arXiv subjects

Jay W. McMahon

Publications and source records attributed to Jay W. McMahon.

12 recordsLinked to original sources

arXiv2026

Approximate Relative Entropy Constraints for Nonlinear Covariance Steering Under Distribution Ambiguity

Covariance steering provides an efficient framework for designing linear stochastic feedback policies, but its extension to nonlinear systems relies on a Gaussian surrogate obtained through local linearization. Because this surrogate may differ substantially from the true nonlinear state distribution, risk-sensitive quantities such as collision probability and mean-squared error may be inaccurately estimated. This work develops a distributionally robust covariance-steering framework based on the relative entropy, also known as the Kullback-Leibler divergence (KLD), to account for ambiguity in the propagated probability density function. Using a variational representation of exponential integrals, we derive computable upper bounds on risk-sensitive quantities over a KLD ambiguity set. We then formulate an upper bound on the time rate of change of the KLD between the true nonlinear distribution and a Gaussian reference surrogate. Under some assumptions, this bound is controlled by decision variables within a covariance-steering formulation. The resulting constraints are incorporated into a sequential convex programming algorithm to design stochastic guidance policies that keep the true distribution close to its Gaussian surrogate while enforcing bounds on risk-sensitive performance measures. The proposed approach is demonstrated on a challenging nonlinear spacecraft transfer between two near-rectilinear halo orbits.

cs.RO↗

arXiv2026

Relative Entropy-Bounded Ambiguous Chance Constraints for Robust Planning in Nonlinear Systems

We consider defining risk probability in stochastic control problems under distribution ambiguity. Current approaches for chance-constrained control typically assume that the true state distribution is known and Gaussian distributed. These assumptions are not amenable to many real-world engineering applications where system dynamics are nonlinear and only approximately modeled. In this work, we define a distribution ambiguity set and, with a variational expression for exponential integrals, bound the expected risk value under an unknown distribution that resides within a relative entropy distance of a nominal Gaussian reference distribution. Our bound recovers the reference risk value in the zero-divergence limit. A method is presented to determine the relative entropy distance defining the ambiguity set that is a function of the reference covariance evolution and second-order dynamical truncation errors. The resulting contributions provide a framework for handling distributional ambiguity in nonlinear covariance steering problems. A stochastic spacecraft guidance example is presented to demonstrate our contributions.

math.OC↗

arXiv2026

Information-Based Trajectory Planning for Spacecraft-to-Spacecraft Tracking and Navigation in Cislunar Space

We present a trajectory planning method that balances information collection and control effort to improve cislunar spacecraft-to-spacecraft absolute tracking. Expanding use of cislunar space requires alternative navigation and tracking procedures that minimize reliance on ground-based support. Among efforts to address this need, spacecraft-to-spacecraft tracking exploits nonlinear dynamical tracers encoded in a series of relative measurements to infer absolute states of both an observer and a target. The geometry between spacecraft operating under this mode can significantly influence tracking performance. This work considers this geometrical impact by designing observer trajectories that jointly balance control effort and an information-theoretic quantification of the expected spacecraft-to-spacecraft tracking performance. Our methods are designed for multiple low-thrust observation platforms of various sensing modalities and can incorporate multiple space object targets in planning. By leveraging information gain in the optimal control problem, we report almost an order of magnitude improvement in the expected navigation and tracking errors for an optical observer operating in a Distant Retrograde Orbit (DRO). This work demonstrates the feasibility and value of information-optimal low-thrust spacecraft trajectory design for current and upcoming cislunar missions.

cs.RO↗

arXiv2026

Improved Directional State Transition Tensors for Accurate Aerocapture Performance Analysis

Aerocapture is particularly challenging for semi-analytical propagation because the dynamics are dominated by nonconservative forces whose magnitudes vary significantly throughout the trajectory. State transition tensors (STTs), higher-order Taylor series expansions of the solution flow, have been widely used as a computationally efficient semi-analytical propagation method for orbital scenarios, but have not previously been applied to aerocapture. However, computing higher-order STTs requires integrating exponentially many equations as the state dimension increases. Directional state transition tensors (DSTTs) mitigate this cost by projecting the state into a reduced-dimension basis. This work develops novel dynamics analysis techniques to identify effective bases for this reduction, including augmented higher-order Cauchy Green tensors tailored to quantities of interest such as apoapsis radius. Results show that DSTTs constructed along these bases significantly reduce computational cost while maintaining accuracy in predicted apoapsis radius and terminal energy. In particular, certain of these DSTTs outperform traditional DSTTs in nonlinear perturbation propagation for key state subsets and quantities of interest. These results establish STTs and DSTTs as practical tools for aerocapture performance analysis to enable robust guidance and navigation.

