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In this manuscript, an impulsive zone MPC formulation is proposed to tackle the problem of the spacecraft rendezvous control. The control objective is to maintain the follower spacecraft in a given subspace with respect to a leader vehicle by stabilizing the set of periodic relative orbits included in a given hovering zone. The idea is to incorporate this hovering zone as a target set into the MPC cost function, in order to permit a single MPC formulation and a receding horizon implementation. The control algorithm takes advantages of a relative motion parametrization for which the set of the equilibrium states represent the set of periodic orbits to prove the stability of the hovering zone and to enlarge significantly the domain of attraction. Several simulation results show that, in addition, performances in terms of convergence and fuel consumption are improved in comparison with previous works.

This paper presents a model predictive control strategy for the spacecraft rendezvous hovering phases. Using a sequence of impulsive velocity changes, the spacecraft is controlled to reach and remain on a periodic trajectory inside a given box-type hover zone, while minimizing the fuel consumption. The path constraints (box-type and periodicity) are satisfied continuously in time, based on a particular parametrization of the linearized relative spacecraft trajectories. The control saturation constraint is enforced by re-planning. First, a sequence of saturated impulsive controls is selected such that the spacecraft gets on a periodic trajectory. Second, a fixed-length sequence of saturated impulses brings the spacecraft closer to the hover zone. The convergence of this approach is proved. Numerical methods are proposed to solve the required constrained optimization problems. Finally, hardware-in-the-loop simulations, using a synthesized LEON3 microprocessor, are performed to assess the efficiency and robustness of the proposed approach.

During guidance and control procedures of orbiting spacecraft, the respect of positioning and space constraints is decisive for successful missions achievement. The development of algorithms capable of fulfilling these constraints is directly related to how precisely the spacecraft trajectories are known. Since accuracy is essential for these procedures, the prevention and estimation of errors arising from approximations and numerical computations become critical. In this context, we consider solving linear ordinary differential equations via rigorous polynomial approximations in Chebyshev series. These are polynomials together with an error bound accounting for both approximation and rounding errors. Our method allows for the computation of validated approximations of the transition matrices describing the evolution of spacecraft trajectories. The proposed approach is employed in the following applications: first, we consider the linearized impulsive rendezvous framework, demonstrating how to use rigorous polynomials approximations to provide a validated propagation of the relative dynamics between spacecraft; this is then exploited for the hovering phases of the spacecraft rendezvous, where we conceive a validated model predictive control based on semi-definite programs. Finally, we propose a semi-analytical transition matrix for a simplified model of geostationary station keeping, linearizing the spacecraft dynamics which take into account the J2 Earth oblateness effect.