Onboard Exact Solution to the Full-Body Relative Orbital Motion Problem

This paper provides a representation theorem of the onboard exact solution for the six-degree-of-freedom relative orbital motion problem. This problem is quite important, due to its numerous applications: spacecraft formation flying, rendezvous operations, autonomous missions. The common approach is to consider the relative translation and rotation dynamics for the leader–deputy spacecraft formation to be modeled using vector-based formalisms. The proposed approach makes use of a complete dual orthogonal tensor-based construction, which allows for a new description of the full-body relative orbital motion problem. The approach chosen for representing the solution is very short in comparison with the previous reports on the same problem and gives a new formulation that could give important computational benefits.