PHD MSCA COFUND BEST

Researcher Profile: First Stage Researcher (R1) Positions: PhD Positions Application Deadline: 23 Nov 2026 - 12:00 (Europe/Paris) Country: Spain Type of Contract: Temporary Job Status: Full-time Hours Per Week: 35 Offer Starting Date: 1 Sep 2027 Is the job funded through the EU Research Framework Programme? Horizon Europe – COFUND Marie Curie Grant Agreement Number: 101261439 Is the Job related to staff position within a Research Infrastructure? No Offer Description PHD MSCA COFUND BEST The proposed PhD project is entitled: “Autonomous Collision Avoidance Guidance for Low-Thrust Spacecraft: A Combined Pontryagin Principle and Learning-Based Approach”. The PhD will be funded through a European Marie Curie fellowship and is expected to start in September 2027 . The project will be jointly supervised by professor Christophe Louembet at the Université de Toulouse and professor Julio C. Sanchez from the University of Seville . The PhD research will be primarily carried out in Toulouse , but several research stays at the University of Seville are already planned, amounting to a minimum total duration of one year . Candidates must have completed their degree by the time they submit their application. In addition, due to the Marie Curie mobility eligibility requirements, candidates must not have resided or carried out their main activity (work, studies, etc.) in France for more than 12 months during the three years immediately preceding the application deadline . Periods of stay as a tourist, refugee, or time spent in national service, are not considered as residency The application must be submitted on the website https://edd-projets.utoulouse.fr/ . The submission deadline is 23rd November at 12:00 PM CET . The description of the PhD project is available here (click on the English version): https://adum.fr/as/ed/voirproposition.pl?site=toulouse&matricule_prop=76476#version Information about the recruitment process will also be available here: https://doctorat.univ-toulouse.fr/cofund-best . (click on the English version) If there are any questions on the process, please send a message to best-helpdesk@utoulouse.fr The best candidates will be invited for interviews during the first quarter of 2027 . 1 PROJECT DESCRIPTION The aim of this PhD project is to develop an autonomous guidance algorithm for satellites, ensuring collision avoidance in the event of a detected conjunction between two spacecraft or between a spacecraft and orbital debris. This guidance function must both plan the avoidance maneuver and ensure tracking of this nominal trajectory , despite orbital perturbations. The key requirements for designing this collision avoidance guidance function include: Optimality , ensuring efficient fuel use while respecting the capabilities of the spacecraft (propulsion capacity, battery charge level, eclipse periods, etc.); Numerical efficiency , aiming to provide algorithms with a computational footprint compatible with onboard computation capabilities; Reliability , ensuring control stability under nominal conditions; Robustness, ensuring performance in the face of errors and orbital disturbances, particularly regarding stability. To address this complex challenge, the chosen strategy relies on three pillars: Optimal control theory , Machine learning and neural networks, Closed-loop control theory. While optimal control tools enable the description of optimal collision avoidance maneuvers that satisfy the satellite’s capabilities through a set of mathematical conditions, machine learning with neural networks must provide a low computational-cost solution for resolving these constraints during operation. Finally , the theoretical framework of automatic control will ensure stability and robustness, which are essential for the guidance function, by accounting for errors in the calculation of the optimal control and rejecting perturbations. The proposed approach must guarantee safe and sustainable response to collision risks while respecting the operational limits of the satellite. 2 CONTEXT Ensuring the safety of space operations has become a critical challenge due to the proliferation of space debris and the saturation of key orbital regimes, particularly in Low Earth Orbit (LEO) and Geostationary Orbit (GEO). According to the European Space Agency’s (ESA) 2024 Annual Space Environment Report, approximately 35,000 objects larger than 10 cm are actively tracked by ground-based sensors, while 900,000 objects ranging from 1 cm to 10 cm—difficult to detect but capable of causing catastrophic damage to operational satellites—and an estimated 128 million objects between 1 mm and 1 cm further contribute to the orbital hazard. This congestion has been exacerbated by the rapid deployment of satellite