arXiv subjects

Felipe Arenas-Uribe

Publications and source records attributed to Felipe Arenas-Uribe.

3 recordsLinked to original sources

arXiv2026

Higher-Order Gravitational Models: A Tutorial on Spherical Harmonics and the Newtonian Model

Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit deviations from spherical symmetry, including oblateness, localized mass concentrations, and higher-order shape irregularities. These features can significantly perturb spacecraft trajectories, especially in low-altitude or long-duration missions, leading to cumulative orbit prediction errors and increased control demands. This article presents a tutorial introduction to spherical harmonic gravity models, outlining their theoretical foundations and underlying assumptions. Higher-order gravitational fields are derived as solutions to the Laplace equation, providing a systematic framework to capture the effects of non-uniform mass distributions. The impact of these higher-order terms on orbital dynamics is illustrated through examples involving Low Earth Orbit satellites and spacecraft near irregularly shaped asteroids, highlighting the practical significance of moving beyond the point-mass approximation.

astro-ph.EP↗

arXiv2025

Geometric Conditions for Lossless Convexification in Linear Optimal Control with Discrete-Valued Inputs: Real-Time Implementation for Spacecraft Rendezvous

Optimal control problems with discrete-valued inputs are inherently challenging due to their mixed-integer nature, rendering them generally intractable for real-time, safety-critical aerospace applications. Lossless convexification offers a powerful alternative by reformulating these mixed-integer programs into computationally efficient convex programs. This paper develops a lossless convexification framework for the optimal control of linear time-varying systems with discrete-valued inputs. We extend existing theoretical results by demonstrating that system normality is preserved when reformulating Lagrange-form problems into Mayer-form via an epigraph transformation. Furthermore, we establish that under simple geometric conditions on the input set, the solution to the relaxed convex problem strictly satisfies the original non-convex input constraints. This framework enables the real-time computation of optimal discrete-valued controls without resorting to mixed-integer optimization. The proposed algorithm is validated on a spacecraft rendezvous maneuver utilizing discrete-valued reaction thrusters in an elliptical orbit. Numerical results from Monte Carlo simulations confirm that the algorithm consistently yields exact discrete-valued control inputs with computational timelines compatible with safety-critical, on-board applications.

math.OC↗

arXiv2025

Safe Landing on Small Celestial Bodies with Gravitational Uncertainty Using Disturbance Estimation and Control Barrier Functions

Soft landing on small celestial bodies (SCBs) poses unique challenges, as gravitational models poorly characterize the higher-order gravitational effects of SCBs. Existing control approaches lack guarantees for safety under gravitational uncertainty. This paper proposes a three-stage control architecture that combines disturbance estimation, trajectory tracking, and safety enforcement. An extended high-gain observer estimates gravitational disturbances online, a feedback-linearizing controller tracks a reference trajectory, and a minimum-intervention quadratic program enforces state and input constraints while remaining close to the nominal control. The proposed approach enables aggressive yet safe maneuvers despite gravitational uncertainty. Numerical simulations demonstrate the effectiveness of the controller in achieving soft-landing on irregularly shaped SCBs, highlighting its potential for autonomous SCB missions.

eess.SY↗