Showing 1–11 of 11 results for author: McMahon, J W

Improved Directional State Transition Tensors for Accurate Aerocapture Performance Analysis

Authors: Grace E. Calkins, Jay W. McMahon, David C. Woffinden

Abstract: Aerocapture is a unique challenge for semi-analytical propagation because its nonconservative dynamics lead to force magnitudes that vary substantially across 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 previous… ▽ More Aerocapture is a unique challenge for semi-analytical propagation because its nonconservative dynamics lead to force magnitudes that vary substantially across 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, obtaining the higher-order STTs requires integrating exponentially more equations. 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 apoapsis and energy prediction. 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. △ Less

Submitted 13 December, 2025; originally announced December 2025.

Comments: Submitted to AIAA Journal of Guidance, Control, and Dynamics for publication

Optimal Rank-1 Directional State Transition Tensors

Authors: Grace E. Calkins, Jay W. McMahon, Jackson Kulik

Abstract: 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 st… ▽ More 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. △ Less

Submitted 9 November, 2025; originally announced November 2025.

Comments: Submitted to AIAA Journal of Guidance, Control, and Dynamics

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

Authors: Kya C. Sorli, Paul O. Hayne, Rachel H. Cueva, Chloe J. Long, Jay W. McMahon, Daniel J. Scheeres

Abstract: 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… ▽ More 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. △ Less

Submitted 25 August, 2025; originally announced August 2025.

Comments: Accepted and published by Icarus, available at https://doi.org/10.1016/j.icarus.2025.116527

Journal ref: Icarus, Volume 434 (2025) 116527

Risk-Aware Aerocapture Guidance Through a Probabilistic Indicator Function

Authors: Grace E. Calkins, Jay W. McMahon, Alireza Doostan, David C. Woffinden

Abstract: 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 performance. A risk-aware aerocapture guidance algorithm is proposed that uses a generative-modeling-based probabilistic indicator function to estimate escape, impact, or captur… ▽ More 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 performance. A risk-aware aerocapture guidance algorithm is proposed that uses a generative-modeling-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, 69% to 100% of recoverable cases are saved in near-escape and near-impact scenarios. In addition, the probabilistic indicator is compared to a first-order fading memory filter for density estimation, showing improvements in apoapsis error even when a fading filter is included. The probabilistic indicator function can also accurately predict failure probability for dispersions outside its training data, showing generalizability. The proposed risk-aware aerocapture guidance algorithm improves capture performance and robustness to entry interface state dispersions, especially for missions with high navigation uncertainty. △ Less

Submitted 7 July, 2025; originally announced July 2025.

Comments: Currently under revision for the AIAA Journal of Guidance Control and Dynamics

PoleStack: Robust Pole Estimation of Irregular Objects from Silhouette Stacking

Authors: Jacopo Villa, Jay W. McMahon, Issa A. D. Nesnas

Abstract: 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 silhouet… ▽ More 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. △ Less

Submitted 5 February, 2025; originally announced February 2025.

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

Authors: Bo-Chuan Lin, Chun-Wei Kong, Simone Semeraro, Jay W. McMahon

Abstract: 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 vect… ▽ More 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. △ Less

Submitted 1 December, 2024; originally announced December 2024.

Density Estimation for Entry Guidance Problems using Deep Learning

Authors: Jens A. Rataczak, Davide Amato, Jay W. McMahon

Abstract: 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 accelera… ▽ More 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. △ Less

Submitted 30 October, 2023; originally announced October 2023.

Comments: Currently under revision for the AIAA Journal of Guidance Control and Dynamics

Internal rubble properties of asteroid (101955) Bennu

Authors: P. Tricarico, D. J. Scheeres, A. S. French, J. W. McMahon, D. N. Brack, J. M. Leonard, P. Antreasian, S. R. Chesley, D. Farnocchia, Y. Takahashi, E. M. Mazarico, D. Rowlands, D. Highsmith, K. Getzandanner, M. Moreau, C. L. Johnson, L. Philpott, E. B. Bierhaus, K. J. Walsh, O. S. Barnouin, E. E. Palmer, J. R. Weirich, R. W. Gaskell, M. G. Daly, J. A. Seabrook , et al. (2 additional authors not shown)