mega-constellations, such as Starlink, which significantly increase the frequency of conjunction events and necessitate reliable Collision Avoidance Maneuvers (CAMs). In response, Space Situational Awareness (SSA), encompassing Space Surveillance and Tracking (SST) and Space Traffic Management (STM), have emerged as essential frameworks. Mitigation strategies—such as satellite design optimization, end-of-life disposal plans, and Conjunction Analysis (CA)—alongside remediation efforts to actively reduce debris, aim to preserve the long-term sustainability of space activities. However, the current human-in-the-loop approach to CAM design and execution is becoming unsustainable with the emergence of mega-constellations. For instance, the Starlink constellation requires an average of 12 avoidance maneuvers per satellite annually over approximately six thousand spacecraft. The demand for 24/7 expert intervention is economically and operationally impractical. The shift toward autonomous decision-making will be pivotal in shaping future operational pipelines, balancing energy efficiency , robustness, and cost reduction while safeguarding the sustainability of space missions. To address these challenges, we will consider spacecraft equipped with electric propulsion systems, known for their low thrust but extended operational lifespan compared to chemical thrusters. Then our goal is to develop autonomous guidance algorithms enables fuel-efficient maneuvering, ensuring both precision and reliability in collision avoidance. 3 METHODOLOGY Low-thrust trajectory optimization relies on continuous, long-duration thrusting, typically implemented using electromagnetic propulsion systems, solar sails, or similar mechanisms. To enhance computational efficiency and reliability in Collision Avoidance Maneuver (CAM) problems, we propose a hybrid analytical-machine learning approach based on the following key steps. It is expected that such combination will improve computational efficiency compared to traditional numerical methods maintaining high level of optimality and accuracy. Establishing Optimality Conditions via Pontryagin’s Minimum Principle (PMP): We first derive necessary optimality conditions using the Pontryagin Minimum Principle (PMP), incorporating operational constraints (e.g., propulsion limits, power availability , and eclipse periods). This formulation yields a Two-Point Boundary Value Problem (TPBVP) that governs both state and costate dynamics within a system of ordinary differential equations (ODEs). Learning Optimal Control Strategies with Pontryagin Neural Networks (PoNNs): The unknown solutions of the TPBVP are then modeled using neural networks, enabling Pontryagin Neural Networks (PoNNs) to learn optimal control strategies directly. This approach eliminates the need for separate interpolation, offering higher accuracy and reduced computational load compared to classical numerical methods. Validation and Reliability Assessment: If preliminary results is demonstrated to be promising, a dedicated phase of the PhD research will focus on demonstrating the reliability of the inference model. This involves: Developing a rigorous validation procedure to ensure the model produces expected results under nominal conditions. Assessing generalization capabilities and robustness against uncertainties. Stability Analysis of Model Predictive Control (MPC) Loop In parallel, we will ensure the stability of the MPC loop based on the inference model. This step is critical to guarantee real-time applicability and robust performance in dynamic orbital environments. This methodology integrates theoretical optimality with neural networks efficiency , providing an autonomous, fuel-optimal MPC controller for collision avoidance in space missions. The main contribution will consist in optimal collision avoidance guidance algorithms which account for operational constraints (e.g., propulsion limits, battery charge, and eclipse periods). Such contribution to Space traffic management will support the broader goals of SSA and sustainable space operations opening opportunities to reduce reliance on human intervention, enabling autonomous decision-making for frequent conjunction events, particularly in large satellite constellations. We aim to develop robust stable Model Predictive Controller for CAM that integrates a Pontryagin Neural Network (PoNN) with real-time applicability. To this goal, PoNN capable of solving Two-Point Boundary Value Problems (TPBVPs) with higher accuracy and lower computational cost compared to traditional numerical methods will be developed. It will be demonstrated that PoNNs can learn open-loop control strategies directly from the TPBVP ,eliminating the need for separate interpolation and reducing computational overhead. This PoNN inference model will be rigorously validated ensuring that it reliably produces expected results under nominal conditions. Also benchmarks against state-of-the-art tools will be performed. 