arXiv subjects

Roberto Armellin

Publications and source records attributed to Roberto Armellin.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2025

A polynomial-based Monte Carlo approach for estimating long-term collision probabilities

This paper introduces a versatile approach for computing the risk of collision specifically tailored for scenarios featuring low relative encounter velocities, but with potential applicability across a wide range of situations. The technique employs Differential Algebra (DA) to express the non-linear dynamical flow of the initial distribution in the primary-secondary objects relative motion through high-order Taylor polynomials. The entire initial uncertainty set is subdivided into subsets through Automatic Domain Splitting (ADS) techniques to control the accuracy of the Taylor expansions. The methodology samples the initial conditions of the relative state and evaluates the polynomial expansions for each sample while retaining their temporal dependency. The classical numerical integration of the initial statistics over the set of conditions for which a collision occurs is thus reduced to an evaluation of mono-dimensional time polynomials. Specifically, samples reaching a relative distance below a critical value are identified along with the time at which this occurs. The approach is tested against a Monte Carlo (MC) simulation for various literature test cases, yielding accurate results and a consistent gain in computational time.

physics.space-ph↗

arXiv2025

Maneuver Detection via a Confidence Dominance Maneuver Indicator

Accurate and efficient maneuver detection is critical for ensuring the safety and predictability of spacecraft trajectories. This paper presents a novel maneuver detection approach based on comparing the confidence levels associated with the orbital state estimation and the observation likelihood. First, a confidence-dominance maneuver indicator (CDMI) is proposed by setting a confidence level for the state estimation and computing the maximum likelihood of the observation and its confidence level. The CDMI then flag a maneuver when the observation's confidence level exceeds that of the state estimation, indicating that the observation is unlikely under the no-maneuver hypothesis while maintaining consistency with the prior state estimation confidence. To efficiently compute the maximum likelihood of the observation and obtain the CDMI, a recursive polynomial optimization method is developed, taking advantage of convex optimization and polynomial approximation. In addition, an integrated CDMI approach is developed to eliminate the need to manually select the state confidence level. The integrated CDMI approach maintains high detection accuracy while simultaneously providing an indication of maneuver likelihood, thereby enhancing robustness and practical applicability. The performance of the proposed CDMI-based maneuver detection approaches is evaluated against an optimal control distance metric and two mixture-based approaches. The simulation results demonstrate that the proposed integrated CDMI approach can achieve up to 99.33\% detection accuracy, at least 10% higher than the competing methods, while substantially reducing computational costs.

eess.SY↗

arXiv2025

Extensive Database of Spatial Ballistic Captures with Application to Lunar Trailblazer

For low-energy missions to the Moon and beyond, Ballistic Capture has proven to be a valuable technique for enabling orbital insertion while alleviating propulsion system requirements. This approach offers two key advantages. First, it extends the insertion window, allowing multiple maneuver opportunities to mitigate potential failures at the nominal insertion point. Second, it enables the required insertion maneuver to be distributed across multiple revolutions, reducing propulsion system constraints in terms of single-burn thrust. Prior research introduced the concept of Energy Transition Domain to support the creation of a comprehensive database of Ballistic Captures in the planar Circular Restricted Three-Body Problem. However, to apply these trajectories to a real mission scenario, a three-dimensional, spatial analysis and transition to an ephemeris model are necessary. This paper first extends the Energy Transition Domain framework to the spatial case, constructing an extensive database of spatial Ballistic Captures. Then, using Lunar Trailblazer as a case study, a subset of the trajectories is filtered using a mission-specific distance metric, and transitioned into an ephemeris model. Finally, interesting features of this subset are analyzed, and sample high-fidelity trajectories are selected as potential backup options for Lunar Trailblazer.

math.NA↗

arXiv2025

Using the Translation Theorem for the Automated Stationkeeping of Extremely-Low Lunar Missions

