Our team and mission

This internship will take place within ESA's Advanced Concepts Team (ACT). The ACT is a team of scientists who originate from a broad variety of academic fields and are aiming for an academic career. Its task is to monitor, perform and foster research on advanced space systems, innovative concepts and working methods. It interacts externally almost exclusively with academia and operates as a truly interdisciplinary team bound to high scientific standards. Through its research, the team acts as a pathfinder to explore novel, potentially promising areas for ESA and the space sector, ranging from applied to fundamental research topics. An important task of the team is to communicate scientific trends and results, as input to the strategic planning of the Agency. Visit our webpages at Advanced Concepts Team of ESA.

Candidates interested are encouraged to visit the ESA website: http://www.esa.int

Field(s) of activity for the internship

You can choose among the following topics:

1) Topic 1: Autodiscovery of search strategies for large Keplerian Travelling Salesperson Problem instances and variants

The Keplerian Traveling Salesperson Problem (KTSP) is a combinatorial optimisation problem arising in spacecraft trajectory design, where a spacecraft must visit targets moving on Keplerian orbits. In contrast to the classical TSP, transfer costs are time-dependent and asymmetric. The KTSP is relevant to applications including active debris removal, in-orbit servicing, and multi-rendezvous mission planning [1–3].

Existing approaches use metaheuristics such as Ant Colony Optimisation (ACO), beam search, and Monte Carlo Tree Search (MCTS). Hybrid methods, for example Beam P-ACO, combine probabilistic solution construction with bounded tree search and have shown promising results for multi-rendezvous trajectory optimisation [3]. However, their performance depends on manually designed elements such as beam-width policies, rollout rules, pheromone updates, and local-search procedures.

Recent work in automated heuristic design combines evolutionary computation and language models to generate and refine optimisation heuristics. This internship will investigate whether an open framework based on evolutionary search and compact open-source language models (e.g. CHATOSS) can automatically discover effective search strategies for large KTSP instances and variants [4–6].

Objectives:
The goal of this internship is to develop and evaluate an LLM based framework for the automatic discovery of search strategies for large KTSP instances.

The objectives of this internship include:

• a survey of KTSP, related spacecraft trajectory optimisation problems, and the development of new large instances of KTSP and a few useful variants;
• development of a modular representation of heuristic components, including ACO rules, beam-search policies, MCTS rollout strategies, and hybrid approaches;
• implementation of an agentic framework that generates, evaluates, selects, and refines heuristic variants;
• benchmarking on KTSP instances in terms of solution quality, runtime, robustness, and scalability;
• comparison of automatically discovered strategies with manually designed ACO, beam search, MCTS, and hybrid baselines.

References:
[1] M. Bannach, G. Acciarini, and D. Izzo, The Keplerian Traveling Salesperson Problem, arXiv:2605.00010, 2026.
[2] D. Izzo, I. Getzner, D. Hennes, and L. F. Simões, Evolving solutions to TSP variants for active space debris removal, Proceedings of GECCO, 2015.
[3] L. F. Simões, D. Izzo, E. Haasdijk, and A. E. Eiben, Multi-rendezvous spacecraft trajectory optimization with beam P-ACO, Evolutionary Computation in Combinatorial Optimization, 2017.
[4] M. Schmidt and H. Lipson, Distilling free-form natural laws from experimental data, Science, 324(5923), 81–85, 2009.
[5] F. Liu, X. Tong, M. Yuan, X. Lin, F. Luo, Z. Wang, Z. Lu, and Q. Zhang, Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model, Proceedings of the 41st International Conference on Machine Learning, PMLR 235, 32201–32223, 2024. 
[6] H. Ye, J. Wang, Z. Cao, F. Berto, C. Hua, H. Kim, J. Park, and G. Song, ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution, Advances in Neural Information Processing Systems 37, 43571–43608, 2024.

2) Topic 2: Informing Guidance and Control Networks through Physics

Guidance and Control Networks (G&CNETs) are neural architectures that map the current state of a system directly to control actions, combining guidance and control in a single inference step. They are commonly trained using behavioural cloning: large datasets of optimal trajectories are generated offline and used to learn state-action mappings. This approach has been successfully demonstrated for spacecraft landing as well as low-thrust interplanetary transfers, where neural policies can reproduce near-optimal guidance in real time [1–3].

