Frozen orbit design and maintenance with an application to small body exploration

Frozen orbits are ideal options for global mapping and observation. In this paper, a design and maintenance method of frozen orbit is presented and applied to the small body exploration. On the basis of the Legendre addition theorem, an analytic solution of the frozen orbit is developed, which can obtain frozen orbits with arbitrary orders of zonal harmonic coefficients in concise forms. Based on the proposed method, the distribution and properties of frozen orbits around Vesta are discussed. Then, an anti-chattering self-adaptive control law is proposed to maintain the frozen orbits in a high-fidelity environment. The control law is proved to be stable and robust against model uncertainties and unmodeled perturbations. Simulation results show that the proposed method can obtain the frozen orbit efficiently with desired performance, while the self-adaptive control law can keep the orbit stable with satisfactory fuel consumption. This study provides a new option for frozen orbit design in future exploration missions.