Non-cooperative rendezvous and interception —A direct parametric control approach

In this paper, the dynamical model in a matrix second-order nonlinear form is firstly established in the Sight of Line coordinate system for the problems of non-cooperative rendezvous and interception of spacecrafts, which are 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 noncooperative rendezvous and interception 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 model. The approach possesses two important features. Firstly, with the proposed controller parametrization, the spacecraft rendezvous and the interception systems, though highly nonlinear, can be turned into constant linear systems with desire eigenstructure. Secondly, in such a design there are still degrees of freedom which may be further utilized to improve the system performance. Examples are considered to demonstrate the use of the proposed approach.