Stochastic optimization of spacecraft rendezvous trajectories

Many recent and proposed satellite missions involve the rendezvous of two or more satellites in different orbits. The relative motion of two orbiting bodies can be described by the traditional Clohessy-Wiltshire (CW) equations. With these equations, one of the satellites is designated the reference point. and by definition is located at the origin of a rotating coordinate system. The other satellite is then navigated relative to the reference point. The orbital dynamics of both satellites is governed by twehody dynamics. The relative distances between the satellite and reference point are generally small compared to the reference point semi-major axis. The drawback of the CW equations is that they are based on the assumption of an Earth point mass gravity field and a circular reference point orbit with no disturbing forces. Thus, they typically decrease in accuracy with increasing eccentricity, and with perturbing forces. In real-world applications (especially for low-Earth orbits), orbit eccentricity and perturbing forces (such as non-spherical Earth gravitational potential, atmospheric drag, third body effects, etc.) are always present. The purpose of this research effort is to develop an optimization tool to generate optimal variations of traditional Clohessy-Wiltshire solutions to provide rendezvous trajectories in the presence of gravitational perturbations, as represented by a high-fidelity Earth gravity model. The specific optimization technique to be considered is a continuous-parameter genetic algorithm. Genetic algorithms use a stochastic process to escape local minima and explore wide regions of the solution space via a perturbative process. The output of this study is an optimization tool that will generate minimum-error rendezvous trajectories between two low-Earth orbiting satellites. This optimization tool consistently outperforms the traditional Clohessy-Wiltshire approach when a highfidelity gravity model is used instead of the Earth point mass assumption.