arXiv subjects

Roberto Armellin

Publications and source records attributed to Roberto Armellin.

At least 19 recordsLinked to original sources

arXiv2026

Polynomial-Based Solutions to Targeting Problems for Onboard Applications

This paper solves the targeting problem focusing on accuracy, computational efficiency, and reliability. The trajectory optimization problem is first recast as a polynomial optimization problem (POP) by leveraging differential algebra to compute high-order Taylor expansions of the nonlinear dynamics and constraints. Moment-sum-of-squares (SOS) optimization is then utilized to solve this POP. A convex formulation based on a second-order expansion of the dynamics is also proposed. For impulsive targeting, the moment-SOS and convex approaches are compared against traditional nonlinear programming (NLP) solvers and map inversion techniques. Results indicate that the moment-SOS approach provides solutions as accurate as traditional NLP, but with the critical advantage of guaranteeing convergence to the global optimum under mild assumptions. Furthermore, the method excels at handling large maneuvers and long propagation times, conditions in which standard linear approximations rapidly degrade. To demonstrate its versatility, the methodology is extended to a continuous low-thrust station keeping (SK) scenario in the Earth-Moon Circular Restricted Three-Body Problem. The algorithm's performance is then evaluated in the presence of significant state errors. The ability to directly handle non-convex constraints and recast complex, nonlinear dynamics into formulations with reliable convergence properties makes the moment-SOS approach suitable for autonomous onboard applications.

math.OC↗

arXiv2026

Exoplanetary Tour Design with Solar Sails: TheAntipodes Results in the GTOC13 Problem

Solar sails present an attractive but challenging propulsion method for large-scale, long-duration trajectory design problems. In 2025, the 13th Global Trajectory Optimization Competition (GTOC13) presented a trajectory design problem involving an exoplanetary solar sailing spacecraft in the fictional Altaira system, where the goal is to collect scientific return from flybys of planets, comets, and asteroids. High-scoring solutions combine combinatorial gravity assist tour design with continuous solar sail trajectory optimization. This paper presents the solution approach developed by the team `TheAntipodes' during GTOC13. The approach combines several search and optimization stages: (1) trade studies to identify competitive entry opportunities, (2) large-scale beam search over ballistic gravity assist tours to identify beneficial planetary structures, (3) resonant targeting strategies for Vulcan flyby sequences, and (4) multi-leg solar sail trajectory refinement using sequential convex programming (SCP). A key component of the refinement process is the use of a lossless control-convex solar sail formulation, which allows for large portions of the trajectory, including all gravity assist geometry and flyby timing, to be optimized simultaneously to maximize score. The resulting trajectory placed third, with a score of 337.878 from 133 scoring flybys, and exhibited a structure broadly similar to those of the other high-scoring solutions. This demonstrates the scalability of methods such as SCP for very large trajectory design problems.

astro-ph.IM↗

arXiv2026

Distribution-Agnostic Robust Trajectory Optimization via Chance-Constrained Reinforcement Learning

This paper presents a distribution-agnostic robust trajectory-optimization framework based on chance-constrained reinforcement learning. The uncertainty is represented here through initial conditions and process noise, with the only requirement being that it can be sampled. A deterministic nominal trajectory is first computed offline, and reinforcement learning is then used only to robustify that baseline through a structured affine closed-loop correction law comprising a feedforward control adjustment and time-varying feedback gains. Probabilistic feasibility is enforced empirically through rollout-based upper-tail quantiles, while terminal dispersion is regulated through covariance-feasibility penalties. The framework is assessed on two materially different trajectory design problems. The flagship case study is a three-dimensional multi-impulse Earth-Mars transfer, where the learned policy is benchmarked against a recent robust trajectory-optimization reference under Gaussian uncertainty and then evaluated under bounded uniform uncertainty and under process disturbances not seen during training. The second case study is a stochastic atmospheric pinpoint rocket landing problem, used to assess portability to a short-horizon continuous-thrust setting with drag, mass depletion, and glide-slope constraints. The results show that the proposed framework can remain competitive in upper-tail fuel cost while preserving probabilistic feasibility, and that the same robustification scaffold can be carried across heterogeneous spacecraft trajectory planning problems without redesign of its core stochastic-control structure.