4. REFERENCES A. D’Ambrosio, E. Schiassi, F. Curti, and R. Furfaro. Pontryagin neural networks with functional interpolation for optimal intercept problems. Mathematics, 9:996, 2021. doi:10.3390/math9090996. A. De Vittori, M. F. Palermo, P. Lizia, and R. Armellin. Low-thrust collision avoidance maneuver optimization. Journal of Guidance, Control, and Dynamics, 2022. doi:10.2514/1.G006630. J. Gonzalo, C. Colombo, and P. Lizia. Analytical framework for space debris collision avoidance maneuver design. Journal of Guidance, Control, and Dynamics, 2020. doi:10.2514/1.G005398. Z. Pavanello, L. D. Maria, A. De Vittori, M. Maestrini, P. Lizia, and R. Armellin. Cammary: A review of spacecraft collision avoidance manoeuvre design methods. Acta Astronautica, 2025. doi:10.1016/j.actaastro.2025.07.027. R. G. Sanfelice and B. Altın. Model predictive control of hybrid dynamical systems. IEEE Transactions on Automatic Control, 71:5112–5127, 2026. doi:10.1109/TAC.2026.3674015. E. Schiassi, F. Calabr`o, and D. D. De Falco. Pontryagin neural networks for the class of optimal control problems with integral quadratic cost. Aerospace Research Communications, 2024. doi:10.3389/arc.2024.13151. M. Schwenzer, M. Ay, T. Bergs, and D. Abel. Review on model predictive control: An engineering perspective. The International Journal of Advanced Manufacturing Technology, 117:1327–1349, 2021. doi:10.1007/s00170-021-07682-3. Where to apply Website: https://edd-projets.utoulouse.fr Requirements Research Field: Engineering » Aerospace engineering Education Level: Master Degree or equivalent Skills/Qualifications M.Sc. graduated fellow in Aerospace/Space Engineering is required . Knowledge of astrodynamics, machine-learning, optimization and scientific computing are highly appreciated for this position. Curiosity and openness of mind towards learning and implementing state-of-the-art numerical methods and algorithms is required. A proficient English level (C1) is required to favour scientific diffusion and international collaboration. Languages: ENGLISH Level: Excellent Research Field: Engineering » Aerospace engineering; Engineering » Control engineering Internal Application form(s) needed: projetTheseBEST20267.pdf (English, 113.03 KB - PDF) Additional Information Benefits EMPLOYMENT CONDITIONS Contract: Full-time, 36-month fixed-term French doctoral employment contract with an implementing partner (UT, UT Capitole, UT2J, ISAE, INP, INSA, IMT-MA, ENAC, INSERM, IRD, INRAE, INUC). Salary: Competitive net monthly salary for a BEST PhD fellow under French doctoral contract conditions is approximately €2,800 before income tax (see detail on application guide). Allowances: Monthly travel and mobility allowance (€350). Eligibility criteria Academic Requirements: By the call deadline, candidates must hold a master’s degree or equivalent diploma; and must not hold a doctoral degree. Mobility Rule: Applicants must not have resided or conducted their primary activity (work, studies, etc.) in the France for more than 12 months in the 36 months preceding the call deadline. Periods of stay as a tourist, refugee, or time spent in national service, are not considered as residency. Selection process TIMELINE Call for application opens: 21 September 2026 Submission deadline: 23 November 2026 12:00 PM Paris time (UTC +2) Eligibility check: 24 November - 30 November 2026 Written evaluation : December 4th to Janyary 15th Consolidation of pre-selected projects : January 19th to March 19th Oral evaluation: March 29th to April 4th Notification of results: From April 9th 2027 Additional comments The application must be submitted on the website https://edd-projets.utoulouse.fr/ . The submission deadline is 23rd November at 12:00 PM CET . The description of the PhD project is available here (click on the English version): https://adum.fr/as/ed/voirproposition.pl?site=toulouse&matricule_prop=76476#version Information about the recruitment process will also be available here: https://doctorat.univ-toulouse.fr/cofund-best . (click on the English version) If there are any questions on the process, please send a message to best-helpdesk@utoulouse.fr Website for additional job details: https://doctorat.univ-toulouse.fr/cofund-best Work Location(s) Number of offers available: 1 Company/Institute: Laboratory for Analysis and Architecture of Systems, Université de Toulouse Country: France City: Toulouse Postal Code: 31400 Street: 7 Av. du Colonel Roche Contact State/Province: Sevilla City: Sevilla Website: https://www.us.es/ ; https://www.utoulouse.fr Street: San Fernando 4 Postal Code: 41004