This work describes the design of an impulsive manoeuvres' planner meant for onboard autonomous optimum formation flying reconfigurations in near-circular orbit. The whole variation of the relative orbit is stepwise achieved through intermediate configurations, so that passive safety and delta-v consumption minimisation are pursued. The description of the relative motion is accomplished in terms of relative orbital elements and the reconfiguration plan takes into account mean effects due to the Earth oblateness coefficient and differential drag. Manoeuvres consist of sets of triple tangential impulses and a single out-of-plane burn to establish each intermediate configuration. They are scheduled in time intervals compliant with the user-defined permissible time control windows.

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This work revisits the modeling of the relative motion between satellites flying in near-circular low-Earth-orbits. The motion is described through relative orbital elements and both Earth's oblateness and differential drag perturbations are addressed. With respect to the former formulation, the description of the J 2 effect is improved by including also the changes that this perturbation produces in both relative mean longitude and relative inclination vector during a drifting phase, when a non-vanishing relative semi-major axis is required. The second major improvement consists in a general empirical formulation to include the mean effects produced by non-conservative perturbations, such as the differential aerodynamic drag acceleration. As a result, in addition to the well-known actions on the relative semi-major axis and on the mean along-track separation, the model is able to reflect the mean variation of the relative eccentricity vector due to atmospheric density oscillations produced by day and night transitions.

This work addresses the design and implementation of a prototype relative navigation tool that uses camera-based measurements collected by a servicer spacecraft to perform far-range rendezvous with a noncooperative client in low Earth orbit. The development serves the needs of future on-orbit servicing missions planned by the German Aerospace Center. The focus of the paper is on the design of the navigation algorithms and the assessment of the expected performance and robustness under real-world operational scenarios. The tool validation is accomplished through a high-fidelity simulation environment based on the Multi Satellite Simulator in combination with the experience gained from actual flight data from the GPS and camera systems onboard the Prototype Research Instruments and Space Mission Technology Advancement mission. Nomenclaturê A, A = matrices of the partials of the nonlinear dynamics equations for the complete linear time-varying system and its relative dynamics subpart a = semimajor axis of the servicer satellitê B, B = control input matrices for the complete linear timevarying system and its subpart b = biases vector of the relative orbit estimatê C, C = measurement sensitivity matrices for the complete linear time-varying system and its subpart e = eccentricity of the servicer satellite H = matrix of accumulated partials of measures with respect to the initial state i = inclination of the servicer satellite K = condition number of a matrix m i = ith merit function n = mean angular motion of the servicer satellite P = covariance matrix of the estimation state R y x = rotation matrix from frame x to y r = relative position vector between the servicer and client t = time u = mean argument of latitude of the servicer satellite u c = line-of-sight unit vector in camera frame v = relative velocity vector between the servicer and client W = covariance matrix of the measurements W o = observability Gramian of the linear time-varying systemÂ,Ĉ x = filter state vector y = linearly modeled measurements via sensitivity matrix z = modeled observations: couple of azimuth and elevation Δ•= finite variation of a quantity δα = nondimensional relative orbital elements set δe = nondimensional relative eccentricity vector δi = nondimensional relative inclination vector δλ = nondimensional relative mean longitude δ• = relative quantity ϵ = uncorrelated measurement errors ζ = true observations η = azimuth angle of line-of-sight unit vector from servicer to client θ = ascending node of the relative orbit κ = one pixel camera resolution in radians Λ = information matrix μ = Earth constant ξ = single measure to refer either to azimuth or to elevation angles σ = standard deviation of state and/or measurement errorŝ Φ, Φ, Φ b = state transition matrices for the complete system and its subparts ϕ = mean argument of latitude of the relative perigee ψ = elevation angle of line-of-sight unit vector from servicer to client Ω = right ascension of the ascending node of the servicer satellite ω = argument of perigee of the servicer s...