Pattern transition in spacecraft formation flying using bifurcating potential field

Many new and exciting space mission concepts have developed around
spacecraft formation flying, allowing for autonomous distributed systems that
can be robust, scalable and flexible. This paper considers the development of
a new methodology for the control of multiple spacecraft. Based on the artificial
potential function method, research in this area is extended by considering
the new approach of using bifurcation theory as a means of controlling
the transition between different formations. For real, safety or mission critical
applications it is important to ensure that desired behaviours will occur.
Through dynamical systems theory, this paper also aims to provide a step
in replacing traditional algorithm validation with mathematical proof, supported
through simulation. This is achieved by determining the non-linear
stability properties of the system, thus proving the existence or not of desired
behaviours. Practical considerations such as the issue of actuator saturation
and communication limitations are addressed, with the development of a new
bounded control law based on bifurcating potential fields providing the key
contribution of this paper. To illustrate spacecraft formation flying using
the new methodology formation patterns are considered in low-Earth-orbit
utilising the Clohessy-Wiltshire relative linearised equations of motion. It is
shown that a formation of spacecraft can be driven safely onto equally spaced
projected circular orbits, autonomously reconfiguring between them, whilst
satisfying constraints made regarding each spacecraft.