However, supervised learning alone does not explicitly enforce the optimality principles that generated the training data, such as Pontryagin’s Maximum Principle, the Hamilton–Jacobi–Bellman (HJB) equation, Hamiltonian minimisation, and costate dynamics. Recent work has highlighted the potential of embedding these principles directly into neural guidance architectures, while physics-informed and Pontryagin neural networks have been applied to low-thrust transfers and planetary landing problems [4–5].

Objectives:
The goal of this internship is to develop the next generation of G&CNETs architecture combining behavioural cloning with optimal-control constraints during training in a PINN-like architecture.

The objectives of this internship include:

• a survey of G&CNETs, physics-informed neural networks, and neural methods based on the HJB equation and Pontryagin’s Maximum Principle;
• development and test of composite training losses combining supervised control imitation with HJB residuals, Hamiltonian minimisation, and costate-consistency constraints;
• validation on benchmark spacecraft guidance problems, such as planetary landing or low-thrust interplanetary transfers;
• comparison with standard supervised G&CNETs in terms of accuracy, robustness, closed-loop performance, and propellant optimality.

References:
[1] C. Sánchez-Sánchez and D. Izzo, Real-Time Optimal Control via Deep Neural Networks: Study on Landing Problems, Journal of Guidance, Control, and Dynamics, 41(5), 2018.
[2] D. Izzo and E. Öztürk, Real-Time Optimal Guidance and Control for Interplanetary Transfers Using Deep Networks, Journal of Guidance, Control, and Dynamics, 44(2), 315–327, 2021.
[3] D. Izzo, E. Blazquez, R. Ferede, S. Origer, C. De Wagter, and G. C. H. E. de Croon, Optimality Principles in Spacecraft Neural Guidance and Control, Science Robotics, 9(91), 2024.
[4] D. Izzo, E. Öztürk, and M. Märtens, Interplanetary Transfers via Deep Representations of the Optimal Policy and/or of the Value Function, 2019.
[5] A. Addario et al., Learning Fuel-Optimal Trajectories for Space Applications via Pontryagin Neural Networks, Aerospace, 11(3), 228, 2024.

3) Topic 3: Low-discrepancy deployment heuristics for competitive mega-constellations

Mega-constellations in low Earth orbit (LEO) are progressively deployed and replenished as multiple operators launch, insert, and replace satellites over several years. During this growth phase, the geometry of individual constellations and of the shared orbital environment changes continuously, generating close approaches both within and between satellite systems. Studies of large constellations have shown that self-induced conjunctions can represent an important component of the overall collision risk [3,4]. Conventional Walker constellations provide simple and structured final configurations [2], but their phasing rules do not directly prescribe how available orbital slots should be filled safely as a populated environment evolves.

This internship will develop and evaluate greedy deployment heuristics to determine where a new operator should place its next N satellites within an already populated LEO environment. The approach will treat conjunctions as a quantifiable operational cost and seek insertion rules that preserve a well-spread population in orbital-element space. Low-discrepancy sequences, such as Halton and Sobol' sequences, will provide one possible class of space-filling rules [5]; alternative maximin, greedy-packing, or risk-aware heuristics will also be considered.

The focus will be on the assignment of orbital phases, primarily mean anomaly and, where relevant, right ascension of the ascending node (RAAN). Satellites will be introduced one at a time or in small batches, and each candidate placement will be evaluated against the existing population in terms of close approaches, minimum separation, and collision-risk indicators. Large orbital populations will be propagated and analysed using ESA's cascade library [1].

Objectives:

• survey conjunction risk, self-induced collision risk, orbital slotting, and deployment strategies for growing LEO mega-constellations [3,4];
• develop greedy insertion rules for selecting orbital slots in mean anomaly and RAAN in the presence of an existing multi-operator background population;
• investigate low-discrepancy sequences as incremental space-filling rules [5], alongside alternative maximin and conjunction-aware placement heuristics;
• simulate progressive deployment scenarios using ESA's cascade library [1] and evaluate close-approach statistics, minimum-distance distributions, and collision-risk indicators at successive growth stages;
• compare the proposed heuristics with Walker-type [2] and random-deployment baselines in terms of conjunction frequency, risk, coverage, and operational practicality;
• formulate preliminary guidelines for safer incremental deployment in shared, multi-operator LEO environments.