math.OC↗

arXiv2026

Station-Keeping Approach for Extremely Low Lunar Orbits with Solar Sailing

Renewed interest in cislunar space has created opportunities for sustained operations in extremely low-lunar orbits (eLLOs), where altitudes below 50~km enable close surface proximity. However, these orbits are strongly perturbed by the irregular lunar gravity field, leading to rapid eccentricity growth, high station-keeping costs or even surface impact. Recent advances in our understanding of the lunar `translation theorem' have revealed predictable behavior in the eccentricity vector, offering new opportunities for efficient control. This paper introduces a two-stage framework for solar sail station-keeping in eLLOs. First, a mixed-integer second-order cone programming (MISOCP) approach leverages the translational behavior of the eccentricity vector to identify orbit and sail configurations favorable for station-keeping. Second, a lightweight sequential convex programming (SCP) formulation refines these into high-fidelity trajectories, enabled by a recently developed lossless convexification of solar sail dynamics. A case study inspired by the Lunar Reconnaissance Orbiter (LRO) mission demonstrates that a realistic solar sail spacecraft can be maintained within the eLLO regime for at least 1~year without propellant expenditure, suggesting that longer-duration, or even indefinite station-keeping, may be feasible. The approach remains effective at reduced control update frequencies (down to monthly) and exhibits low sensitivity to uncertainties.

astro-ph.IM↗

arXiv2026

Time-Optimal Collision Avoidance Via a Greedy Polynomial Backward Sweep

Spacecraft collision avoidance for low-thrust satellites often requires determining not only how to maneuver, but also how late a maneuver can begin while still ensuring safety. This paper presents a greedy time-optimal (GTO) backward-sweep method to find the latest maneuver initiation time. The method starts from the nominal time of closest approach and iteratively propagates the maneuver backward in time, selecting at each step the thrust direction that locally minimizes the chosen danger metric. Differential algebra is used to efficiently propagate state sensitivities and update the time of closest approach online. The method is tested on a large dataset of conjunctions, using both miss distance and probability of collision as safety metrics. The approach achieves accurate results and only a small loss of optimality relative to an optimal-control benchmark, while retaining runtimes suitable for on-board implementation.

math.OC↗

arXiv2026

Tiny Recursive Models for Solving the J2-Perturbed Lambert Problem

This paper presents a fast, recursive neural solver for the J2-perturbed Lambert problem based on Tiny Recursive Models (TRM), termed the TRM-Perturbed Lambert (TRM-PL) model. TRM is a weight-shared architecture whose effective capacity emerges from iteration depth rather than parameter count: a compact reasoning module is applied repeatedly within a two-level latent hierarchy, refining a candidate departure velocity by simulating the J2 trajectory and correcting it from the resulting tracking error. This unifies initial-guess generation and iterative correction in a single, end-to-end differentiable architecture. The recursive refinement loop is a learned alternative to the homotopy and continuation schemes of classical perturbed-Lambert solvers: rather than following a hand-designed path from the Keplerian to the perturbed solution, the network learns its own sequence of corrections. We evaluate TRM-PL on three test cases of increasing difficulty: single-revolution low-Earth-orbit (LEO) transfers, multi-revolution LEO transfers, and multi-revolution Jovian transfers. Three training paradigms are compared: jointly learning the Lambert solution and the J2 correction; refining the Lambert initial velocity with target-position and J2-corrected velocity supervision; and refining it with target-position supervision alone. Across all cases, the refinement-only approaches are the most reliable. The position-supervised variant reduces the median terminal-position error from 21.7 km to 0.027 km on single-revolution LEO, from 340.9 km to 0.31 km on multi-revolution LEO, all with the same 2.3M-parameter architecture. A single Newton corrector iteration on the TRM-PL output tightens the Jovian median to 0.063 km, yielding compact models accurate enough for embedded deployment.

