Path planning and position control and of an underactued [sic] electromagnetic formation flight satellite system in the near field

Abstract

Electromagnetic formation flight is the process of using electromagnetic actuators (coils) on multiple spacecraft to produce relative (internal) forces in order to control the relative position and orientation of the spacecraft. This thesis demonstrates the ability to experimentally generate the relative internal electromagnetic forces in a short duration full 6DOF environment. Next the thesis limits itself to a two-satellite system and thus is able to perform a state reduction that constrains the motion to an arbitrary two-dimensional plane in 3-dimensional space showing that this is not actually a constraint on the real system for a two satellite formation. A feedback control law is proposed and simulated in this constrained space demonstrating position control of the underactuated system. Some theoretical guarantees are derived from contraction analysis. Finally time and energy optimal paths for a series of maneuvers are conceived by application of the GPOPS - II numerical optimization software. The results show further that the underactuated system is capable of arbitrary position control with the limitation being that it is unable to simultaneously control attitude and position to desired states because the attitude is used to "steer" the magnetic dipole therefore the desired angle is set by the position controller rather than an external reference. Overall this thesis shows the viability from the controllability perspective of underactuated electromagnetic formation flight for future space missions.