Massimiliano Vasile

Massimiliano Vasile, Edmondo Minisci, Marco Locatelli

In this paper we define a discrete dynamical system that governs the evolution of a population of agents. From the dynamical system, a variant of Differential Evolution is derived. It is then demonstrated that, under some assumptions on the differential mutation strategy and on the local structure of the objective function, the proposed dynamical system has fixed points towards which it converges with probability one for an infinite number of generations. This property is used to derive an algorithm that performs better than standard Differential Evolution on some space trajectory optimization problems. The novel algorithm is then extended with a guided restart procedure that further increases the performance, reducing the probability of stagnation in deceptive local minima.

Massimiliano Vasile, Paolo DePascale

In this paper the preliminary design of multiple gravity-assist trajectories is formulated as a global optimization problem. An analysis of the structure of the solution space reveals a strong multimodality, which is strictly dependent on the complexity of the model. On the other hand it is shown how an oversimplification could prevent finding potentially interesting solutions. A trajectory model, which represents a compromise between model completeness and optimization problem complexity is then presented. The exploration of the resulting solution space is performed through a novel global search approach, which hybridizes an evolutionary based algorithm with a systematic branching strategy. This approach allows an efficient exploration of complex solution domains by automatically balancing local convergence and global search. A number of difficult multiple gravity-assist trajectory design cases demonstrates the effectiveness of the proposed methodology.

Massimiliano Vasile, Camilla Colombo

This paper presents an analysis of optimal impact strategies to deflect potentially dangerous asteroids. To compute the increase in the minimum orbit intersection distance of the asteroid due to an impact with a spacecraft, simple analytical formulas are derived from proximal motion equations. The proposed analytical formulation allows for an analysis of the optimal direction of the deviating impulse transferred to the asteroid. This ideal optimal direction cannot be achieved for every asteroid at any time; therefore, an analysis of the optimal launch opportunities for deviating a number of selected asteroids was performed through the use of a global optimization procedure. The results in this paper demonstrate that the proximal motion formulation has very good accuracy in predicting the actual deviation and can be used with any deviation method because it has general validity. Furthermore, the characterization of optimal launch opportunities shows that a significant deviation can be obtained even with a small spacecraft.

Matteo Ceriotti, Massimiliano Vasile

Given a set of celestial bodies, the problem of finding an optimal sequence of swing-bys, deep space manoeuvres (DSM) and transfer arcs connecting the elements of the set is combinatorial in nature. The number of possible paths grows exponentially with the number of celestial bodies. Therefore, the design of an optimal multiple gravity assist (MGA) trajectory is a NP-hard mixed combinatorial-continuous problem. Its automated solution would greatly improve the design of future space missions, allowing the assessment of a large number of alternative mission options in a short time. This work proposes to formulate the complete automated design of a multiple gravity assist trajectory as an autonomous planning and scheduling problem. The resulting scheduled plan will provide the optimal planetary sequence and a good estimation of the set of associated optimal trajectories. The trajectory model consists of a sequence of celestial bodies connected by twodimensional transfer arcs containing one DSM. For each transfer arc, the position of the planet and the spacecraft, at the time of arrival, are matched by varying the pericentre of the preceding swing-by, or the magnitude of the launch excess velocity, for the first arc. For each departure date, this model generates a full tree of possible transfers from the departure to the destination planet. Each leaf of the tree represents a planetary encounter and a possible way to reach that planet. An algorithm inspired by Ant Colony Optimization (ACO) is devised to explore the space of possible plans. The ants explore the tree from departure to destination adding one node at the time: every time an ant is at a node, a probability function is used to select a feasible direction. This approach to automatic trajectory planning is applied to the design of optimal transfers to Saturn and among the Galilean moons of Jupiter.

Massimiliano Vasile, Franco Bernelli-Zazzera

In this paper a direct method based on a transcription by finite elements in time has been used to design optimal interplanetary trajectories, exploiting a combination of gravity assist maneuvers and low-thrust propulsion. A multiphase parametric approach has been used to introduce swing-bys, treated as coast phases between two thrusted or coasting trajectory arcs. Gravity maneuvers are at first modeled with a linked-conic approximation and then introduced through a full three-dimensional propagation including perturbations by the Sun. The method is successfully applied to the design of a mission to planet Mercury, for which different options corresponding to different sequences of gravity maneuvers or launch opportunities are presented.