eess.SY↗

arXiv2026

Risk-Aware Aerocapture Guidance Through a Probabilistic Indicator Function

Aerocapture is sensitive to trajectory errors, particularly for low-cost missions with imprecise navigation. For such missions, considering the probability of each failure mode when computing guidance commands can increase capture rate. A risk-aware aerocapture guidance algorithm is proposed that uses a generative model-based probabilistic indicator function to estimate escape, impact, or capture probabilities. The probability of each mode is incorporated into corrective guidance commands to increase the likelihood of successful capture. The proposed method is evaluated against state-of-the-art numeric predictor-corrector guidance algorithms in high-uncertainty scenarios where entry interface dispersions lead to nontrivial failure probabilities. When using a probabilistic indicator function in guidance, 71.43% to 100% of recoverable cases are saved for a variety of initial distributions and atmosphere models. The probabilistic indicator function is capable of predicting failure probability for dispersions and atmosphere models outside its training data, showing generalizability. In addition, the probabilistic indicator is compared to a fading memory filter for density estimation, demonstrating improvements in accuracy when both are used in conjunction. The proposed risk-aware aerocapture guidance algorithm improves capture performance and robustness to entry interface state dispersions, especially for missions with high navigation uncertainty.

eess.SY↗

arXiv2025

Optimal Rank-1 Directional State Transition Tensors

An optimal rank-1 approximation of state transition tensors was developed as an efficient alternative to state transition tensors for nonlinear uncertainty quantification. While previous directional state transition tensors used the dominant right singular subspace of the state transition matrix to construct a reduced-dimension representation of the state transition tensors, optimal directional state transition tensors are constructed to maximize the information retained in a rank-1 approximation of the state transition tensors in the Frobenius-norm sense. The optimal rank-1 directional state transition tensor is found by solving a tensor z-eigenpair problem of the "square" of the state transition tensor. This construct leads to increased approximation accuracy of the state transition tensors and improved Gaussian moment propagation for nonlinear flight scenarios like aerocapture.

eess.SY↗

arXiv2025

A 3D thermophysical model for binary asteroid systems: Application to the BYORP effect on (175706) 1996 FG3

Differential heating and radiation on asymmetric asteroids can cause measurable changes in their rotation rates and spin axes, known as the YORP effect. In binary systems, such radiation-driven torques can change the mutual asteroid orbits, termed the binary YORP or BYORP effect. To study how binary asteroid shapes and thermophysical properties affect surface temperatures and BYORP, we developed a new 3D thermophysical model which balances insolation, 1D conduction, visible light reflection, and mutual heating through scattered infrared radiation. Using 3D ray tracing, we include eclipses, shadowing from horizons and topography, and mutual radiation exchange between the primary and secondary asteroids. We perform global modeling of the binary asteroid (175706) 1996 FG3, a Janus mission target. At perihelion, we find that the 1996 FG3 system experiences temperatures between 100 and 475 K. We find that eclipses and thermal inertia can alter secondary surface temperatures by up to 14%, with a mean difference due to radiation from the primary of just over 1%. We also present a model for calculating the BYORP effect using binary thermophysical model results. This model compares well to analytical approximations of the BYORP coefficient B, and suggests that thermal effects like eclipses and thermal inertia can reduce torque in the 1996 FG3 system and alter the BYORP coefficient by up to several percent. For 1996 FG3, eclipses alter B by approximately 7%, resulting in a lower torque on the secondary. Though small, in the absence of tidal effects this would reduce the contraction of the semimajor axis by about 20 meters over 10,000 years. Our findings suggest that thermal effects can alter temperatures and BYORP calculations sufficiently that they should be included when modeling binaries. The relative importance of each effect is predicted to vary with the properties of the studied system.

astro-ph.EP↗

arXiv2025

PoleStack: Robust Pole Estimation of Irregular Objects from Silhouette Stacking

We present an algorithm to estimate the rotation pole of a principal-axis rotator using silhouette images collected from multiple camera poses. First, a set of images is stacked to form a single silhouette-stack image, where the object's rotation introduces reflective symmetry about the imaged pole direction. We estimate this projected-pole direction by identifying maximum symmetry in the silhouette stack. To handle unknown center-of-mass image location, we apply the Discrete Fourier Transform to produce the silhouette-stack amplitude spectrum, achieving translation invariance and increased robustness to noise. Second, the 3D pole orientation is estimated by combining two or more projected-pole measurements collected from different camera orientations. We demonstrate degree-level pole estimation accuracy using low-resolution imagery, showing robustness to severe surface shadowing and centroid-based image-registration errors. The proposed approach could be suitable for pole estimation during both the approach phase toward a target object and while hovering.

