Formation Attitude Optimization with a Multi-Impulse Design

The proposed Magnetospheric Multi-scale (MMS) formation flight mission requires regular tetrahedron geometry as it follows a highly eccentric orbit through the Earth’s magnetosphere, but formation attitude is not constrained. Due to potential corruption of the local magnetic field with particles output by satellite thrusters, we examine a mission design in which multiple impulses per orbit are used to maximize tetrahedron quality with minimal disruption to data acquisition. This paper extends previous efforts by optimizing MMS over formation (tetrahedron) attitude as well as position relative to a reference orbit. Candidate solutions are checked to ensure satellites do not collide. The effects of perturbations on formation quality, fuel use, and drift away from the Keplerian orbit are analyzed. This paper also presents an iterative Lambert’s method that enables optimization over perturbed dynamics and compares perturbed results with the original Keplerian solutions.