Master 2 Internship Proposal

Unified Modeling of Cable-Driven Robotic Endoscopes Based on Cosserat Theory

Supervisors: Y. Adagolodjo, J. Dequidt, H. Courtecuisse
Duration: 6 months
Location : DEFROST-Team Inria Université de Lille

Context

Flexible robotic endoscopes represent a major advancement in minimally invasive surgery, enabling access to difficult-to-reach anatomical areas while minimizing patient trauma. These complex devices consist of several critical components: an outer sheath, actuation cables, internal channels, and imaging systems.

Currently, endoscope modeling relies on segmented approaches where each component is treated independently, limiting simulation accuracy and complicating integration for real-time control. The ANR project in which this internship takes place aims to develop a unified modeling framework to represent the endoscope as a single flexible body actuated by cables, thereby simplifying simulation while maintaining high accuracy.

Internship Objectives

The main objective of this internship is to develop a unified hybrid model for a flexible robotic endoscope using Cosserat theory. Specifically, the intern will:

1. Master Cosserat theory: Understand the mathematical foundations of Cosserat theory and its application to flexible structure modeling, particularly its ability to describe coupled deformations (bending, stretching, twisting, shearing).
2. Reformulate equations of motion: Adapt the traditional Cosserat formulation (material space) to a generalized Cartesian coordinate system. This reformulation aims to maintain the efficiency of stiffness matrix computation while overcoming mass matrix limitations for real-time dynamic simulations.
3. Develop a unified model: Implement an integrated endoscope model that captures its nonlinear mechanical response and complex deformations during interaction with soft tissues, while considering cable actuation.
4. Validation and simulation: Implement the model in the SOFA framework (open-source) and validate its performance in terms of accuracy and computation time for real-time simulation applications.

Scientific Challenges

• Mathematical reformulation: Transform Cosserat equations from material space to a generalized Cartesian system while preserving essential mechanical properties.
• Computational efficiency: Ensure that the developed model is fast enough for real-time simulation applications, particularly for robotic control.
• Numerical stability: Ensure model stability under large nonlinear deformations, typical of endoscope-tissue interactions.
• Actuation integration: Correctly model cable actuation within the unified Cosserat framework.

Required Skills

• Strong background in continuum mechanics and numerical computation
• Proficiency in programming (C++, Python)
• Knowledge of numerical methods (finite elements, time integration)
• Interest in medical robotics and physical simulation
• Autonomy and ability to work on complex problems
• (Optional) Experience with simulation frameworks (SOFA, or similar)

Expected Work

1. Months 1-2: Comprehensive literature review on Cosserat theory, flexible endoscope models, and familiarization with the SOFA framework.
2. Months 2-3: Theoretical development of Cosserat equations reformulation in generalized Cartesian coordinates.
3. Months 3-5: Model implementation in SOFA, cable actuation integration, and validation tests.
4. Months 5-6: Performance optimization, comparative validation with existing models, internship report writing, and scientific paper contributions.

Deliverables

• Source code of the model implemented in SOFA (open-source plugin)
• Detailed internship report with theoretical analysis and experimental results
• Technical documentation for code reuse
• Contribution to a scientific publication on the obtained results

Work Environment

The internship will take place within a research team working on medical robotics and real-time simulation. The intern will benefit from:

• Close scientific supervision
• Access to computational infrastructure and laboratory equipment
• Integration into an ANR project with national collaborations
• Opportunity to present work at scientific conferences

Perspectives

This internship can lead to a PhD thesis within the ANR project framework, with prospects for publications in leading international conferences and journals in medical robotics and numerical simulation.

Key References

1. Adagolodjo, Y., Renda, F., & Duriez, C. (2021). “Coupling Numerical Deformable Models in Global and Reduced Coordinates for the Simulation of the Direct and the Inverse Kinematics of Soft Robots.” IEEE Robotics and Automation Letters, 6(2), 3910-3917. doi: 10.1109/LRA.2021.3061977
2. Ouyoucef, A., Peyron, Q., Zheng, G., & Boyer, F. (2025). “Modeling, analysis and design of an extensible planar parallel tendon actuated continuum robot.” 2025 IEEE 8th International Conference on Soft Robotics (RoboSoft), Lausanne, Switzerland, pp. 1-8. doi: 10.1109/RoboSoft63089.2025.11020851

Application

Interested candidates should send:

• Detailed CV
• Cover letter
• Master’s transcripts (M1 and M2 if available)
• Letter of recommendation (optional)

Contact: yinoussa.adagolodjo@inria.fr, jeremie.dequidt@inria.fr