cs.CV↗

arXiv2024

A Control Framework for CUBESAT Rendezvous and Proximity Operations using Electric Propulsion

A control framework is presented to solve the rendezvous and proximity operations (RPO) problem of the EP-Gemini mission. In this mission, a CubeSat chaser is controlled to approach and circumnavigate the other uncooperative CubeSat target. Such a problem is challenging because the chaser operates on a single electric propulsion thruster, for which coupling between attitude control and thrust vector, and charging of the electric propulsion system must be taken into consideration. In addition, the access to relative states in real time is not achievable due to the onboard hardware constraints of the two CubeSats. The developed control framework addresses these limitations by applying four modularized maneuver blocks to correct the chaser's mean orbit elements in sequence. The control framework is based on a relative motion called safety ellipse to ensure a low collision risk. The complete EP-Gemini mission is demonstrated by the implementation of the proposed control framework in a numerical simulation that includes high order perturbations for low Earth orbit. The simulation result shows that a safety ellipse is established after a 41-day RPO maneuver, which consumes 44$\%$ of the total fuel in terms of $ΔV$. The resulting 3-dimensional safety ellipse circumnavigates the target with an approximate dimension of 14 km $\times$ 27 km $\times$ 8 km.

eess.SY↗

arXiv2023

Density Estimation for Entry Guidance Problems using Deep Learning

This work presents a deep-learning approach to estimate atmospheric density profiles for use in planetary entry guidance problems. A long short-term memory (LSTM) neural network is trained to learn the mapping between measurements available onboard an entry vehicle and the density profile through which it is flying. Measurements include the spherical state representation, Cartesian sensed acceleration components, and a surface-pressure measurement. Training data for the network is initially generated by performing a Monte Carlo analysis of an entry mission at Mars using the fully numerical predictor-corrector guidance (FNPEG) algorithm that utilizes an exponential density model, while the truth density profiles are sampled from MarsGRAM. A curriculum learning procedure is developed to refine the LSTM network's predictions for integration within the FNPEG algorithm. The trained LSTM is capable of both predicting the density profile through which the vehicle will fly and reconstructing the density profile through which it has already flown. The performance of the FNPEG algorithm is assessed for three different density estimation techniques: an exponential model, an exponential model augmented with a first-order fading-memory filter, and the LSTM network. Results demonstrate that using the LSTM model results in superior terminal accuracy compared to the other two techniques when considering both noisy and noiseless measurements.

eess.SY↗

arXiv2019

Detection of Rotational Acceleration of Bennu using HST Lightcurve Observations

We observed the near-Earth asteroid (101955) Bennu from the ground in 1999 and 2005, and with the Hubble Space Telescope in 2012, to constrain its rotation rate. The data reveal an acceleration of $2.64 \pm 1.05 \times 10^{-6} \mathrm{deg\ day}^{-2}$, which could be due to a change in the moment of inertia of Bennu or to spin up from the YORP effect or other source of angular momentum. The best solution is within 1 sigma of the period determined by Nolan et al. (2013). The OSIRIS-REx mission will determine the rotation state independently in 2019. Those measurements should show whether the change in rotation rate is a steady increase (due, for example, to the YORP effect) or some other phenomenon. The precise shape and surface properties measured by the OSIRIS-REx science team will allow for a better understanding of variations in rotation rate of small asteroids.

astro-ph.EP↗

arXiv2012

Dynamic Limits on Planar Libration-Orbit Coupling Around an Oblate Primary

This paper explores the dynamic properties of the planar system of an ellipsoidal satellite in an equatorial orbit about an oblate primary. In particular, we investigate the conditions for which the satellite is bound in librational motion or when the satellite will circulate with respect to the primary. We find the existence of stable equilibrium points about which the satellite can librate, and explore both the linearized and non-linear dynamics around these points. Absolute bounds are placed on the phase space of the libration-orbit coupling through the use of zero-velocity curves that exist in the system. These zero-velocity curves are used to derive a sufficient condition for when the satellite's libration is bound to less than 90 degrees. When this condition is not satisfied so that circulation of the satellite is possible, the initial conditions at zero libration angle are determined which lead to circulation of the satellite. Exact analytical conditions for circulation and the maximum libration angle are derived for the case of a small satellite in orbits of any eccentricity.

astro-ph.EP↗