Combining Global and Local Strategies to Optimize Parameters in Magnetic Spacecraft Control via Attitude Feedback

The attitude control of a spacecraft using magnetorquers can be obtained by using attitude feedback, instead of state feedback, with the advantage of not requiring the installation of attitude rate sensors, thus saving cost, volume, and weight. In this work, an attitude feedback with four design parameters is considered. The practical determination of appropriate values for these parameters is a critical open issue. We propose here to search for the parameters’ values which minimize the convergence time to reach the desired attitude. Such a systematic approach has several advantages but requires overcoming a number of difficulties to be realized. First, convergence time cannot be expressed in analytical form as a function of these parameters. Therefore, we develop a solution approach based on derivative-free optimization algorithms. Secondly, design parameters may range over very wide intervals. As a consequence, the feasible set cannot be explored densely in reasonable time. Thus, we propose a fast probing technique based on local search to identify which regions of the search space have to be explored densely. Thirdly, convergence time depends also on the initial conditions of the spacecraft, which are not known in advance. Hence, we formulate a min–max model to find robust parameters, namely parameters aiming at minimizing convergence time under the worst initial conditions.