math.OC↗

arXiv2026

DebrisWatch II: Digging deeper for geosynchronous debris

The geosynchronous (GSO) debris environment is continually evolving. Regular monitoring of the region is consequently of great importance, though the trade-off between coverage and sensitivity makes this challenging for the population of optically faint debris, where collecting area becomes a pivotal factor. Surveys conducted with large-aperture telescopes have provided crucial insights into the nature of this largely uncharacterised population. In this paper, we revisit a survey conducted with the 2.54 m Isaac Newton Telescope (INT), presenting an overhaul of the astrometric calibration and object detection stages of the original analysis pipeline. We apply a blind stacking technique to boost target recovery, unearthing 25 tracklets previously missed by single-frame extraction methods, and pushing the sensitivity limit fainter by 1 magnitude. The same algorithm is applied to a contemporaneous dataset, captured with a 36 cm astrograph, enabling performance benchmarking through the attempted recovery of INT detections from commercial-off-the-shelf observations. We achieve sub-arcsecond astrometric accuracy through a combination of improved star trail centroiding and iterative distortion fitting, allowing short arc initial orbit solutions to be obtained. High-cadence light curves extracted for trailing detections indicate that faint fragments are proportionally more variable than bright derelicts, with many exhibiting photometric signatures of rapid tumbling, often straddling the image noise floor. Lastly, we present preliminary findings from a follow-up multi-national observation campaign, utilising telescopes in Australia, Japan and La Palma. As space traffic management concerns begin to extend beyond GSO altitudes, scientifically-driven surveys of high-altitude orbits have an important role to play in characterising the faint debris environment.

astro-ph.IM↗

arXiv2026

Non-linear stochastic trajectory optimisation

Designing robust space trajectories in nonlinear dynamical environments, such as the Earth-Moon circular restricted three-body problem (CR3BP), poses significant challenges due to sensitivity to initial conditions and non-Gaussian uncertainty propagation. This work introduces a novel solver for discrete-time chance-constrained trajectory optimization under uncertainty, referred to as stochastic optimization with differential algebra (SODA). SODA combines differential algebra (DA) with adaptive Gaussian mixture decomposition to efficiently propagate non-Gaussian uncertainties, and enforces Gaussian multidimensional chance constraints. This work further introduces a risk allocation strategy across mixture components that enables tight and adaptive distribution of safety margins. The framework is validated on four trajectory design problems of increasing dynamical complexity, from heliocentric transfers to challenging Earth-Moon CR3BP scenarios. A linear variant, the linear stochastic optimization with differential algebra (L-SODA) solver, recovers deterministic performance with minimal overhead under small uncertainties, while the nonlinear SODA solver yields improved robustness and tighter constraint satisfaction in strongly nonlinear regimes. Results highlight SODA's ability to generate accurate, robust, and computationally tractable solutions, supporting its potential for future use in uncertainty-aware space mission design.

math.OC↗

arXiv2026

Taylor polynomial-based constrained solver for fuel-optimal low-thrust trajectory optimisation

This paper presents differential algebra-based differential dynamic programming (DADDy), a publicly available C++ framework for constrained, fuel-optimal low-thrust trajectory optimisation. The method uses differential algebra (DA) for two purposes: automatic differentiation and high-order Taylor expansions of the dynamics. These expansions replace many expensive numerical propagations with polynomial evaluations, reducing computational effort while preserving solution quality. The framework combines two complementary modules. First, a differential dynamic programming (DDP)/iterative linear-quadratic regulator (iLQR) stage computes an almost-feasible trajectory from imperfect initial guesses. Second, a polynomial-accelerated Newton stage enforces full feasibility with fast local convergence. Equality and inequality constraints are handled through an augmented Lagrangian formulation, and a pseudo-Huber homotopy is used to improve robustness for fuel-optimal objectives. The solver is evaluated on benchmark transfers in Sun-centred, Earth-Moon, and Earth-centred dynamical environments. Across these cases, the most robust configuration (iLQRDyn) converged systematically and reduced run time by 70% (Sun-centred), 51-88% (Earth-Moon), and 41-55% (Earth-centred) relative to the corresponding baseline. When convergent, the DDP-based variants are faster still. Overall, the results show that DA-based acceleration can substantially improve practical efficiency while retaining robust convergence behaviour on the tested benchmark set.

math.OC↗

arXiv2026

Chance constraints transcription and failure risk estimation for stochastic trajectory optimisation

