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Stage - Non-linear Optimizer for the Dynamic generation of trajectories H/F

Vacancy details

General information


The French Alternative Energies and Atomic Energy Commission (CEA) is a key player in research, development and innovation in four main areas :
• defence and security,
• nuclear energy (fission and fusion),
• technological research for industry,
• fundamental research in the physical sciences and life sciences.

Drawing on its widely acknowledged expertise, and thanks to its 16000 technicians, engineers, researchers and staff, the CEA actively participates in collaborative projects with a large number of academic and industrial partners.

The CEA is established in ten centers spread throughout France



Position description


Mathematics, information, scientific, software



Job title

Stage - Non-linear Optimizer for the Dynamic generation of trajectories H/F


Non-linear Optimizer for the Dynamic generation of trajectories of an AGV fleet in a logistics context

Contract duration (months)


Job description

This internship is a continuation of research carried out to automate a fleet of vehicles designed to efficiently supply shelving in logistics warehouses, while guaranteeing the safety of people and property ([1], [2], [3]).

The mobile robot evolves in the presence of traditional static obstacles (walls, shelving, stored crates...) but also dynamic obstacles such as other robots or human operators. The objective is to share the workspace between mobile robot(s) and human(s) by performing a dynamic re-planning of the robot's trajectory, secure and efficient, in a partially known environment. Indeed, in a real operating context, uncertainty remains about robot positions and communication delays.

The SLSQP (Sequential Least Squares Quadratic Programming) optimizer used for optimizing trajectories is gradient-based, meaning it requires the derivatives of objective functions and constraints to find a solution. Some observed instabilities of this algorithm might be correlated to the round-off errors from numerical differentiation. Also, in cases where the computation time reserved for finding a solution elapses before the convergence of the optimizer, the solution from the last iteration could not be safely used, since it is not guaranteed to respect the non-linear problem constraints.
That is why, other solutions (CFSQP [3], g2o [4] or artificial neural network) will be investigated for solving this constrained optimization problem.

First, the student will have to take in hand an approach to generating movements on a sliding horizon, distributed to a fleet of robots communicating with each other. This method, developed under ROS Gazebo, will then be modified with the use of a new solution (deterministic or machine learning) to solve the constrained optimization problem.

Thus, the student will have to:
Ø  Adopt the proposed dynamic trajectory planning method and the associated state of the art;
Ø  Increase the initial method in a Gazebo simulation environment, based on a new optimizer.

Profile of the candidate         
- Knowledge of robotics: modeling, control, planning;
- Knowledge of C++ computer programming under ROS Gazebo;
- Fluency in French and English.

[1]       José MENDES FILHO. Planification de Mouvements en Ligne et Distribuée de Systèmes Multi-Robots Mobiles. PhD Thesis, 2019.
[2]       Debord, A. and Lucet, E. and Ben Amar, F. (2016). Mobile Robot Behavior Adaptation in Navigation Space Shared with Human. Proc. of MCG 2016.
[3]       Sainte Catherine, M. and Lucet, E. A modified Hybrid Reciprocal Velocity Obstacles approach for multi-robot motion planning without communication. In Proceedings of IROS 2020.
[4]       Tits, A., Lawrence, C., and Zhou, J. (1999). User’s guide for cfsqp version 2.5: A c code for solving (large scale) constrained nonlinear (minimax) optimization problems, generating iterates satisfying all inequality constraints.

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Candidate criteria

Prepared diploma

Bac+5 - Master 2

Recommended training

Master Robotique ou équivalent ingénieur

PhD opportunity