arXiv subjects

Dario Izzo

Publications and source records attributed to Dario Izzo.

At least 19 recordsLinked to original sources

arXiv2026

The Maximum Initial Mass

We introduce the maximum-initial-mass problem as a standalone optimal-control formulation for low-thrust trajectory design and analyze its structure within Pontryagin's framework. For fixed transfer time and final state, the formulation seeks the largest initial mass from which the transfer is feasible, and its necessary conditions imply a full-throttle control law in the nondegenerate case together with the standard primer-vector steering direction. We then establish a correspondence between extremals of the maximum-initial-mass and minimum-time problems, showing that each minimum-time extremal induces a maximum-initial-mass extremal on the associated time interval, and conversely. This viewpoint also clarifies the role of the terminal Hamiltonian condition in indirect formulations of minimum-time problems, which we interpret as a gauge choice rather than an independent necessary condition in the setting considered. Finally, we show that the maximum-initial-mass framework provides a smooth and effective continuation strategy for multiple-revolution low-thrust transfers. Applied to a benchmark GTO-to-GEO transfer, the approach recovers the global minimum-time solution, reveals additional extremal branches, and makes explicit that some trajectories previously reported in the literature correspond to local maxima of transfer time along iso-M curves rather than to local minima.

astro-ph.EP↗

arXiv2026

Deflective Sunshades: conceptual design and origami-inspired folding strategy

Space-based solar radiation management has been proposed as a direct means of modulating Earth's radiative balance by reducing incident solar flux. A prominent concept consists of large sunshades operating near the Sun-Earth L1 region. However, feasibility is constrained by a fundamental lower bound on the required mass, arising from the coupled requirements of achieving sufficient insolation reduction while maintaining dynamical equilibrium under solar radiation pressure (SRP). We introduce a class of sunshades, termed deflective, designed to shape the effective SRP through macroscopic surface geometry. By employing inclined reflective elements, these systems redirect incident radiation to simultaneously control flux attenuation and the resulting momentum exchange, enabling the use of conventional high-reflectivity materials (e.g., aluminium films). The concept admits multiple geometrical realizations, including conical, pyramidal, and louvered (venetian-blind) configurations. A conical configuration is then studied in more detail as a representative implementation of this broader design principle. To improve its packaging efficiency and scalability, we consider a distributed constellation of units and propose a flat-folding strategy based on a Miura-Ori pattern adapted to the conical geometry finding its optimal configuration parameters resulting in a favourable geometry.

physics.space-ph↗

arXiv2026

Pretrained Approximators for Low-Thrust Trajectory Cost and Reachability

Low-thrust trajectory design relies heavily on repeated evaluations of fuel consumption and transfer feasibility, which require expensive optimal control solutions. In this work, we show these quantities can be accurately approximated by machine learning surrogates, enabling fast and scalable evaluation across a wide range of scenarios. By increasing both dataset size and model capacity, we observe that low-thrust trajectory optimization follows a scaling law, with performance improving linearly with the logarithm of training data and network parameters, and no evidence of saturation within the explored regime. Guided by this observation, we construct a large-scale dataset using the proposed homotopy-ray strategy tailored to mission design requirements. A key is the introduction of a self-similar transformation, which allows generalization across semi-major axes, inclinations, and central bodies avoiding retraining. As a result, the same neural approximator can be applied to diverse orbital environments and mission classes. The proposed models accurately predict optimal fuel consumption and minimum transfer time for single- and multi-revolution transfers. Their performance and generalization are demonstrated on a public dataset, a multi-asteroid flyby problem from the Global Trajectory Optimization Competition, and an asteroid rendezvous mission design. The models and datasets are released as open-source to support the space community.

