Faster-than-natural spacecraft circumnavigation via way points

Circumnavigation relative motion is considered for applications such as inspecting a space object for damage, or characterizing space debris before engaging a remediation operation. Faster-than-natural circumnavigation is a guidance method in which the deputy spacecraft is advanced ahead of the natural Keplerian relative motion. A state transition matrix method of generating a discrete way point guidance solution is proposed for faster-than natural circumnavigation. The state transition matrix methodology is applied to both circular and elliptical chief orbits. For the circular chief case, natural relative trajectories are planar in nature. With the faster-than-natural circumnavigation, this work illustrates how the required relative trajectories become three-dimensional curves. This methodology allows for closed-form impulsive control solutions and the associated fuel cost. Numerical simulations illustrate and validate the proposed method.