Stochastic trajectory optimisation under uncertainty requires robust constraint satisfaction through chance constraints. However, existing transcription methods remain limited to scalar constraints or highly specific structures while introducing substantial conservatism. This work presents two general-purpose transcription methods for multi-dimensional Gaussian chance constraints for trajectory optimisation problems under uncertainty. The spectral radius method extends existing methods to arbitrary multi-dimensional constraints with reduced conservatism. The refined first-order method achieves superior tightness with linear complexity. In addition, a d-th order risk estimation methodology provides conservative failure probability estimates with limited conservatism in high dimensions in quadratic complexity. Applied to an optimal control with uncertainties setting, the first-order transcription achieves near-optimal fuel consumption while maintaining the failure risk below the target. The spectral radius method incurs approximately 0.7 kg additional fuel consumption due to excessive conservatism and a 51% increase in computational time due to its cubic complexity. High-dimensional tests show that the proposed risk estimation method provides accurate risk estimates, while previously developed methods exhibit exponential growth in conservatism with respect to constraint dimension.

math.OC↗

arXiv2026

Robust Angles-Only Initial Relative Orbit Determination Using Polynomial Optimization

This paper develops a robust angles-only IROD method based on polynomial optimization for arbitrary nonlinear dynamics. First, the relative motion is approximated by high-order Taylor polynomials within the differential algebra framework, and the resulting cross-product-residual minimization problem is solved through a recursive polynomial optimization procedure. Second, a reduced-order weighting strategy is introduced by projecting the residual onto the two-dimensional tangent subspace of the line of sight, thereby structurally removing the intrinsic singularity of conventional three-dimensional weighting. Third, a zero-solution-avoidance constraint together with an adaptive threshold-selection mechanism is developed to improve robustness against poor initialization, strong measurement noise, and unfavorable observation geometries. Numerical simulations show that the proposed method improves IROD accuracy by about three orders of magnitude relative to the baseline methods, while also reducing the downstream orbit-refinement burden. The reduced-order weighting strategy further improves accuracy by about 43% in the nominal case and remains stable under large-noise conditions, outperforming the conventional three-dimensional weighting by about 81%.

astro-ph.IM↗

arXiv2026

NSF-DOE Vera C. Rubin Observatory Observations of Interstellar Comet 3I/ATLAS (C/2025 N1)

We report on the observation and measurement of astrometry, photometry, morphology, and activityof the interstellar object 3I/ATLAS, also designated C/2025 N1 (ATLAS) with the NSF-DOE Vera C. Rubin Observatory. Comet 3I/ATLAS, the third known interstellar object, was discovered on UT 2025 July 1. Rubin Observatory had coincidentally collected images of the object's region of the sky during routine commissioning. Facilitated by Rubin's high resolution and large aperture, we successfully recovered object detections from Rubin observations spanning UT 2025 June 21 (10 days before discovery, when 3I/ATLAS was 4.5 au from the Sun) through the date of discovery, and we acquired additional images through UT 2025 July 20 as part of commissioning. We measure on-sky locations of 3I/ATLAS in Rubin ugrizy bands, with a typical precision of about 70 mas, and briefly describe the reason this is coarser than our measured static source astrometric precision of about 3 mas in Rubin images. We measure grizy magnitudes of 3I/ATLAS photometry at about 0.01 mag precision, detecting no short-term photometric variability above 0.01 mag. We derive an estimated near-nucleus dust-to-nucleus scattering cross-section ratio of eta >= 13 on UT 2025 July 2 based on Rubin photometry and an upper limit nucleus size computed from Hubble Space Telescope observations. We find Rubin colors of g - r = (0.657 +/- 0.013) mag, r - i = (0.235 +/- 0.018) mag, i - z = (0.147 +/- 0.042) mag, z - y = (0.047 +/- 0.052) mag. These data represent the earliest observations of this object by a large (>=8-meter class) telescope and illustrate the type of measurements (and discoveries) Rubin's Legacy Survey of Space and Time (LSST) will begin to provide after it begins in early 2026.

