs brings a wealth of advantages including, among others, higher insights into the formation geometry for baseline design, collision avoidance, and motion monitoring, easier handling of Earth’s oblateness and atmospheric drag perturbations, and straightforward computation of orbit control maneuvers.
Based on an elegant formulation of the linearized equations of relative motion, this work has extended the concept of relative eccentricity/inclination vector separation from the colocation of geostationary satellites to near-circular formation-flying and rendezvous scenarios. The technique has been successfully applied within the few formation-flying missions currently operational, namely GRACE, TanDEM-X, and PRISMA. Today the methodology is being applied to challenging on-orbit servicing scenarios where collision avoidance is of utmost importance. Even the release of nanosatellites from small satellite carriers can take advantage of this approach.
Current research is oriented to the generalization of the relative eccentricity/inclination vector method to orbits of high or even arbitrary eccentricity. In addition efforts are put into the inclusion of higher order perturbations in the resulting dynamics model. Recent results show that the relative eccentricity/inclination vectors can provide distinctive advantages in angles-only navigation thanks to the observability properties of the dynamics system. Future research will focus on a review of linear covariance analysis for proximity operations using relative orbital elements.
 
Recent Publications (2013-2014)
 
Wermuth M., D’Amico S., Gaias G.;
Safe Release of a Picosatellite from a Small Satellite Carrier in Low Earth Orbit;
24th AAS/AIAA Space Flight Mechanics Meeting, 26-30 Jan. 2014, Santa Fe, USA (2014).