Cooperative spacecraft rendezvous—A direct parametric control approach

In this paper, the dynamical model in a matrix second-order nonlinear form with respect to the three Euler angles is firstly established for the rendezvous system of a spacecraft, which is complete in the sense that no approximation is taken. Then, with the help of a recently proposed general parametric design approach for general fully-actuated second-order nonlinear systems, a direct parametric approach for spacecraft rendezvous control via proportional plus derivative feedback is proposed, which gives a complete parametrization of the pair of feedback gains, and allows usage of the established complete nonlinear model in matrix second-order format. The approach possesses two important features. Firstly, with the proposed controller parametrization, the spacecraft rendezvous system, though highly nonlinear, can be turned into a constant linear system with desire eigenstructure. Secondly, in such a design there are still degrees of freedom which may be further utilized to improve the system performance. An example is considered to demonstrate the use of the proposed approach.