There has been increased interest in visiting small planetary bodies such as comets and asteroids, but proximity operations around these bodies remain challenging due to large uncertainties in their gravity fields and mass distribution. These uncertainties strongly influence spacecraft motion, limit the reliability of analytical dynamical models, and have historically forced missions to take conservative approach strategies. For example, the NEAR Shoemaker mission spent several months characterizing asteroid 433 Eros before entering a stable orbit, and the Hayabusa mission required optical navigation techniques with high uncertainty to safely execute surface sampling. As mission goals become increasingly challenging, the need for techniques that can support earlier, safer proximity operations is increasing.
 
Mission planners must choose to either spend several months learning about the gravity field of the small body or accept a high degree of uncertainty and choose to explore closer for various science operations. This work presents a data-driven approach that does not rely on gravity modeling for proximity operations by constructing a linear surrogate model of spacecraft motion directly from onboard telemetry. Dynamic Mode Decomposition (DMD) is used to identify a linear operator that approximates the local dynamics using only recorded state histories. Because DMD relies on a least-squares formulation and singular value decomposition, it provides a mechanism for model reduction. This makes it well suited for environments where high-fidelity gravity representations are not yet available. Additionally, the reduced dimensionality and linearity reduce the computational demand on an onboard system improving the feasibility for an real-time implementation. Existing approaches to proximity operations in uncertain gravity environments include learning-based MPC and sliding-mode control formulations that jointly estimate spherical harmonic coefficients and the spacecraft state and chance-constrained control methods that rely on probabilistic disturbance models. While effective, these approaches typically require an explicit parameterization of the gravitational field. In contrast, the method proposed here avoids gravity modeling entirely by constructing a surrogate dynamical model directly from flight data and embedding its uncertainty within a Tube MPC framework.

To safely exploit this technique, we integrate it with a control architecture based on Tube Model Predictive Control (Tube MPC). In this framework, a nominal linear MPC is responsible for tracking the reference trajectory, while an ancillary feedback controller maintains the true system within a guaranteed tube around the nominal trajectory. A key contribution of this work is the treatment of DMD modeling error as a bounded exogenous disturbance. The residual error between the DMD-predicted state evolution and the state time history is analyzed, and this error is used to define the disturbance set for the Tube MPC formulation. By characterizing model mismatch directly from data rather than from analytical uncertainty models, the framework remains entirely gravity-agnostic and does not rely on assumptions about the gravitational environment other than smoothness and boundedness.

The tube dynamics are then propagated forward in time by using DMD again, allowing us to assess how uncertainty in the surrogate model evolves. This yields a MPC scheme that will meet given constraints. In the present work, we assume perfect state knowledge.

A high-fidelity simulation environment is constructed using the spherical harmonic gravity representation of asteroid 433 Eros. Several candidate reference trajectories are examined, including polar and equatorial bound orbits. As expected, the nonlinear and highly irregular gravity field causes the uncontrolled spacecraft to drift significantly from these orbits. With the proposed DMD-based Tube MPC framework, the spacecraft can track each desired trajectory with small, bounded error while remaining inside the invariant tube successfully. 
 
Overall, this approach shows strong potential for enabling earlier and safer proximity operations during small-body exploration missions. By replacing long-duration gravitational characterization with real-time onboard model identification, mission planners may reduce operational timelines and reduce navigation risk, allowing spacecraft to approach scientifically interesting regions far sooner than with traditional techniques. The integration of DMD-based modeling with Tube MPC provides a unified architecture that is computationally tractable, offering a promising direction for future autonomous navigation systems.