Extremely-Low Lunar Orbits (eLLOs) (altitudes $\leq 50$ km) exhibit severe perturbations due to the highly non-spherical lunar gravitational field, presenting unique challenges to orbit maintenance. These altitudes are too low for the existence of stable `frozen' orbits, and naive stationkeeping methods, such as circularization, perform poorly. However, mission designers have noticed a particular characteristic of low lunar orbits, which they have found useful for stationkeeping and dubbed the "translation theorem", wherein the eccentricity vector follows a predictable monthly pattern that is independent of its starting value. We demonstrate this feature results from the low orbital eccentricity combined with the dominant effect of a particular subset of sectoral and tesseral harmonics. Subsequently, automated stationkeeping strategies for eLLOs are presented, utilizing this theorem for eccentricity vector control. Several constraints within the eccentricity vector plane are explored, including circular, annular, and elevation-model derived regions, each forming distinct stationkeeping strategies for varying orbital configurations. Subsequently, the optimal control profiles for these maneuvers within the eccentricity plane are obtained using Sequential Convex Programming (SCP). The proposed strategies offer computational simplicity and clear advantages when compared to traditional methods and are comparable to full trajectory optimization.

astro-ph.IM↗

arXiv2025

CAMmary: A Review of Spacecraft Collision Avoidance Manoeuvre Design Methods

Ensuring safety for spacecraft operations has become a paramount concern due to the proliferation of space debris and the saturation of valuable orbital regimes. In this regard, the Collision Avoidance Manoeuvre (CAM) has emerged as a critical requirement for spacecraft operators, aiming to efficiently navigate through potentially hazardous encounters. Currently, when a conjunction is predicted, operators dedicate a considerable amount of time and resources to designing a CAM. Given the increased frequency of conjunctions, autonomous computation of fuel-efficient CAMs is crucial to reduce costs and improve the performance of future operations. To facilitate the transition to an autonomous CAM design, it is useful to provide an overview of its state-of-the-art. In this survey article, a collection of the most relevant research contributions in the field is presented. We review and categorize existing CAM techniques based on their underlying principles, such as (i) analytic, semi-analytic, or numerical solutions; (ii) impulsive or continuous thrust; (iii) deterministic or stochastic approaches, (iv) free or fixed manoeuvring time; (v) free or fixed thrust direction. Finally, to determine the validity of the algorithms potentially implementable for autonomous use, we perform a numerical comparison on a large set of conjunctions. With this analysis, the algorithms are evaluated in terms of computational efficiency, accuracy, and optimality of the computed policy. Through this comprehensive survey, we aim to provide insights into the state-of-the-art CAM methodologies, identify gaps in current research, and outline potential directions for future developments in ensuring the safety and sustainability of spacecraft operations in increasingly congested orbital environments.

math.OC↗

arXiv2025

Using Co-Located Range and Doppler Radars for Initial Orbit Determination

With debris larger than 1 cm in size estimated to be over one million, precise cataloging efforts are essential to ensure space operations' safety. Compounding this challenge is the oversubscribed problem, where the sheer volume of space objects surpasses ground-based observatories' observational capacity. This results in sparse, brief observations and extended intervals before image acquisition. LeoLabs' network of phased-array radars addresses this need by reliably tracking 10 cm objects and larger in low Earth orbit with 10 independent radars across six sites. While LeoLabs tracklets are extremely short, they hold much more information than typical radar observations. Furthermore, two tracklets are generally available, separated by a couple of minutes. Thus, this paper develops a tailored approach to initialize state and uncertainty from a single or pair of tracklets. Through differential algebra, the initial orbit determination provides the state space compatible with the available measurements, namely an orbit set. This practice, widely used in previous research, allows for efficient data association of different tracklets, thus enabling the addition of accurate tracks to the catalog following their independent initialization. The algorithm's efficacy is tested using real measurements, evaluating the IOD solution's accuracy and ability to predict the next passage from a single or a pair of tracklets.

