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.
Typically, the center of mass and inertia tensor of a spacecraft are estimated pre-launch using a mass properties table and/or a CAD model of the spacecraft. If these estimates are not sufficiently accurate to meet mission requirements, they can be refined after launch using sensor data from the spacecraft. In order to refine pre-launch estimates of these properties, variations of the Kalman filter are developed to estimate the attitude and angular rate of the spacecraft, as well as a representation of the inertia tensor. Two parametrizations of the inertia tensor are investigated: the standard moments and products of inertia representation and a representation formed from the principal moments of inertia and the attitude of the principal axes. Monte Carlo analysis is considered for three scenarios in which the mass properties are estimated, and it is shown that both methods are statistically consistent and capable of improving upon inertia estimates but suffer from linearization error when uncertainty in the moment of inertia tensor is large.
A predictive controller was modified and applied to a microsatellite to show that attitude stabilization about two axes can be achieved using only magnetic actuators. The predictive controller is based on previous works by other authors with modifications for a spacecraft without gyroscopic stiffness. The system is described by a discrete-update law and uses a predictive control approach to calculate the control effort. In order to test the controller, a truth model using two body dynamics and Euler's equations along with solar radiation pressure, atmospheric drag, and gravity gradient perturbations was developed. To analyze the fidelity of the controller, a Monte Carlo analysis was conducted and showed that all simulated scenarios achieved the desired attitude and attitude rates. In addition, power consumption, time to reach desired attitude, and state errors were analyzed.
Polynomial chaos expresses a probability density function (pdf) as a linear combination of basis polynomials. If the density and basis polynomials are over the same field, any set of basis polynomials can describe the pdf; however, the most logical choice of polynomials is the family that is orthogonal with respect to the pdf. This problem is well-studied over the field of real numbers and has been shown to be valid for the complex unit circle in one dimension. The current framework for circular polynomial chaos is extended to multiple angular dimensions with the inclusion of correlation terms. Uncertainty propagation of heading angle and angular velocity is investigated using polynomial chaos and compared against Monte Carlo simulation.
