Space Trajectories. Orbital Rendezvous

A space rendezvous consists in reaching position and/or velocity conditions on a given date. This type of problem arises for a wide variety of missions: transporting crew to an orbital station, supplying propellants or maintaining operational satellites, positioning geostationary, sun-synchronous or satellite constellations, capturing space debris, intercepting ballistic threats...

The mission scenario comprises a launch to a stable orbit, phasing with the target position, a propulsive transfer to the final orbit, and then the actual rendezvous. To control these operations, lighting and visibility conditions must be respected from ground stations.

When the target is in circular orbit, which is the most frequent case, the relative dynamics are described by the Hill-Clohessy-Wiltshire equations. The associated analytical solutions provide a simple way of preparing a preliminary scenario and defining the sequence of maneuvers to be carried out.

The primary objective of a rendezvous is to reach the target with sufficient accuracy, despite the disturbances encountered in flight. This requires simplified controls compatible with on-board guidance. The linear quadratic formulation of the rendezvous problem provides a compromise between optimality in power consumption and simplicity of solution.

This article presents the phases of a rendezvous scenario with their constraints, rendezvous modeling in the circular case and the main control laws used operationally.