math.NA↗

arXiv2025

Single-Impulse Reachable Set in Arbitrary Dynamics Using Polynomials

This paper presents a method to determine the reachable set (RS) of spacecraft after a single velocity impulse with an arbitrary direction, which is appropriate for the RS in both the state and observation spaces under arbitrary dynamics, extending the applications of current RS methods from two-body to arbitrary dynamics. First, the single-impulse RS model is generalized as a family of two-variable parameterized polynomials in the differential algebra scheme. Then, using the envelope theory, the boundary of RS is identified by solving the envelope equation. A framework is proposed to reduce the complexity of solving the envelope equation by converting it to the problem of searching the root of a one-variable polynomial. Moreover, a high-order local polynomial approximation for the RS envelope is derived to improve computational efficiency. The method successfully determines the RSs of two near-rectilinear halo orbits in the cislunar space. Simulation results show that the RSs in both state and observation spaces can be accurately approximated under the three-body dynamics, with relative errors of less than 0.0658%. In addition, using the local polynomial approximation, the computational time for solving the envelope equation is reduced by more than 84%.

astro-ph.IM↗

arXiv2025

Efficient Multifidelity Uncertainty Propagation in the Presence of Process Noise

A multifidelity method for the nonlinear propagation of uncertainties in the presence of stochastic accelerations is presented. The proposed algorithm treats the uncertainty propagation (UP) problem by separating the propagation of the initial uncertainty from that of the process noise. The initial uncertainty is propagated using an adaptive Gaussian mixture model (GMM) method which exploits a low-fidelity dynamical model to minimize the computational costs. The effects of process noise are instead computed using the PoLynomial Algebra Stochastic Moments Analysis (PLASMA) technique, which considers a high-fidelity model of the stochastic dynamics. The main focus of the paper is on the latter and on the key idea to approximate the probability density function (pdf) of the solution by a polynomial representation of its moments, which are efficiently computed using differential algebra (DA) techniques. The two estimates are finally combined to restore the accuracy of the low-fidelity surrogate and account for both sources of uncertainty. The proposed approach is applied to the problem of nonlinear orbit UP and its performance compared to that of Monte Carlo (MC) simulations.

math.NA↗

arXiv2025

Multi-Target Spacecraft Mission Design using Convex Optimization and Binary Integer Programming

The optimal design of multi-target rendezvous and flyby missions is challenging due to the combination of traditional spacecraft trajectory optimization and high-dimensional combinatorial problems. This often requires large-scale global search techniques or simplified approximations that rely on manual tuning to be performant. While global search techniques are typically computationally expensive, limiting their use in time- or cost-constrained scenarios, this work proposes a computationally efficient nested-loop approach. The problem is split into separate combinatorial and optimal control subproblems: the combinatorial problem is solved using Binary Integer Programming (BIP) with a fixed rendezvous time schedule, while the optimal control problem is handled with adaptive-mesh Sequential Convex Programming (SCP), which also optimizes the time schedule. By iterating these processes in a nested-loop structure, the approach can efficiently find high-quality solutions. When, applied to the Global Trajectory Optimization Competition 12 (GTOC 12) problem, this method results in several new best-known solutions.

astro-ph.IM↗

arXiv2025

Learning-Based Stable Optimal Guidance for Spacecraft Close-Proximity Operations

Machine learning techniques have demonstrated their effectiveness in achieving autonomy and optimality for nonlinear and high-dimensional dynamical systems. However, traditional black-box machine learning methods often lack formal stability guarantees, which are critical for safety-sensitive aerospace applications. This paper proposes a comprehensive framework that combines control Lyapunov functions with supervised learning to provide certifiably stable, time- and fuel-optimal guidance for rendezvous maneuvers governed by Clohessy-Wiltshire dynamics. The framework is easily extensible to nonlinear control-affine systems. A novel neural candidate Lyapunov function is developed to ensure positive definiteness. Subsequently, a control policy is defined, in which the thrust direction vector minimizes the Lyapunov function's time derivative, and the thrust throttle is determined using minimal required throttle. This approach ensures that all loss terms related to the control Lyapunov function are either naturally satisfied or replaced by the derived control policy. To jointly supervise the Lyapunov function and the control policy, a simple loss function is introduced, leveraging optimal state-control pairs obtained by a polynomial maps based method. Consequently, the trained neural network not only certifies the Lyapunov function but also generates a near-optimal guidance policy, even for the bang-bang fuel-optimal problem. Extensive numerical simulations are presented to validate the proposed method.