cs.LG↗

arXiv2026

Reachability for Low-Thrust Trajectories via Maximum Initial Mass

Reachability analysis plays a central role in low-thrust spacecraft trajectory optimization by identifying which target states can be achieved under constraints on time, thrust, and propellant. Classical approaches construct reachable sets by solving many optimal control problems over grids of terminal states, requiring extensive forward simulations with fixed initial conditions. While effective, this approach is computationally expensive and becomes impractical for high-dimensional systems or strongly nonlinear dynamics, such as those encountered in cislunar environments or solar sail missions. This work introduces a dual formulation of the reachability problem. Instead of computing reachable sets directly, we determine, for fixed transfer time and boundary conditions, the maximum allowable initial mass (or, for solar sails, a scalar sail-strength parameter) that permits a successful transfer. A target is reachable if the spacecraft's initial mass does not exceed this threshold. This reformulation reduces reachability assessment to a scalar optimization problem for each target, producing a smooth scalar field that encodes equivalent feasibility information to classical reachable sets. We develop indirect maximum-initial-mass (MIM) formulations for both electric low-thrust and solar-sail dynamics and show how they can serve as efficient reachability oracles. Building on this formulation, we construct data-driven surrogate models to approximate the MIM-based reachability indicator. We investigate fully connected neural networks and demonstrate that residual networks provide the best trade-off between accuracy, training stability, and model complexity. The resulting surrogates enable rapid reachability evaluation while preserving the numerical advantages of the dual formulation, offering a practical tool for preliminary mission design and feasibility assessment.

eess.SY↗

arXiv2026

Post-Newtonian orbital mechanics around a black hole in modified gravity

Scalar-tensor-vector gravity, also known as modified gravity (MOG), has emerged as an alternative to General Relativity (GR). It aims to explain astrophysical phenomena without invoking dark matter. The S-stars orbiting the supermassive black hole at the Galactic centre provide a unique opportunity to test the predictions of MOG because the orbital measurements are highly precise. We investigate the perturbations in the orbits of S-stars under MOG, focusing on the effects on orbital elements, observables such as right ascension, declination, and radial velocity, and the potential degeneracy with dark matter scenarios. We numerically integrated the first post-Newtonian equations of motion for S-stars within the MOG framework, considering contributions from the space-time geometry and the fifth force. We analysed the time evolution of orbital elements and projected the orbits onto the plane of the sky to assess deviations from GR. Furthermore, we compared the MOG-induced effects with those expected from a dark matter distribution. We found that MOG significantly alters the orbital precession, particularly for higher values of the MOG parameter $\alpha$. For sufficiently large $\alpha$ or long observational baselines, the deviations in the observables can reach amplitudes comparable to current observational precision. Furthermore, we demonstrate that MOG effects can mimic those of a dark matter distribution, particularly in the argument of pericentre, and we reveal an unexplored connection between MOG and GR with electromagnetism. The effects of MOG on stellar orbits are distinct from those predicted by GR and can be tested with precise astrometric and spectroscopic measurements of the S-stars. However, a potential degeneracy with dark matter signatures necessitates careful interpretation of observational data.

gr-qc↗

arXiv2026

A practical guide to implementing zero-order-hold interplanetary trajectory legs

We study the practical implementation of zero-order-hold (ZOH) transcriptions for spacecraft trajectory optimisation, identifying a set of design principles that render them robust across a broad class of dynamical settings without problem-specific tuning. The contributions are fourfold: (i) a thorough study of the forward--backward shooting construction, denoted $\mathrm{ZOH}_\alpha$; (ii) a redundant four-dimensional throttle parameterization that eliminates the singularity of the control influence matrix along ballistic arcs; (iii) a softmax time-grid encoding that avoids ordering constraints on segment durations while preserving full differentiability; and (iv) the TOPS benchmark (Trajectory Optimisation Problems in Space), a suite of 28 problems spanning four dynamical models, two-body Cartesian, modified equinoctial elements, circular restricted three-body, and solar sailing, designed to be extended over time.

astro-ph.IM↗

arXiv2026

The Keplerian Traveling Salesperson Problem

We address a fundamental challenge in space mission design and space logistics: planning interplanetary trajectories for missions that must rendezvous with multiple bodies. Such mission occur, for instance, in active debris removal, in-orbit servicing, or asteroid belt exploration. We model these problems as a variant of the Traveling salesperson problem (TSP), which we term the Keplerian TSP (KTSP). Unlike the well-studied TSP, the KTSP accounts for the motion of orbital targets, leading to time-dependent and asymmetric transfer costs that capture key real-world effects in astrodynamics. We provide a rigorous formalization of the KTSP and release a benchmark suite to support its study. Central to our approach is a time-unfolding technique that reformulates the continuous problem as a discrete optimization task in a time-expanded network. This representation makes the benchmark accessible to researchers in discrete optimization even without prior knowledge of celestial mechanics. We also develop an alternative encoding as an integer linear program using Interval-based Dynamic Discretization Discovery to handle the time-dependent nature of transfers. We leverage state-of-the-art ILP solvers to solve the KTSP instances, accompanied by a detailed computational study that highlights their strengths and limitations. We complement these exact methods with an initial solution heuristic, an improvement heuristic, and preprocessing routines that preserve optimality.

