arXiv subjects

Ethan R. Burnett

Publications and source records attributed to Ethan R. Burnett.

7 recordsLinked to original sources

arXiv2026

Analytical Confidence Boundaries for Non-Gaussian Uncertainty in Perturbed Spacecraft Dynamics

This work investigates nonlinear uncertainty propagation in perturbed astrodynamics, focusing on the rapid characterization of non-Gaussian distributions and the construction of three-dimensional "banana-shaped" confidence boundaries. To bridge the gap between computationally intensive high-fidelity methods and inaccurate linear approximations, this paper introduces a fully analytical, sample-free framework for higher-order moments extraction. Leveraging Differential Algebra to bypass repeated numerical integration, statistical moments are extracted analytically via Isserlis' theorem and a monomial-to-Hermite basis transformation. A pair-product projection strategy is exploited to overcome the severe computational bottleneck of full fourth-order tensor contractions and compute only relevant terms via efficient polynomial algebra. The extracted skewness and kurtosis components directly parameterize non-elliptical confidence geometries that capture spatial bending and out-of-plane coupling of typical non-Gaussian distributions in astrodynamics. The approach is validated in high-fidelity environments including a cislunar Near-Rectilinear Halo Orbit and close-proximity trajectories around Apophis during Earth's flyby, where the analytical approach achieves geometric accuracy comparable to expensive Monte Carlo simulations while reducing computational runtime by orders of magnitude.

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arXiv2026

An Efficient Non-Gaussian Chance Constraint Method for Stochastic Nonlinear Problems in Spaceflight

Standard chance-constrained spacecraft guidance typically relies on the assumption that uncertainties in vehicle states obey Gaussian statistics. In frontier applications such as the cislunar environment or deep space flybys, the dynamics can be particularly nonlinear, and time between measurements can be long, leading to the need to make decisions whose outcomes produce non-Gaussian distributions. This paper demonstrates a non-Gaussian confidence boundary technique for stochastic guidance in such applications. Our approach is to consider the true confidence contour as a perturbation of the one predicted from covariance, then to derive perturbed boundary geometry from computed higher-order statistical moments. Applying this technique to so-called "banana-shaped distributions", found in orbital mechanics problems, enables a simple parameterization of the confidence contour using the skew and kurtosis tensors. This parameterization is then applied to a stochastic and nonlinear impulsive spacecraft maneuver targeting problem, with special treatment of a relevant non-convex constraint.

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arXiv2026

Efficient Nonlinear Uncertainty Quantification for Spaceflight Leveraging Nonlinear Expansions

This paper provides a comparative study of modern uncertainty quantification (UQ) methods. To greatly enhance real-time performance, both differential algebra (DA) and a directional differential algebra (DDA) approach are employed. This can enable fast UQ in the case of non-Gaussian statistics. Higher-order moments, namely skew and kurtosis, can be computed quickly by several means. This motivates their implementation in an analytic approximation of the confidence bounds for the so-called "banana-shaped" non-Gaussian distributions encountered often in nonlinear astrodynamics problems. This method improves greatly on a linear covariance approach, with only 5x its runtime in numerical tests, even before DA methods are employed. Test problems in this work include a restricted three-body cislunar example and an Earth-return aerocapture example.

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arXiv2026

Convex Trajectory Optimization via Monomial Coordinates Transcription for Cislunar Rendezvous

This paper proposes a nonlinear guidance algorithm for fuel-optimal impulsive trajectories for rendezvous operations close to a reference orbit. The approach involves overparameterized monomial coordinates and a high-order approximation of the dynamic flow precomputed using differential algebra, which eliminates the need for real-time integration. To address non-convexity in the monomial coordinate formulation of the guidance problem, sequential convex programming is applied. Using the methodology presented in this paper, repeatedly evaluating the nonlinear dynamics is not necessary, as in shooting or collocation methods. Instead, only the monomial equations require updating between iterations, drastically reducing computational burden. The proposed algorithm is tested in the circular restricted three-body problem framework with the target spacecraft on a near-rectilinear halo orbit. The results demonstrate stability, efficiency, and low computational demand while achieving minimal terminal guidance errors. Compared to linear methods, this nonlinear convex approach exhibits superior performance in open-loop propagation of impulsive maneuvers in cislunar space, particularly in terms of accuracy. These advantages make the algorithm an attractive candidate for autonomous onboard guidance for rendezvous operations in the cislunar domain.

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arXiv2025

Exploring tidal dissipation in rubble pile binary secondaries using a discrete element model

In this work, models of rubble pile binary secondaries are simulated in different spin states in a system similar in size and scale to Didymos-Dimorphos. The numerical modeling is performed in the N-body Chrono-based software GRAINS, which simulates gravity, contact, and friction forces acting on non-spherical mass elements. Tidal dissipation successfully emerges in the simulations as an aggregate of the effects of inter-element contact and friction across thousands of simulated mass elements. We devise computational techniques for simulating and studying such systems, establishing rigorous numerical procedures for computing tidal quantities of interest. We compute $Q/k_{2} \sim 71.6^{+99.6}_{-43.6}$ for the secondary, smaller than previously predicted ranges $10^{2} < Q/k_{2} < 10^{6}$, and thus a rather dissipative result. From our simulations, we observe non-classical variation of the tidal lag angle with the topographic longitude, and dependence of $Q/k_{2}$ on the rotation rate. Further study is required to see if the enhanced dissipativity holds with other geometries and regolith properties.

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arXiv2024

Rapid nonlinear convex guidance using a monomial method

This paper addresses the challenge of accommodating nonlinear dynamics and constraints in rapid trajectory optimization, envisioned for use in the context of onboard guidance. We present a novel framework that uniquely employs overparameterized monomial coordinates and pre-computed fundamental solution expansions to facilitate rapid optimization while minimizing real-time computational requirements. The fundamental solution expansions are pre-computed using differential algebra. Unlike traditional approaches that repeatedly evaluate the nonlinear dynamics and constraints as part of complex shooting or collocation-based schemes, this method replaces the nonlinearity inherent to dynamics and constraint functions entirely with a computationally simpler manifold constraint. With this approach, trajectory optimization is posed efficiently as a path planning problem on the manifold. This problem is entirely convex except for the manifold constraint, readily lending itself to solution via sequential convex programming. We demonstrate the effectiveness of our approach in computing fast and accurate delta-V optimal solutions for long-range spacecraft rendezvous, including problems with nonlinear state constraints.

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arXiv2024

Chance-Constrained, Drift-Safe Guidance for Spacecraft Rendezvous

A robust drift-safe rendezvous trajectory optimization tool is developed in this work, with applications to orbital rendezvous and proximity operations. The method is based on direct collocation and utilizes a sequential convex programming framework, and is extended from previous work to include passive safety constraints. The tool is then paired with a dispersion analysis framework to allow trajectories to be optimized subject to plant, navigation, and actuator uncertainties. The timing, direction, and magnitude of orbital maneuvers are optimized subject to the expected propellant usage, for a given navigation system performance. Representative trajectories are presented for the LEO flight regime, but the approach can also be applied to GEO and NRHO with minimal modification.

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