Pattern transition in spacecraft formation flying via the artificial potential field method and bifurcation theory

In recent years many new and exciting space concepts have developed around spacecraft formation flying. This form of distributed system has the advantages of being extremely flexible and robust. This paper considers the development of new control methodologies based on the artificial potential function method and extends previous research in this area by considering bifurcation theory as a means of controlling the transition between different formations. For real, safety critical applications it is important to prove the stability of the system. This paper therefore aims to replace algorithm validation with mathematical proof through dynamical systems theory. Finally we consider the transition of formations at the Sun-Earth L2 point