Massimiliano Vasile, Stefano Campagnola

This paper presents the design of a mission to Europa using solar electric propulsion as main source of thrust. A direct transcription method based on Finite Elements in Time was used for the design and optimisation of the entire low-thrust gravity assist transfer from the Earth to Europa. Prior to that, a global search algorithm was used to generate a set of suitable first guess solutions for the transfer to Jupiter, and for the capture in the Jovian system. In particular, a fast deterministic search algorithm was developed to find the most promising set of swing-bys to reach Jupiter A second fast search algorithm was developed to find the best sequence of swing-bys of the Jovian moons. After introducing the global search algorithms and the direct transcription through Finite Elements in Time, the paper presents a number of first guess Solutions and a fully optimised transfer from the Earth to Europa.

Massimiliano Vasile, Lewis Walker, Andrew Campbell et al.

This paper presents a data processing pipeline designed to extract information from the hyperspectral signature of unknown space objects. The methodology proposed in this paper determines the material composition of space objects from single pixel images. Two techniques are used for material identification and classification: one based on machine learning and the other based on a least square match with a library of known spectra. From this information, a supervised machine learning algorithm is used to classify the object into one of several categories based on the detection of materials on the object. The behaviour of the material classification methods is investigated under non-ideal circumstances, to determine the effect of weathered materials, and the behaviour when the training library is missing a material that is present in the object being observed. Finally the paper will present some preliminary results on the identification and classification of space objects.

Alvaro Francisco Gil, Walther Litteri, Victor Rodriguez-Fernandez et al.

The Three-Body Problem has fascinated scientists for centuries and it has been crucial in the design of modern space missions. Recent developments in Generative Artificial Intelligence hold transformative promise for addressing this longstanding problem. This work investigates the use of Variational Autoencoder (VAE) and its internal representation to generate periodic orbits. We utilize a comprehensive dataset of periodic orbits in the Circular Restricted Three-Body Problem (CR3BP) to train deep-learning architectures that capture key orbital characteristics, and we set up physical evaluation metrics for the generated trajectories. Through this investigation, we seek to enhance the understanding of how Generative AI can improve space mission planning and astrodynamics research, leading to novel, data-driven approaches in the field.

Tathagata Basu, Edoardo Patelli, Gianluca Filippi et al.

Drones are becoming popular as a complementary system for \ac{ems}. Although several pilot studies and flight trials have shown the feasibility of drone-assisted \ac{aed} delivery, running a full-scale operational network remains challenging due to high capital expenditure and environmental uncertainties. In this paper, we formulate a reliability-informed Bayesian learning framework for designing drone-assisted \ac{aed} delivery networks under environmental and operational uncertainty. We propose our objective function based on the survival probability of \ac{ohca} patients to identify the ideal locations of drone stations. Moreover, we consider the coverage of existing \ac{ems} infrastructure to improve the response reliability in remote areas. We illustrate our proposed method using geographically referenced cardiac arrest data from Scotland. The result shows how environmental variability and spatial demand patterns influence optimal drone station placement across urban and rural regions. In addition, we assess the robustness of the network and evaluate its economic viability using a cost-effectiveness analysis based on expected \ac{qaly}. The findings suggest that drone-assisted \ac{aed} delivery is expected to be cost-effective and has the potential to significantly improve the emergency response coverage in rural and urban areas with longer ambulance response times.

Luis Sanchez, Massimiliano Vasile, Silvia Sanvido et al.

The paper presents an approach to the modelling of epistemic uncertainty in Conjunction Data Messages (CDM) and the classification of conjunction events according to the confidence in the probability of collision. The approach proposed in this paper is based on the Dempster-Shafer Theory (DSt) of evidence and starts from the assumption that the observed CDMs are drawn from a family of unknown distributions. The Dvoretzky-Kiefer-Wolfowitz (DKW) inequality is used to construct robust bounds on such a family of unknown distributions starting from a time series of CDMs. A DSt structure is then derived from the probability boxes constructed with DKW inequality. The DSt structure encapsulates the uncertainty in the CDMs at every point along the time series and allows the computation of the belief and plausibility in the realisation of a given probability of collision. The methodology proposed in this paper is tested on a number of real events and compared against existing practices in the European and French Space Agencies. We will show that the classification system proposed in this paper is more conservative than the approach taken by the European Space Agency but provides an added quantification of uncertainty in the probability of collision.

