Proximity operations around small bodies require high levels of autonomy to ensure safe and reliable solutions. Spacecrafts in these regimes must navigate weak gravitational fields, rapidly varying orbital geometries, and significant navigation uncertainties. As mission architectures evolve toward greater onboard autonomy and extended multi-orbit observation campaigns, spacecrafts must safely transfer between different science orbits without relying on continuous ground intervention.
For upcoming Apophis missions, Periodic (PTO) and Resonant Terminator Orbits (RTO) are emerging as particularly valuable due to their sun-stabilized nature and diverse geometries suited for global mapping campaigns. This class of orbits will be central to planned post-encounter science campaigns around Apophis, such as NASA’s OSIRIS-Apex and
ESA’s RAMSES missions.

In this setting, the conventional use of deterministic trajectory design and heuristic safety margins becomes increasingly inadequate, as small errors in navigation, modeling, or control can accumulate rapidly, compromising safety or science objectives. A probabilistic approach is therefore desirable, to quantify risk and ensure the reliability of autonomous operations in this highly nonlinear dynamical environment.
Despite the growing interest in autonomous operations around asteroids, very limited work has examined trajectory transfers between these Terminator Orbits, especially addressing these transfers within a unified probabilistic, risk-aware formulation.
Recent advances in stochastic optimal control and covariance steering under uncertainty motivate the probabilistic framework developed in this work.

This paper formulates the autonomous science-orbit transfer as a chance-constrained optimal control problem, enforcing probabilistic bounds on state dispersion and trajectory safety while accounting for navigation, maneuver execution, and modeling uncertainties, ensuring also probabilistic passive-safety in case of loss of control authority during the transfer.
We adopt a sequential covariance-steering strategy via Sequential Convex Programming, leveraging the recently developed SCvx* algorithm, which provides reliable numerical behavior for nonlinear trajectories and ensures a theoretical guarantee of convergence to a feasible local optimum of the original non-convex problem.
Two complementary covariance-propagation formulations are evaluated: the classical Block Cholesky decomposition, and the more computationally efficient Full Covariance approach, recently introduced in the literature. Their relative performance is evaluated in the context of small-body transfers to assess trade-offs between computational cost and robustness of the optimal control policies.

In addition to the standard fuel-optimal objective based on minimizing the ?V99 expenditure, we also evaluate a recently proposed cost function designed to minimize the spacecraft’s exposure to regions where linear covariance propagation becomes inaccurate, which would break the underlying assumptions of our linear covariance steering controller. This metric combines State Transition Tensors (STTs) with the Tensor Eigenpair Measure of Nonlinearity (TEMoN)
to construct a convex upper bound on the nonlinear dynamical errors. Incorporating this objective enables the algorithm to preserve the Gaussian structure assumed by sequential covariance steering, significantly improving reliability in the highly nonlinear regimes near Apophis.

The proposed framework is applied to representative Apophis Terminator Orbits transfers, and the results are validated through nonlinear Monte Carlo simulations. Comparative analysis highlights the respective strengths of the Block-Cholesky and Full Covariance formulations, while the nonlinearity-minimizing cost function significantly reduces deviations from Gaussian assumptions in highly nonlinear dynamics.
Overall, this work presents an important step forward in designing risk-aware orbit transfers under uncertainty for autonomous small-body proximity operations.