math.OC↗

arXiv2025

Simulation of Active Soft Nets for Capture of Space Debris

In this work, we propose a simulator, based on the open-source physics engine MuJoCo, for the design and control of soft robotic nets for the autonomous removal of space debris. The proposed simulator includes net dynamics, contact between the net and the debris, self-contact of the net, orbital mechanics, and a controller that can actuate thrusters on the four satellites at the corners of the net. It showcases the case of capturing Envisat, a large ESA satellite that remains in orbit as space debris following the end of its mission. This work investigates different mechanical models, which can be used to simulate the net dynamics, simulating various degrees of compliance, and different control strategies to achieve the capture of the debris, depending on the relative position of the net and the target. Unlike previous works on this topic, we do not assume that the net has been previously ballistically thrown toward the target, and we start from a relatively static configuration. The results show that a more compliant net achieves higher performance when attempting the capture of Envisat. Moreover, when paired with a sliding mode controller, soft nets are able to achieve successful capture in 100% of the tested cases, whilst also showcasing a higher effective area at contact and a higher number of contact points between net and Envisat.

cs.RO↗

arXiv2025

Vision-Guided Optic Flow Navigation for Small Lunar Missions

Private lunar missions are faced with the challenge of robust autonomous navigation while operating under stringent constraints on mass, power, and computational resources. This work proposes a motion-field inversion framework that uses optical flow and rangefinder-based depth estimation as a lightweight CPU-based solution for egomotion estimation during lunar descent. We extend classical optical flow formulations by integrating them with depth modeling strategies tailored to the geometry for lunar/planetary approach, descent, and landing, specifically, planar and spherical terrain approximations parameterized by a laser rangefinder. Motion field inversion is performed through a least-squares framework, using sparse optical flow features extracted via the pyramidal Lucas-Kanade algorithm. We verify our approach using synthetically generated lunar images over the challenging terrain of the lunar south pole, using CPU budgets compatible with small lunar landers. The results demonstrate accurate velocity estimation from approach to landing, with sub-10% error for complex terrain and on the order of 1% for more typical terrain, as well as performances suitable for real-time applications. This framework shows promise for enabling robust, lightweight on-board navigation for small lunar missions.

cs.RO↗

arXiv2025

MasconCube: Fast and Accurate Gravity Modeling with an Explicit Representation

The geodesy of irregularly shaped small bodies presents fundamental challenges for gravitational field modeling, particularly as deep space exploration missions increasingly target asteroids and comets. Traditional approaches suffer from critical limitations: spherical harmonics diverge within the Brillouin sphere where spacecraft typically operate, polyhedral models assume unrealistic homogeneous density distributions, and existing machine learning methods like GeodesyNets and Physics-Informed Neural Networks (PINN-GM) require extensive computational resources and training time. This work introduces MasconCubes, a novel self-supervised learning approach that formulates gravity inversion as a direct optimization problem over a regular 3D grid of point masses (mascons). Unlike implicit neural representations, MasconCubes explicitly model mass distributions while leveraging known asteroid shape information to constrain the solution space. Comprehensive evaluation on diverse asteroid models including Bennu, Eros, Itokawa, and synthetic planetesimals demonstrates that MasconCubes achieve superior performance across multiple metrics. Most notably, MasconCubes demonstrate computational efficiency advantages with training times approximately 40 times faster than GeodesyNets while maintaining physical interpretability through explicit mass distributions. These results establish MasconCubes as a promising approach for mission-critical gravitational modeling applications requiring high accuracy, computational efficiency, and physical insight into internal mass distributions of irregular celestial bodies.

astro-ph.EP↗

arXiv2025

Reconfiguration of pivoting cube ensembles under local sensing constraints using geometric deep learning

