Nonlinear Control and Orbit Estimation of Target-Pointing Spacecraft using Geomagnetic Field-Based Error Representation

Abstract

In this dissertation, we discuss the nonlinear control and orbit estimation of spacecraft by developing a novel control error representation using geomagnetic field measurements, where a magnetometer is used as a sole attitude sensor. The use of magnetic devices is a popular solution in spacecraft design because of its simplicity, low cost, power efficiency, and reliability. However, the magnetometer can not be used to calculate a control error since it does not directly provide attitude information, but only measures the direction and strength of geomagnetic field at the current spacecraft location and its attitude orientation. Thus, calculating a control error using only magnetometer, without applying any complicated attitude estimation filter, is a very challenging problem. We consider a target pointing problem of spacecraft in an inertial frame in order to derive a control error representation, where the control objective is to control spacecraft orientation to align the specified spacecraft body axis with the designated target direction. Any rotational orientation along the target direction satisfies the pointing requirement, resulting in a set of expected magnetic field vectors that constitutes the lateral surface of circular cone with cone axis of the designated target direction. Based on this idea, an alternate control objective is equivalently substituted with aligning a current geomagnetic field measurement with a preferred magnetic field vector. The preferred magnetic field vector is ingeniously chosen among all expected magnetic field vectors at current spacecraft location in orbit in order to provide the minimum angular path to the substituted control objective. The resulting control error, which is simply calculated using the measured magnetic field vector, the preferred magnetic field vector and the specified spacecraft body axis, results in the Euler`s eigen-axis rotation, which explicitly represents the attitude error between the target orient...