Lyapunov-based Spacecraft Rendezvous Maneuvers using Differential Drag

Abstract

This work presents a Lyapunov-based control strategy to perform spacecraft rendezvous maneuvers exploiting differential drag forces. The differential drag is a virtually propellantfree alternative to thrusters for generating control forces at low Earth orbits, by varying the aerodynamic drag experienced by different spacecraft, thus generating differential accelerations between the vehicles. The variation in the drag can be induced, for example, by closing or opening flat panels attached to the spacecraft, hence effectively modifying their cross-sectional area. In a first approximation, the relative control forces can be assumed to be of bang-off-bang nature. The proposed approach controls the nonlinear dynamics of spacecraft relative motion using differential drag on-off control, and by introducing a linear model. A control law, designed using Lyapunov principles, forces the spacecraft to track the given guidance. The interest towards this methodology comes from the decisive role that efficient and autonomous spacecraft rendezvous maneuvering will have in future space missions. In order to increase the efficiency and economic viability of such maneuvers, propellant consumption must be optimized. Employing the differential drag based methodology allows for virtually propellant-free control of the relative orbits, since the motion of the panels can be powered by solar energy. The results here presented represent a breakthrough with respect to previous achievements in differential drag based rendezvous. Nomenclature a D = Relative acceleration caused by differential drag a J2 = Relative acceleration caused by J 2 a,b,d = Constants in the transformation matrix A d = Linear guidance state space matrix A , B = Matrices for the state space representation of the Schweighart and Sedwick equations c = Coefficient from the Schweighart and Sedwick equations C o = Initial spacecraft drag coefficient for chaser and target (two plates deployed) C max = Maximum spacecraft drag coefficient for chaser and target (four plates deployed) C min = Minimum spacecraft drag coefficient for chaser and target (zero plates deployed) e = Tracking error vector e 0 = Time-varying eccentricity of the Harmonic Oscillator Motion before Rendezvous f(x) = Nonlinearities in the spacecraft dynamics I nxn = nxn Identity Matrix i T = Target initial spacecraft orbit inclination J 2 = Second-order harmonic of Earth gravitational potential field (Earth flattening) [108263 × 10−8, Ref. [1]] l = Linearized time rate of change of the amplitude of the cross-track separation (Coefficient from the Schweighart and Sedwick equations) m S = Spacecraft mass n = Mean motion (Coefficient from the Schweighart and Sedwick equations) P = Solution matrix of the Lyapunov equation q = Linearized argument of the cross-track separation (Coefficient from the Schweighart and Sedwick equations) Q = Selected Lyapunov equation matrix Q LQR = Matrix from the LQR problem R = Earth mean radius (6378.1363 km, Ref. [1] ) Downloaded by CARLETON UNIVERSITY LIBRARY on July 31, 2015 | htt...

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