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For the challenging problem that a spacecraft approaches a tumbling target with non-cooperative maneuver, an anti-saturated proximity control method is proposed in this paper. First, a brand-new appointed-time convergent performance function is developed via exploring Bézier curve to quantitatively characterize the transient and steady-state behaviors of the pose tracking error system. The major advantage of the proposed function is that the actuator saturation phenomenon at the beginning can be effectively reduced. Then, an anti-saturated pose tracking controller is devised along with an adaptive saturation compensator. Wherein, the finite-time stability of both the pose and its velocity error signals are guaranteed simultaneously in the presence of actuator saturation. Finally, 2 groups of illustrative examples are organized and verify that the close-range proximity is effectively realized even with unknown target maneuver.

In this work, two novel dynamics indicators are introduced and used to characterise the uncertain dynamics around a binary asteroid. These indicators are derived from the propagated expansion of the states in polynomial series of the uncertainty in initial conditions and dynamical model parameters. Thus, each indicator encapsulates in a single scalar the effect of the uncertainty in multiple model parameters. The first indicator directly calculates the second statistical moment of the propagated uncertainty set. This indicator gives a measure of the rate of divergence of an ensemble of trajectories in phase space. The second indicator estimates the approximation error of the polynomial expansion. Hence, it captures the nonlinearity in the distribution of the propagated states that is induced by the uncertainty. The two indicators are then used to create a map in phase space, which relates initial conditions to the sensitivity of the state over time to multiple realisation of the uncertain parameters. The case of the a spacecraft orbiting the binary asteroid system Didymos is considered in this paper. The uncertainty maps proposed in this paper are shown to reveal the characteristics of the motion around Didymos under uncertainty in the masses of both bodies.

The existence and characteristics of periodic orbits (POs) in the vicinity of a contact binary asteroid are investigated with an averaged spherical harmonics model. A contact binary asteroid consists of two components connected to each other, resulting in a highly bifurcated shape. Here, it is represented by a combination of an ellipsoid and a sphere. The gravitational field of this configuration is for the first time expanded into a spherical harmonics model up to degree and order 8. Compared with the exact potential, the truncation at degree and order 4 is found to introduce an error of less than 10 % at the circumscribing sphere and less than 1 % at a distance of the double of the reference radius. The Hamiltonian taking into account harmonics up to degree and order 4 is developed. After double averaging of this Hamiltonian, the model is reduced to include zonal harmonics only and frozen orbits are obtained. The tesseral terms are found to introduce significant variations on the frozen orbits and distort the frozen situation. Applying the method of Poincaré sections, phase space structures of the single-averaged model are generated for different energy levels and rotation rates of the asteroid, from which the dynamics driven by the 4 × 4 harmonics model is identified and POs are found. It is found that the disturbing effect of the highly irregular gravitational field on orbital motion is Northwestern Polytechnical University, Xiaan, China weakened around the polar region, and also for an asteroid with a fast rotation rate. Starting with initial conditions from this averaged model, families of exact POs in the original non-averaged system are obtained employing a numerical search method and a continuation technique. Some of these POs are stable and are candidates for future missions.

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