ELLIPTIC RENDEZVOUS IN THE CHASER SATELLITE FRAME

The analysis of satellite rendezvous in planetary orbits typically derives control laws in a frame rotating with the target satellite. However, since the control law is ultimately required in the chaser satellite's frame, knowledge of the chaser satellite's motion with respect to the planet may be required to correctly transform the control laws. The transformation may also result in sub-optimal or infeasible control laws. This paper analyzes the rendezvous problem in the chaser satellite's frame directly. A nonlinear transformation between the chaser and target frames, in terms of relative position and velocity variables is derived. This is used to formulate and solve the rendezvous problem using optimal power-limited propulsion analytically, that includes nonlinear effects. A framework is thus developed, that can be used to solve the orbital transfer problem. The efficacy of the derived control algorithm is demonstrated by means of an example.