Ian Groves, Andrew Campbell, James Fernandes et al.

Foundation Models, pre-trained on large unlabelled datasets before task-specific fine-tuning, are increasingly being applied to specialised domains. Recent examples include ClimaX for climate and Clay for satellite Earth observation, but a Foundation Model for Space Object Behavioural Analysis has not yet been developed. As orbital populations grow, automated methods for characterising space object behaviour are crucial for space safety. We present a Space Safety and Sustainability Foundation Model focusing on space object behavioural analysis using light curves (LCs). We implemented a Perceiver-Variational Autoencoder (VAE) architecture, pre-trained with self-supervised reconstruction and masked reconstruction on 227,000 LCs from the MMT-9 observatory. The VAE enables anomaly detection, motion prediction, and LC generation. We fine-tuned the model for anomaly detection & motion prediction using two independent LC simulators (CASSANDRA and GRIAL respectively), using CAD models of boxwing, Sentinel-3, SMOS, and Starlink platforms. Our pre-trained model achieved a reconstruction error of 0.01%, identifying potentially anomalous light curves through reconstruction difficulty. After fine-tuning, the model scored 88% and 82% accuracy, with 0.90 and 0.95 ROC AUC scores respectively in both anomaly detection and motion mode prediction (sun-pointing, spin, etc.). Analysis of high-confidence anomaly predictions on real data revealed distinct patterns including characteristic object profiles and satellite glinting. Here, we demonstrate how self-supervised learning can simultaneously enable anomaly detection, motion prediction, and synthetic data generation from rich representations learned in pre-training. Our work therefore supports space safety and sustainability through automated monitoring and simulation capabilities.

Simão da Graça Marto, Massimiliano Vasile, Andrew Campbell et al.

Spectral lightcurves consisting of time series single-pixel spectral measurements of spacecraft are used to infer the spacecraft's attitude and rotation. Two methods are used. One based on numerical optimisation of a regularised least squares cost function, and another based on machine learning with a neural network model. The aim is to work with minimal information, thus no prior is available on the attitude nor on the inertia tensor. The theoretical and practical aspects of this task are investigated, and the methodology is tested on synthetic data. Results are shown based on synthetic data.

Bin Yang, Shuang Li, Jinglang Feng et al.

This paper presents a novel and fast solver for the J2-perturbed Lambert problem. The solver consists of an intelligent initial guess generator combined with a differential correction procedure. The intelligent initial guess generator is a deep neural network that is trained to correct the initial velocity vector coming from the solution of the unperturbed Lambert problem. The differential correction module takes the initial guess and uses a forward shooting procedure to further update the initial velocity and exactly meet the terminal conditions. Eight sample forms are analyzed and compared to find the optimum form to train the neural network on the J2-perturbed Lambert problem. The accuracy and performance of this novel approach will be demonstrated on a representative test case: the solution of a multi-revolution J2-perturbed Lambert problem in the Jupiter system. We will compare the performance of the proposed approach against a classical standard shooting method and a homotopy-based perturbed Lambert algorithm. It will be shown that, for a comparable level of accuracy, the proposed method is significantly faster than the other two.

Massimiliano Vasile, Edmondo Minisci, Quirien Wijnands

This paper presents some ideas to reduce the computational cost of evidence-based robust design optimization. Evidence Theory crystallizes both the aleatory and epistemic uncertainties in the design parameters, providing two quantitative measures, Belief and Plausibility, of the credibility of the computed value of the design budgets. The paper proposes some techniques to compute an approximation of Belief and Plausibility at a cost that is a fraction of the one required for an accurate calculation of the two values. Some simple test cases will show how the proposed techniques scale with the dimension of the problem. Finally a simple example of spacecraft system design is presented.

