Nonlinear Optimal Control of Orbital Rendezvous Problem for Circular and Elliptical Target Orbit

The orbital rendezvous and docking with Position and attitude nonlinear dynamics is one of the most challenging problems in the Aerospace engineering. The attitude and position of a chaser spacecraft, desired to rendezvous with a target spacecraft, have to be determined with respect to the target, as a result relative equations have to be considered. The chaser is controlled by actuators to rendezvous safely and stably under the conditions and requirements. In this paper rendezvous dynamics for target in a circular orbit is assumed as nonlinear second-order clohessy-wiltshire relative motion equations. Shauner and hempel relative equations are considered for target in elliptical orbit. Cost function has been chosen in a manner to minimize the control effort and to give smooth states. Nonlinear optimal control for rendezvous with a target in circular orbit using state dependent riccati equation by means of eigen vectors of the Hamiltonian matric is compared with linear quadratic regulator method for both linear and nonlinear systems and then stability and robustness of the results are analysed. Optimal control of a elliptical rendezvous is discussed independently. For navigational porpose it is important to express relative motion in inertial frame, this is accomplished by introducing an appropriate transformation.