astro-ph.EP↗

arXiv2026

Sample-Free Safety Assessment of Neural Network Controllers via Taylor Methods

In recent years, artificial neural networks have been increasingly studied as feedback controllers for guidance problems. While effective in complex scenarios, they lack the verification guarantees found in classical guidance policies. Their black-box nature creates significant concerns regarding trustworthiness, limiting their adoption in safety-critical spaceflight applications. This work addresses this gap by developing a method to assess the safety of a trained neural network feedback controller via automatic domain splitting and polynomial bounding. The methodology involves embedding the trained neural network into the system's dynamical equations, rendering the closed-loop system autonomous. The system flow is then approximated by high-order Taylor polynomials, which are subsequently manipulated to construct polynomial maps that project state uncertainties onto an event manifold. Automatic domain splitting ensures the polynomials are accurate over their relevant subdomains, whilst also allowing an extensive state-space to be analysed efficiently. Utilising polynomial bounding techniques, the resulting event values may be rigorously constrained and analysed within individual subdomains, thereby establishing bounds on the range of possible closed-loop outcomes from using such neural network controllers and supporting safety assessment and informed operational decision-making in real-world missions.

eess.SY↗

arXiv2026

Meta-Reinforcement Learning for Robust and Non-greedy Control Barrier Functions in Spacecraft Proximity Operations

Autonomous spacecraft inspection and docking missions require controllers that can guarantee safety under thrust constraints and uncertainty. Input-constrained control barrier functions (ICCBFs) provide a framework for safety certification under bounded actuation; however, conventional ICCBF formulations can be overly conservative and exhibit limited robustness to uncertainty, leading to high fuel consumption and reduced mission feasibility. This paper proposes a framework in which the full hierarchy of class-$\mathcal{K}$ functions defining the ICCBF recursion is parameterized and learned, enabling localized shaping of the safe set and reduced conservatism. A control margin is computed efficiently using differential algebra to enable the learned continuous-time ICCBFs to be implemented on time-sampled dynamical systems typical of spacecraft proximity operations. A meta-reinforcement learning scheme is developed to train a policy that generates ICCBF parameters over a distribution of hidden physical parameters and uncertainties, using both multilayer perceptron (MLP) and recurrent neural network (RNN) architectures. Simulation results on cruise control, spacecraft inspection, and docking scenarios demonstrate that the proposed approach maintains safety while reducing fuel consumption and improving feasibility relative to fixed class-$\mathcal{K}$ ICCBFs, with the RNN showing a particularly strong advantage in the more complex inspection case.

eess.SY↗

arXiv2026

Can LLMs Do Rocket Science? Exploring the Limits of Complex Reasoning with GTOC 12

Large Language Models (LLMs) have demonstrated remarkable proficiency in code generation and general reasoning, yet their capacity for autonomous multi-stage planning in high-dimensional, physically constrained environments remains an open research question. This study investigates the limits of current AI agents by evaluating them against the 12th Global Trajectory Optimization Competition (GTOC 12), a complex astrodynamics challenge requiring the design of a large-scale asteroid mining campaign. We adapt the MLE-Bench framework to the domain of orbital mechanics and deploy an AIDE-based agent architecture to autonomously generate and refine mission solutions. To assess performance beyond binary validity, we employ an "LLM-as-a-Judge" methodology, utilizing a rubric developed by domain experts to evaluate strategic viability across five structural categories. A comparative analysis of models, ranging from GPT-4-Turbo to reasoning-enhanced architectures like Gemini 2.5 Pro, and o3, reveals a significant trend: the average strategic viability score has nearly doubled in the last two years (rising from 9.3 to 17.2 out of 26). However, we identify a critical capability gap between strategy and execution. While advanced models demonstrate sophisticated conceptual understanding, correctly framing objective functions and mission architectures, they consistently fail at implementation due to physical unit inconsistencies, boundary condition errors, and inefficient debugging loops. We conclude that, while current LLMs often demonstrate sufficient knowledge and intelligence to tackle space science tasks, they remain limited by an implementation barrier, functioning as powerful domain facilitators rather than fully autonomous engineers.

cs.AI↗

arXiv2026

Learning Safety-Guaranteed, Non-Greedy Control Barrier Functions Using Reinforcement Learning

