Guidance design with navigation errors for relative motion in noncircular perturbed orbits

This paper presents a new method to design the rendezvous trajectory with perturbations and navigation errors. Firstly, a new state transition matrices calculation method is used to model the relative motion of two spacecraft in arbitrarily eccentric orbits perturbed by J 2 , differential drag and the differential mass to area ratio. The state transition matrices are derived by first performing a Taylor expansion on the equations of relative motion and subsequently integrating resulting linear differential equations. Secondly, the navigation errors are taken into consideration and a weighting vector is chosen to generate a new objective function to minimize the propellant consumption with the navigation errors. Thirdly, the rendezvous trajectory problem are cast as second order cone programming problem. Finally, a series of simulations are carried out to verify the effectiveness of the new state transition matrices calculation method in eccentric orbits, with the J 2 , differential drag and the differential mass to area ratio for relative motion, and to prove that the new objective function can be better in propellant use. ©2018, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.