Abstract
The analysis of satellite rendezvous in planetary orbits typically derives control laws in a frame rotating with the target satellite. However, because 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 suboptimal or infeasible control laws if control components have different relative weights. A new approach is described that poses 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 transformation is used to formulate and solve the second-order nonlinear rendezvous problem using optimal power-limited propulsion analytically. Thus, a framework is 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.
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