Abstract: Exploration of asteroid (101955) Bennu by the OSIRIS-REx mission has provided an in-depth look at this rubble-pile near-Earth asteroid. In particular, the measured gravity field and the detailed shape model of Bennu indicate significant heterogeneities in its interior structure, compatible with a lower density at its center. Here we combine gravity inversion methods with a statistical rubble-pile… ▽ More Exploration of asteroid (101955) Bennu by the OSIRIS-REx mission has provided an in-depth look at this rubble-pile near-Earth asteroid. In particular, the measured gravity field and the detailed shape model of Bennu indicate significant heterogeneities in its interior structure, compatible with a lower density at its center. Here we combine gravity inversion methods with a statistical rubble-pile model to determine the density and size-frequency distribution (SFD) index of the rubble that constitutes Bennu. The best-fitting models indicate that the SFD of the interior is consistent with that observed on the surface, with a cumulative SFD index of approximately $-2.9$. The rubble bulk density is approximately $1.35$ g/cm$^3$, corresponding to a $12$% macro-porosity. We find the largest rubble particle to be approximately $145$ m, whereas the largest void is approximately $10$ m. △ Less

Submitted 23 August, 2021; originally announced August 2021.

Comments: 14 pages, 5 figures, accepted to Icarus

Detection of Rotational Acceleration of Bennu using HST Lightcurve Observations

Authors: Michael C. Nolan, Ellen S. Howell, Daniel J. Scheeres, Jay W. McMahon, Oleksiy Golubov, Carl W. Hergenrother, Joshua P. Emery, Keith S. Noll, Steven R. Chesley, Dante S. Lauretta

Abstract: 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 so… ▽ More 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. △ Less

Submitted 28 February, 2019; originally announced March 2019.

OSIRIS-REx: Sample Return from Asteroid (101955) Bennu

Authors: D. S. Lauretta, S. S. Balram-Knutson, E. Beshore, W. V. Boynton, C. Drouet dAubigny, D. N. DellaGiustina, H. L. Enos, D. R. Gholish, C. W. Hergenrother, E. S. Howell, C. A. Johnson, E. T. Morton, M. C. Nolan, B. Rizk, H. L. Roper, A. E. Bartels, B. J. Bos, J. P. Dworkin, D. E. Highsmith, D. A. Lorenz, L. F. Lim, R. Mink, M. C. Moreau, J. A. Nuth, D. C. Reuter , et al. (23 additional authors not shown)

Abstract: In May of 2011, NASA selected the Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer (OSIRIS-REx) asteroid sample return mission as the third mission in the New Frontiers program. The other two New Frontiers missions are New Horizons, which explored Pluto during a flyby in July 2015 and is on its way for a flyby of Kuiper Belt object 2014 MU69 on Jan. 1, 2019… ▽ More In May of 2011, NASA selected the Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer (OSIRIS-REx) asteroid sample return mission as the third mission in the New Frontiers program. The other two New Frontiers missions are New Horizons, which explored Pluto during a flyby in July 2015 and is on its way for a flyby of Kuiper Belt object 2014 MU69 on Jan. 1, 2019, and Juno, an orbiting mission that is studying the origin, evolution, and internal structure of Jupiter. The spacecraft departed for near-Earth asteroid (101955) Bennu aboard an United Launch Alliance Atlas V 411 evolved expendable launch vehicle at 7:05 p.m. EDT on September 8, 2016, on a seven-year journey to return samples from Bennu. The spacecraft is on an outbound-cruise trajectory that will result in a rendezvous with Bennu in August 2018. The science instruments on the spacecraft will survey Bennu to measure its physical, geological, and chemical properties, and the team will use these data to select a site on the surface to collect at least 60 g of asteroid regolith. The team will also analyze the remote-sensing data to perform a detailed study of the sample site for context, assess Bennus resource potential, refine estimates of its impact probability with Earth, and provide ground-truth data for the extensive astronomical data set collected on this asteroid. The spacecraft will leave Bennu in 2021 and return the sample to the Utah Test and Training Range (UTTR) on September 24, 2023. △ Less

Submitted 22 February, 2017; originally announced February 2017.

Comments: 89 pages, 39 figures, submitted to Space Science Reviews - OSIRIS-REx special issue

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

Authors: Jay W. McMahon, Daniel J. Scheeres

Abstract: 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… ▽ More 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. △ Less

Submitted 30 May, 2012; originally announced May 2012.

Comments: Submitted to Celestial Mechanics and Dynamical Astronomy