Control Strategy for Long-Term Station-Keeping on Near-Rectilinear Halo Orbits

This work considers the control of a spacecraft in indefinite near-rectilinear halo orbit about the Earth-Moon L2. For indefinite station-keeping, it is important to minimize fuel consumption, while allowing for occasional transfer to a new orbit. The control scheme therefore consists of two components: the first component is the tracking of the nominal NRHO and the second component is an orbit correction maneuver between NRHO trajectories. The nominal NRHO is computed using a multiple-shooting technique that takes into account all forces on the spacecraft whose magnitude is larger than the dominant disturbance forces caused by navigational error. The tracking component is a linear-quadratic regulation scheme that rejects disturbances caused by orbit determination error, using a Lyapunov sublevel set that models the state covariance generated using sequential Kalman filter. The orbit correction maneuver is computed to minimize fuel costs. AAS/AIAA Space Flight Mechanics Meeting This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Copyright c © Mitsubishi Electric Research Laboratories, Inc., 2020 201 Broadway, Cambridge, Massachusetts 02139 Control Strategy for Long-Term Station-Keeping on Near-Rectilinear Halo Orbits∗ Vivek Muralidharan† Purdue University, West Lafayette, IN 47907 Avishai Weiss‡ and Uroš Kalabić§ Mitsubishi Electric Research Laboratories, Cambridge, MA 02139 This work considers the control of a spacecraft in indefinite near-rectilinear halo orbit about the Earth-Moon L2. For indefinite station-keeping, it is important to minimize fuel consumption, while allowing for occasional transfer to a new orbit. The control scheme therefore consists of two components: the first component is the tracking of the nominal NRHO and the second component is an orbit correction maneuver between NRHO trajectories. The nominal NRHO is computed using a multiple-shooting technique that takes into account all forces on the spacecraft whosemagnitude is larger than the dominant disturbance forces caused by navigational error. The tracking component is a linear-quadratic regulation scheme that rejects disturbances caused by orbit determination error, using a Lyapunov sublevel set that models the state covariance generated using sequential Kalman filter. The orbit correction maneuver is computed to minimize fuel costs. Nomenclature Ak,Bk = system matrices ãji = acceleration of body i with respect to j ãiJ2 = J2 perturbing acceleration due to body i ãSRP = acceleration due to solar radiation pressure Cr = coefficient of reflectivity ∆v = maneuver vector, or change in instantaneous velocity states δxk = vector of state deviation at time step k δyk = measurement residue vector at time step k k = measurement noise Hk = measurement matrix at time step k K = gain matrix μi = gravitational parameter of body i P,Q,R = weighting matrices on cost functional P = covariance of state estimation error Q = covariance of process noise R = covariance of measurement noise R = range Û R = range rate ρ = system mass ratio r̄, v̄ = position and velocity substates S = positive definite matrix that represent acceptable bounds on uncertainty T = propagation time tk = k-th time step τ = epoch time ∗This work was supported by Mitsubishi Electric Research Laboratories. †Graduate Student, School of Aeronautics and Astronautics, [email protected]. ‡Principal Research Scientist, [email protected]. §Research Scientist, [email protected].