eess.SY↗

arXiv2024

Time-Varying Directional State Transition Tensor for Orbit Uncertainty Propagation

The directional state transition tensor (DSTT) reduces the complexity of state transition tensor (STT) by aligning the STT terms in sensitive directions only, which provides comparable accuracy in orbital uncertainty propagation. The DSTT assumes the sensitive directions to be constant during the integration and only works at a predefined epoch. This paper proposes a time-varying STT (TDSTT) to improve the DSTT. The proposed TDSTT computes the sensitive directions with time; thereby, it can perform uncertainty propagation analysis at any point instead of only a predefined epoch as the DSTT does. First, the derivatives of the sensitive directions are derived. Then, the differential equations for the high-order TDSTTs are derived and simplified using the orthogonality of sensitive directions. Next, complexity analysis is implemented to show the advantages of the proposed TDSTT over the STT. Finally, the TDSTT is applied to solve orbital uncertainty propagation problems in highly nonlinear three-body systems. Numerical results show that the proposed TDSTT can yield nearly the same level of accuracy as the STT and DSTT. It is approximately 94% faster than the STT and has hundreds of improvements in speed over the DSTT when one wants to investigate the evolutions of orbital uncertainties.

astro-ph.IM↗

arXiv2024

GTOC 12: Results from TheAntipodes

We present the solution approach developed by the team `TheAntipodes' during the 12th edition of the Global Trajectory Optimization Competition (GTOC 12). An overview of the approach is as follows: (1) generate asteroid subsets, (2) chain building with beam search, (3) convex low-thrust trajectory optimization, (4) manual refinement of rendezvous times, and (5) optimal solution set selection. The generation of asteroid subsets involves a heuristic process to find sets of asteroids that are likely to permit high-scoring asteroid chains. Asteroid sequences `chains' are built within each subset through a beam search based on Lambert transfers. Low-thrust trajectory optimization involves the use of sequential convex programming (SCP), where a specialized formulation finds the mass-optimal control for each ship's trajectory within seconds. Once a feasible trajectory has been found, the rendezvous times are manually refined with the aid of the control profile from the optimal solution. Each ship's individual solution is then placed into a pool where the feasible set that maximizes the final score is extracted using a genetic algorithm. Our final submitted solution placed fifth with a score of $15,489$.

astro-ph.IM↗

arXiv2024

Trajectory Design and Guidance for Far-range Proximity Operations of Active Debris Removal Missions with Angles-only Navigation and Safety Considerations

Observability of the target, safety, and robustness are often recognized as critical factors in ensuring successful far-range proximity operations. The application of angles-only (AO) navigation for proximity operations is often met with hesitancy due to its inherent limitations in determining range, leading to issues in target observability and consequently, mission safety. However, this form of navigation remains highly appealing due to its low cost. This work employs Particle Swarm Optimization (PSO) and Reinforcement Learning (RL) for the design and guidance of such far-range trajectories, assuring observability, safety and robustness under angles-only navigation. Firstly, PSO is used to design a nominal trajectory that is observable, robust and safe. Subsequently, Proximal Policy Optimization (PPO), a cutting-edge RL algorithm, is utilized to develop a guidance controller capable of maintaining observability while steering the spacecraft from an initial perturbed state to a target state. The fidelity of the guidance controller is then tested in a Monte-Carlo (MC) manner by varying the initial relative spacecraft state. The observability of the nominal trajectory and the perturbed trajectories with guidance are validated using an Extended Kalman Filter (EKF). The perturbed trajectories are also shown to adhere to the safety requirements satisfied by the nominal trajectory. Results demonstrate that the trained controller successfully determines maneuvers that maintain observability and safety and reaches the target end state.

math.OC↗

arXiv2024

Collision Avoidance Maneuvers Optimization in the Presence of Multiple Encounters

