Journal of Astronautics ›› 2017, Vol. 38 ›› Issue (10): 1057-1067.doi: 10.3873/j.issn.1000-1328.2017.10.006

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Optimal Orbital Control without Radial Thrust Based on SDRE Method

ZHANG Xiang yu, ZHANG Gang, CAO Xi bin   

  1. Research Center of Spacecraft Technology, Harbin Institute of Technology, Harbin 150001, China
  • Received:2016-09-12 Revised:2017-04-21 Online:2017-10-15 Published:2017-10-25


The optimal control problem of spacecraft rendezvous and formation reconfiguration without radial thrust is investigated by using the state dependent Riccati equation (SDRE) method. Considering the thrusters installed in the circumferential and normal directions, the nonlinear relative motion equations influenced by J 2 perturbation are derived and presented via the state-dependent coefficient (SDC). Then the optimal feedback control law is derived by using the SDRE method, and an approximate analytical solution of the state dependent Riccati differential equation is obtained. Moreover, a numerical version of the obtained analytical solution is extended to solve the formation reconfiguration problem. Compared with the Gauss pseudospectral spectral method, the proposed method does not need an initial guess. Numerical results show that the analytical solution of the Riccati differential equation method has high precision for the near circular orbits, and the error of the optimal index of the numerical method is less than 6% even for the elliptical orbits with an eccentricity approaching to 0.3.

Key words: Orbital rendezvous, Formation reconfiguration, State dependent Riccati equation (SDRE), Circumferential thrust, Trajectory optimization

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