We demonstrate that local sensing is sufficient for effective global reconfiguration of homogeneous pivoting cube modular robots in two dimensions. While cube selection (i.e., which cube executes a movement) is assumed to be globally coordinated, each cube in the ensemble is controlled by a neural network that only gains information from other cubes in its local neighbourhood, trained using reinforcement learning. Furthermore, we study the effect of including grid symmetries of the cube ensemble (rotation and mirroring) in the neural network architecture. We find that even the most localised versions succeed in reconfiguring to the target shape, although reconfiguration happens faster the more information about the whole ensemble is available to individual cubes. Near-optimal reconfiguration is achieved with only nearest neighbour interactions by using multiple information passing between cubes, allowing them to accumulate more global information about the ensemble. Compared to standard neural network architectures, including grid symmetries provides only minor benefits during training, but allows for reduced model sizes. The presented approach is transferable to other space-relevant systems with different action spaces, such as sliding cube modular robots and CubeSat swarms.

cs.NE↗

arXiv2025

Memristor-Based Neural Network Accelerators for Space Applications: Enhancing Performance with Temporal Averaging and SIRENs

Memristors are an emerging technology that enables artificial intelligence (AI) accelerators with high energy efficiency and radiation robustness -- properties that are vital for the deployment of AI on-board spacecraft. However, space applications require reliable and precise computations, while memristive devices suffer from non-idealities, such as device variability, conductance drifts, and device faults. Thus, porting neural networks (NNs) to memristive devices often faces the challenge of severe performance degradation. In this work, we show in simulations that memristor-based NNs achieve competitive performance levels on on-board tasks, such as navigation \& control and geodesy of asteroids. Through bit-slicing, temporal averaging of NN layers, and periodic activation functions, we improve initial results from around $0.07$ to $0.01$ and $0.3$ to $0.007$ for both tasks using RRAM devices, coming close to state-of-the-art levels ($0.003-0.005$ and $0.003$, respectively). Our results demonstrate the potential of memristors for on-board space applications, and we are convinced that future technology and NN improvements will further close the performance gap to fully unlock the benefits of memristors.

eess.SY↗

arXiv2025

Guidance and Control Neural Network Acceleration using Memristors

In recent years, the space community has been exploring the possibilities of Artificial Intelligence (AI), specifically Artificial Neural Networks (ANNs), for a variety of on board applications. However, this development is limited by the restricted energy budget of smallsats and cubesats as well as radiation concerns plaguing modern chips. This necessitates research into neural network accelerators capable of meeting these requirements whilst satisfying the compute and performance needs of the application. This paper explores the use of Phase-Change Memory (PCM) and Resistive Random-Access Memory (RRAM) memristors for on-board in-memory computing AI acceleration in space applications. A guidance and control neural network (G\&CNET) accelerated using memristors is simulated in a variety of scenarios and with both device types to evaluate the performance of memristor-based accelerators, considering device non-idealities such as noise and conductance drift. We show that the memristive accelerator is able to learn the expert actions, though challenges remain with the impact of noise on accuracy. We also show that re-training after degradation is able to restore performance to nominal levels. This study provides a foundation for future research into memristor-based AI accelerators for space, highlighting their potential and the need for further investigation.

cs.AR↗

arXiv2025

Comparing Behavioural Cloning and Reinforcement Learning for Spacecraft Guidance and Control Networks

Guidance & control networks (G&CNETs) provide a promising alternative to on-board guidance and control (G&C) architectures for spacecraft, offering a differentiable, end-to-end representation of the guidance and control architecture. When training G&CNETs, two predominant paradigms emerge: behavioural cloning (BC), which mimics optimal trajectories, and reinforcement learning (RL), which learns optimal behaviour through trials and errors. Although both approaches have been adopted in G&CNET related literature, direct comparisons are notably absent. To address this, we conduct a systematic evaluation of BC and RL specifically for training G&CNETs on continuous-thrust spacecraft trajectory optimisation tasks. We introduce a novel RL training framework tailored to G&CNETs, incorporating decoupled action and control frequencies alongside reward redistribution strategies to stabilise training and to provide a fair comparison. Our results show that BC-trained G&CNETs excel at closely replicating expert policy behaviour, and thus the optimal control structure of a deterministic environment, but can be negatively constrained by the quality and coverage of the training dataset. In contrast RL-trained G&CNETs, beyond demonstrating a superior adaptability to stochastic conditions, can also discover solutions that improve upon suboptimal expert demonstrations, sometimes revealing globally optimal strategies that eluded the generation of training samples.

