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This paper analyses the problem of the autonomous absolute orbit control of a spacecraft in low Earth orbit using different on-board feedback control systems. Three types of control are compared. The first implements an analytical control algorithm. The second and third controllers considered are the linear and the quadratic optimum regulator from the classical control theory. For the implementation of the linear regulators the problem has been formulated as a two spacecraft formation keeping in which one of the spacecraft is virtual and not affected by non-gravitational orbit perturbations. The relative Earth-fixed elements have been introduced as a set of parameters which can express the relative motion of two spacecraft in an Earth-fixed reference frame. These relative elements allow the general formalization of the requirements of an absolute orbit control system design and its formulation as a particular case of spacecraft formation flying control problem. A direct mapping between the relative Earth-fixed and orbital elements enables the direct translation of absolute to formation control requirements and the straightforward use of classical control theory techniques for the orbit control of distributed spacecraft systems. The validation, performance estimation and comparison of the control algorithms are realized by means of numerical simulations with a high level of realism. NomenclatureA spacecraft reference area [m 2 ] B ballistic coefficient of the spacecraft [kg/m 2 ] C D drag coefficient [-] J 2 geopotential second-order zonal coefficient [-] M mean anomaly [rad] R E Earth's equatorial radius [m] T E mean period of solar day [s] m spacecraft mass [kg] a semi-major axis [m] e j eccentricity [-] e j eccentricity vector component [-] g j gain i inclination [rad] i j inclination vector component [rad] n mean motion [rad/s] s j characteristic root t time [s] u argument of latitude [rad] * PhD Candidate, Space Advanced Research Team, School of Engineering, v spacecraft velocity [m/s] δκ relative orbital elements vector λ longitude [rad] δa relative semi-major axis [-] δe relative eccentricity vector amplitude [-] δh altitude deviation [m] δi relative inclination vector amplitude [rad] κ mean orbital elements vector κ o osculating orbital elements vector δL j phase difference vector component [m] δr relative position vector [m] δr j relative position vector component [m] δu relative argument of latitude [rad] δv relative velocity vector [m/s] δv j relative velocity vector component [m/s] ∆v j maneuver velocity increment component [m/s] ǫ normalized relative orbital elements vector [m] η normalized altitude [-] φ relative perigee [rad] ϕ latitude [rad] µ Earth gravitational coefficient [m 3 /s 2 ] ω argument of periapsis [rad] ω E Earth rotation rate [rad/s] Ω right ascension of the ascending node [rad] Ω secular rotation of the line of nodes [rad/s] ρ atmospheric density [kg/m 3 ] θ relative ascending node [rad] R + set of positive real numbers Z set of integer numbers Subscript d drag E Earth g gravity R re...

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This paper analyzes the problem of autonomous control of the longitude of the ascending node (LAN) for a satellite in low Earth orbit (LEO) by means of along-track and anti-alongtrack velocity increments which adjust the semimajor axis. The problems related to the possibility of generating the reference orbit (RO) on-board and with the estimation of the atmospheric drag are considered. The Autonomous Orbit Keeping (AOK) experiment of the PRISMA formation flying mission will be the test platform of the control strategy here exposed. The AOK on-board software shall demonstrate autonomous orbit control using a guidance law for the orbit's LAN and shall implement a deterministic control algorithm using along-track and anti-along-track velocity increments. Using GPS-based absolute navigation data, AOK shall command thruster activations in the orbital frame to autonomously control the orbit within a predefined window. The AOK experiment paves the way to the accurate and autonomous orbit control of LEO satellites on a routine basis. The main requirement of the experiment is to demonstrate an orbit control accuracy of the osculating ascending node of 10 m . The paper shows results from real-world software simulations where the accuracy of the reference orbit is limited and GPS sensors and hydrazine actuators are accurately modeled. The fundamental approach on which the software design, validation and testing is based, is also explained.