References:

[1] F. Biscani and D. Izzo, "cascade: A C++/Python library for the propagation of large orbital populations and collision detection," European Space Agency, Advanced Concepts Team, 2023. Available at: cascade — cascade 0.1.10 documentation 
[2] J. G. Walker, "Satellite Constellations," Journal of the British Interplanetary Society, vol. 37, no. 12, pp. 559–572, 1984.
[3] H. G. Lewis, J. Radtke, J. Beck, B. Bastida Virgili, and H. Krag, "Self-induced collision risk analysis for large constellations," Proceedings of the 7th European Conference on Space Debris, Darmstadt, Germany, 2017. Available at: Self-induced collision risk analysis for large constellations | ESA Proceedings Database 
[4] N. Reiland, A. J. Rosengren, R. Malhotra, and C. Bombardelli, "Assessing and Minimizing Collisions in Satellite Mega-Constellations," Advances in Space Research, vol. 67, no. 6, pp. 2013–2025, 2021. doi: 10.1016/j.asr.2021.01.004
[5] J. Dick and F. Pillichshammer, Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration, Cambridge University Press, Cambridge, 2010. doi: 10.1017/CBO9780511761188.

4) Topic 4: Differentiable simulation and orbital control of shape-changing spacecraft in generic spacetimes
 
A spacecraft with movable internal masses can function as a form of propellantless propulsion when it interacts with a non-uniform gravitational field. By changing its internal geometry at different points along the orbit, the spacecraft modifies its gravitational coupling to the local tidal field. 

A simple example is a dumbbell spacecraft or a variable-length tether with masses at its ends. Extending and contracting the dumbbell at selected orbital positions can exchange energy and angular momentum with the orbit without expelling propellant.

Harte and collaborators developed a generic description of this mechanism based on the spacecraft’s mass quadrupole tensor [1–2]. Instead of modelling every movable mass or tether element, the spacecraft is represented by a time-dependent symmetric quadrupole tensor. 

Its eigenvalues describe the principal distribution of mass, while its eigenvectors describe the corresponding principal directions. 

The formalism has been developed for a general class of spacetimes, where forces and torques in Kerr and Schwarzschild metrics are known in closed form, though the practical orbital consequences remain unsolved for rotating black holes. 

Quadrupole modulation can influence orbital energy, eccentricity, apsidal orientation, and orbital stability [1–3]. Jupiter provides an interesting initial test case because of its strong gravity, large tidal gradients, rapid rotation, and significant oblateness. 

The project will investigate whether quadrupole modulation can produce useful secular changes in orbital energy, eccentricity, apsidal orientation, nodal precession, or inclination in strong gravitational regimes including Kerr and Schwarzschild metrics.

Objectives:

• developing a differentiable simulator in heyoka [3] for a shape-changing spacecraft implementing Harte’s formalism for Schwarzschild and Kerr black holes;
• validating the simulator by reproducing published results on eccentricity control, circularisation, apsidal motion, and orbital stabilisation;
• applying automatic differentiation and gradient-based optimisation to identify effective deformation amplitudes, frequencies, phases, and switching conditions;
• testing on Jupiter’s gravity and then reproducing and looking for pure GR effects in a representative Kerr Black Hole.

The project will combine general relativity, analytical mechanics and automatic differentiation. The final outcome will be a reproducible computational framework for studying shape-controlled orbital dynamics and evaluating unconventional orbital-control scenarios around exotic gravitational regimes.
 

References:
[1] M. Harte and M. Gaffney, “Extended-body effects and rocket-free orbital manoeuvring,” Acta Astronautica, vol. 178, pp. 625–633, 2021.
[2] M. Harte and M. Gaffney, “Extended-body motion in black hole spacetimes: What is possible?”, Physical Review D, vol. 102, 124075, 2020.
[3] F. Biscani and D. Izzo, “Revisiting high-order Taylor methods for astrodynamics and celestial mechanics,” Monthly Notices of the Royal Astronomical Society, vol. 504, no. 2, pp. 2614–2628, 2021.

Behavioural competencies

Result Orientation
Operational Efficiency
Fostering Cooperation
Relationship Management
Continuous Improvement
Forward Thinking

For more information, please refer to ESA Core Behavioural Competencies guidebook

Education

You must be a university student, preferably in your final or second-to-last year of university course at Master's level. In addition, you must be able to prove that you will be enrolled at your university for the entire duration of the internship.

Additional requirements

The working languages of the Agency are English and French. A good knowledge of one of these is required. Knowledge of another ESA Member State language is an asset.

During the interview, your motivation for applying to this role will be explored.