eess.SY↗

arXiv2025

Energy efficiency analysis of Spiking Neural Networks for space applications

While the exponential growth of the space sector and new operative concepts ask for higher spacecraft autonomy, the development of AI-assisted space systems was so far hindered by the low availability of power and energy typical of space applications. In this context, Spiking Neural Networks (SNN) are highly attractive due to their theoretically superior energy efficiency due to their inherently sparse activity induced by neurons communicating by means of binary spikes. Nevertheless, the ability of SNN to reach such efficiency on real world tasks is still to be demonstrated in practice. To evaluate the feasibility of utilizing SNN onboard spacecraft, this work presents a numerical analysis and comparison of different SNN techniques applied to scene classification for the EuroSAT dataset. Such tasks are of primary importance for space applications and constitute a valuable test case given the abundance of competitive methods available to establish a benchmark. Particular emphasis is placed on models based on temporal coding, where crucial information is encoded in the timing of neuron spikes. These models promise even greater efficiency of resulting networks, as they maximize the sparsity properties inherent in SNN. A reliable metric capable of comparing different architectures in a hardware-agnostic way is developed to establish a clear theoretical dependence between architecture parameters and the energy consumption that can be expected onboard the spacecraft. The potential of this novel method and his flexibility to describe specific hardware platforms is demonstrated by its application to predicting the energy consumption of a BrainChip Akida AKD1000 neuromorphic processor.

cs.NE↗

arXiv2025

Probability of collision in nonlinear dynamics by moment propagation

Estimating the probability of collision between spacecraft is crucial for risk management and collision-avoidance strategies. Current methods often rely on Gaussian assumptions and simplifications, which can be inaccurate in highly nonlinear scenarios. This paper presents a general and efficient approach for computing collision probabilities without relying on such assumptions. Using high-order multivariate Taylor polynomials, we propagate statistical moments of initial uncertainties to the point of closest approach between the spacecraft. To compute the probability of collision, we derive a semi-analytical expression for the probability density function (PDF) of the closest approach distance, inferred from the propagated moments using orthogonal polynomials. Tested on various short-term and long-term encounters in low-Earth orbit, our method accurately handles nonlinear dynamics, non-Gaussian uncertainties, and irregular distributions. This versatile framework advances space situational awareness by providing precise collision probability estimates in complex dynamical environments. Moreover, our methodology applies to any dynamical system with uncertainty in its initial state and is therefore not restricted to collision probability estimation.

eess.SY↗

arXiv2025

EclipseNETs: Learning Irregular Small Celestial Body Silhouettes

Accurately predicting eclipse events around irregular small bodies is crucial for spacecraft navigation, orbit determination, and spacecraft systems management. This paper introduces a novel approach leveraging neural implicit representations to model eclipse conditions efficiently and reliably. We propose neural network architectures that capture the complex silhouettes of asteroids and comets with high precision. Tested on four well-characterized bodies - Bennu, Itokawa, 67P/Churyumov-Gerasimenko, and Eros - our method achieves accuracy comparable to traditional ray-tracing techniques while offering orders of magnitude faster performance. Additionally, we develop an indirect learning framework that trains these models directly from sparse trajectory data using Neural Ordinary Differential Equations, removing the requirement to have prior knowledge of an accurate shape model. This approach allows for the continuous refinement of eclipse predictions, progressively reducing errors and improving accuracy as new trajectory data is incorporated.

astro-ph.EP↗

arXiv2025

High-order expansion of Neural Ordinary Differential Equations flows

Artificial neural networks, widely recognised for their role in machine learning, are now transforming the study of ordinary differential equations (ODEs), bridging data-driven modelling with classical dynamical systems and enabling the development of infinitely deep neural models. However, the practical applicability of these models remains constrained by the opacity of their learned dynamics, which operate as black-box systems with limited explainability, thereby hindering trust in their deployment. Existing approaches for the analysis of these dynamical systems are predominantly restricted to first-order gradient information due to computational constraints, thereby limiting the depth of achievable insight. Here, we introduce Event Transition Tensors, a framework based on high-order differentials that provides a rigorous mathematical description of neural ODE dynamics on event manifolds. We demonstrate its versatility across diverse applications: characterising uncertainties in a data-driven prey-predator control model, analysing neural optimal feedback dynamics, and mapping landing trajectories in a three-body neural Hamiltonian system. In all cases, our method enhances the interpretability and rigour of neural ODEs by expressing their behaviour through explicit mathematical structures. Our findings contribute to a deeper theoretical foundation for event-triggered neural differential equations and provide a mathematical construct for explaining complex system dynamics.

math.OC↗