Massimiliano Vasile

In this paper, the preliminary design of a space mission is approached introducing uncertainties on the design parameters and formulating the resulting reliable design problem as a multiobjective optimization problem. Uncertainties are modelled through evidence theory and the belief, or credibility, in the successful achievement of mission goals is maximised along with the reliability of constraint satisfaction. The multiobjective optimisation problem is solved through a novel algorithm based on the collaboration of a population of agents in search for the set of highly reliable solutions. Two typical problems in mission analysis are used to illustrate the proposed methodology.

Matteo Ceriotti, Massimiliano Vasile, Giovanni Giardini et al.

In this paper, we propose an approach for assigning an interest level to the goals of a planetary rover. Assigning an interest level to goals, allows the rover autonomously to transform and reallocate the goals. The interest level is defined by data-fusing payload and navigation information. The fusion yields an "interest map", that quantifies the level of interest of each area around the rover. In this way the planner can choose the most interesting scientific objectives to be analyzed, with limited human intervention, and reallocates its goals autonomously. The Dezert-Smarandache Theory of Plausible and Paradoxical Reasoning was used for information fusion: this theory allows dealing with vague and conflicting data. In particular, it allows us directly to model the behavior of the scientists that have to evaluate the relevance of a particular set of goals. The paper shows an application of the proposed approach to the generation of a reliable interest map.

Federico Zuiani, Massimiliano Vasile

This paper presents a novel approach for the preliminary design of Low-Thrust, many-revolution transfers. The main feature of the novel approach is a considerable reduction in the control parameters and a consequent gain in computational speed. Each spiral is built by using a predefined pattern for thrust direction and switching structure. The pattern is then optimised to minimise propellant consumption and transfer time. The variation of the orbital elements due to the thrust is computed analytically from a first-order solution of the perturbed Keplerian motion. The proposed approach allows for a realistic estimation of ΔV and time of flight required to transfer a spacecraft between two arbitrary orbits. Eccentricity and plane changes are both accounted for. The novel approach is applied here to the design of missions for the removal of space debris by means of an Ion Beam Shepherd Spacecraft. In particular, two slightly different variants of the proposed low-thrust control model are used for the different phases of the mission. Thanks to their low computational cost they can be included in a multiobjective optimisation problem in which the sequence and timing of the removal of five pieces of debris are optimised to minimise propellant consumption and mission duration.

Federico Zuiani, Massimiliano Vasile, Alison Gibbings

This paper presents a novel approach to the robust design of deflection actions for Near Earth Objects (NEO). In particular, the case of deflection by means of Solar-pumped Laser ablation is studied here in detail. The basic idea behind Laser ablation is that of inducing a sublimation of the NEO surface, which produces a low thrust thereby slowly deviating the asteroid from its initial Earth threatening trajectory. This work investigates the integrated design of the Space-based Laser system and the deflection action generated by laser ablation under uncertainty. The integrated design is formulated as a multi-objective optimisation problem in which the deviation is maximised and the total system mass is minimised. Both the model for the estimation of the thrust produced by surface laser ablation and the spacecraft system model are assumed to be affected by epistemic uncertainties (partial or complete lack of knowledge). Evidence Theory is used to quantify these uncertainties and introduce them in the optimisation process. The propagation of the trajectory of the NEO under the laser-ablation action is performed with a novel approach based on an approximated analytical solution of Gauss' Variational Equations. An example of design of the deflection of asteroid Apophis with a swarm of spacecraft is presented.

Massimiliano Vasile, Federico Zuiani

This paper presents an algorithm for multiobjective optimization that blends together a number of heuristics. A population of agents combines heuristics that aim at exploring the search space both globally and in a neighborhood of each agent. These heuristics are complemented with a combination of a local and global archive. The novel agent- based algorithm is tested at first on a set of standard problems and then on three specific problems in space trajectory design. Its performance is compared against a number of state-of-the-art multiobjective optimisation algorithms that use the Pareto dominance as selection criterion: NSGA-II, PAES, MOPSO, MTS. The results demonstrate that the agent-based search can identify parts of the Pareto set that the other algorithms were not able to capture. Furthermore, convergence is statistically better although the variance of the results is in some cases higher.