Spacecraft rendezvous and proximity operations (RPO) pose safety risks to high-value assets, so formal safety guarantees are critical. Yet conservative safety controllers can reduce mission efficiency. We propose a unified two-stage reinforcement learning (RL) framework that addresses two complementary limitations of Input-Constrained Control Barrier Functions (ICCBFs) for safety-critical, fuel-limited spacecraft control. Given a certified safe set S, ICCBFs guarantee forward invariance of an inner set C* under input bounds, but the resulting per-step quadratic programme (QP) is greedy and fuel-inefficient within C*, and recoverable states outside C* are conservatively discarded. Stage 1 learns state-dependent class-K-infinity parameters that adapt ICCBF/CLF decay rates, embedding long-horizon cost awareness while preserving invariance in C*. Stage 2 learns a residual barrier h_RL(x) that certifies recoverability for a subset of S minus C*. At run time, the controller selects the appropriate barrier formulation (Stage 1 or Stage 2) and solves a lightweight ZOH QP. Both stages are trained with PPO using rewards that penalise constraint violations, control effort, and task metrics. We evaluate three benchmarks: cruise control, spacecraft rendezvous with a rotating target, and inspection that maximises observability subject to keep-in and keep-out zone constraints. Across test cases, the method reduces median fuel relative to ICCBF baselines by 12 to 25 percent and increases the fraction of trajectories that remain in S by 7 to 8 percent, while retaining real-time QP complexity.

math.OC↗

arXiv2026

Optimization of Transfers linking Ballistic Captures to Earth-Moon Periodic Orbit Families

The design of transfers to periodic orbits in the Earth-Moon system has regained prominence with NASA's Artemis and CNSA's Chang'e programs. This work addresses the problem of linking ballistic capture trajectories - exploiting multi-body dynamics for temporary lunar orbit insertion - with bounded periodic motion described in the circular restricted three-body problem (CR3BP). A unified framework is developed for optimizing bi-impulsive transfers to families of periodic orbits via a high-order polynomial expansion of the CR3BP dynamics. That same expansion underlies a continuous parameterization of periodic orbit families, enabling rapid targeting and analytic sensitivity. Transfers to planar periodic orbit families - such as Lyapunov L1/L2 and distant retrograde orbits (DROs) - are addressed first, followed by extension to spatial families - such as butterfly and halo L1/L2 orbits - with an emphasis towards near-rectilinear halo orbits (NRHOs). Numerical results demonstrate low-Δv solutions and validate the method's adaptability for designing lunar missions. The optimized trajectories can inform an established low-energy transfer database, enriching it with detailed cost profiles that reflect both transfer feasibility and underlying dynamical relationships to specific periodic orbit families. Finally, the proposed transfers provide reliable estimates for rapid refinement, making them readily adaptable for further optimization across mission-specific needs.

astro-ph.EP↗

arXiv2025

Identifying Fixed Points in the Three-Body Problem Using a High-Order Transfer Map

Periodic orbits (POs) play a central role in the circular restricted three-body problem (CRTBP). This paper introduces a method to search for POs by identifying single- and multiple-revolution fixed points in chosen Poincare maps that describe the CRTBP dynamics, with a theoretical capability to detect all fixed points across arbitrary revolution counts exhaustively.First, high-order transfer maps (HOTMs), represented as polynomials, are constructed within the differential algebra (DA) framework for both planar and spatial CRTBP to map states between successive Poincare section crossings, with the Jacobi constant used to reduce the number of independent variables. Next, an automatic domain splitting (ADS) strategy is employed to generate subdomains, preserving HOTM accuracy, with an integrated feasibility estimation to reduce ADS's computation burden.Then, a two-stage HOTM-based polynomial optimization framework is introduced, first identifying combinable subdomain sequences and then refining the fixed point solutions. Finally, the method is applied to the Earth-Moon CRTBP, identifying POs up to nine revolutions in the planar case and four in the spatial case. Known families such as distant retrograde orbits (DROs) and Lyapunov orbits are recovered, along with a previously undocumented family that exhibits a hybrid character between DROs and Lyapunov orbits.

astro-ph.EP↗