Autonomous Formation Flying for the PRISMA Mission

Eberhard Gill, Oliver Montenbruck, Simone D'Amico
2007 Journal of Spacecraft and Rockets  
PRISMA is a technology demonstration mission for satellite formation flying and in-orbit servicing. The space segment comprises the fully maneuverable Main minisatellite and the smaller Target satellite in a low Earth orbit at 700-km altitude. A key mission objective is to demonstrate onboard, fully autonomous, robust, safe, and precise formation flying of spacecraft. This is accomplished by spaceborne global positioning system navigation, guidance, and control functionalities for the
more » ... e of the relative motion between the two spacecraft. An innovative estimation approach employs a common Kalman filter for the absolute states of Main and Target, which accounts for the interdependency of absolute and relative navigation without the need for an explicit relative state. As a result, the onboard navigation system provides absolute and relative orbit information in real time with a position accuracy of 2 and 0.1 m, respectively. The formation control achieves accuracies of a few tenths of meters with minimum usage of thrusters. The guidance and control concept is detailed with emphasis on a relative eccentricity and inclination vector separation strategy. The paper derives estimates of the expected relative orbit control performances based upon realworld simulations using typical global positioning system receiver and propulsion system characteristics. Nomenclature a = semi-major axis a = acceleration vector B = ballistic coefficient C D = drag coefficient c = velocity of light d D = along-track acceleration due to drag dt = time difference of filter updates E = transformation matrix e = eccentricity e = eccentricity vector e N , e R , e T = unit vectors in normal, radial, and tangential directions G = measurement partials vector g = modeled measurement h = numerical integrator step size I = ionospheric bias i = inclination i = inclination vector J 2 = second-order zonal coefficient of the geopotential K = Kalman filter gain vector l = longitude M = mean anomaly N = integer bias of carrier phase N = integer bias vector n = mean motion P = covariance matrix Q = process noise covariance matrix R = Earth equatorial radius r = radius vector of the spacecraft r = acceleration of the spacecraft t = time u = mean argument of latitude v = velocity of the spacecraft W = measurement weight x = Kalman filter state z = measurement = J 2 perturbation coefficient = difference operator l = relative mean longitude t = drift time interval = attitude control error = relative navigation error e = relative eccentricity vector amplitude i = relative inclination vector amplitude t = clock offset = relative difference operator, = differential ballistic coefficient = propulsion system performance = relative ascending node = wavelength = Earth's gravitational coefficient = pseudorange = process noise = time scale of process noise = transition matrix = carrier phase ' = relative perigee = right ascension of the ascending node ! = argument of perigee r = double-difference operator Subscripts a = acceleration clk = clock D = drag emp = empirical acceleration G = gravity GPS = global positioning system i = Kalman filter step M = Main spacecraft of PRISMA formation M = moon N = normal R = radial S = sun SR = solar radiation T = total T = tangential
doi:10.2514/1.23015 fatcat:ei3w2lir3bgjblf4zw2xts22zm