The optimization of fuel-optimal low-thrust collision avoidance maneuvers (CAMs) in scenarios involving multiple encounters between spacecraft is addressed. The optimization's objective is the minimization of the total fuel consumption while respecting constraints on the total probability of collision. The solution methodology combines sequential convex programming, second-order cone programming, and differential algebra to approximate the non-convex optimal control problem progressively. A Gaussian mixture model method is used to propagate the initial covariance matrix of the secondary spacecraft, allowing us to split it into multiple mixands that can be treated as different objects. This leads to an accurate propagation of the uncertainties. No theoretical guarantee is given for the convergence of the method to the global optimum of the original optimal control problem. Nonetheless, good performance is demonstrated through case studies involving multiple short- and long-term encounters, showcasing the generation of fuel-efficient CAMs while respecting operational constraints.

math.OC↗

arXiv2024

Recursive Polynomial Method for Fast Collision Avoidance Maneuver Design

A simple and reliable algorithm for collision avoidance maneuvers (CAMs), capable of computing impulsive, multi-impulsive, and low-thrust maneuvers, is proposed. The probability of collision (PoC) is approximated by a polynomial of arbitrary order as a function of the control, transforming the CAM designinto a polynomial program. The solution procedure is initiated by computing the CAM via a first-order greedy optimization approach, wherein the control action is applied in the direction of the gradient of PoC to maximize its change. Successively, the polynomial is truncated at higher orders, and the solution of the previous order is used to linearize the constraint. This enables achieving accurate solutions even for highly nonlinear safety metrics and dynamics. Since the optimization process comprises only polynomial evaluations, the method is computationally efficient, with run times typically below 1 s. Moreover, no restrictions on the considered dynamics are necessary; therefore, results are shown for Keplerian, J2, and circular restricted three-body problem dynamics.

math.OC↗

arXiv2024

Fuel-Optimal Collision Avoidance Maneuvers in Long-Term Encounters with Station-Keeping Constraints

This work presents a sequential convex program method to compute fuel-optimal collision avoidance maneuvers for long-term encounters. The low-thrust acceleration model is used to account for the control, but the method can compute high-thrust maneuvers by increasing the maximum available acceleration. Dealing with the long-term conjunction poses additional challenges compared to the short-term problem because the encounter is not instantaneous. Thus, under the assumption of Gaussian statistics, the probability of collision is replaced by a simpler metric, the instantaneous probability of collision (IPoC) and a keep-out zone constraint is formulated as a continuous condition to be respected throughout the time frame of interest. The robustness of the solution is improved by introducing a constraint on the sensitivity of the IPoC. Furthermore, the collision avoidance problem is coupled with the classical station-keeping requirement for geostationary Earth orbit satellites and with a return to the nominal orbit condition for low Earth orbit satellites. Even though no guarantee is given for the recovery of the global optimum solution, numerical simulations in different orbital regimes show that the proposed approach can yield a local fuel-optimal solution with a run-time suitable for autonomous applications.

eess.SY↗

arXiv2023

Convex Optimization-based Model Predictive Control for Active Space Debris Removal Mission Guidance

A convex optimization-based model predictive control (MPC) algorithm for the guidance of active debris removal (ADR) missions is proposed in this work. A high-accuracy reference for the convex optimization is obtained through a split-Edelbaum approach that takes the effects of J2, drag, and eclipses into account. When the spacecraft deviates significantly from the reference trajectory, a new reference is calculated through the same method to reach the target debris. When required, phasing is integrated into the transfer. During the mission, the phase of the spacecraft is adjusted to match that of the target debris at the end of the transfer by introducing intermediate waiting times. The robustness of the guidance scheme is tested in a high-fidelity dynamical model that includes thrust errors and misthrust events. The guidance algorithm performs well without requiring successive convex iterations. Monte-Carlo simulations are conducted to analyze the impact of these thrust uncertainties on the guidance. Simulation results show that the proposed convex-MPC approach can ensure that the spacecraft can reach its target despite significant uncertainties and long-duration misthrust events.

math.OC↗