Intern in the Technology Department - Advanced Concepts Team

## Location ESTEC, Noordwijk, Netherlands ## 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 ## 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 gree