Elara is a MATLAB toolbox for efficient simulation and integration of rigid-flexible robotic systems. It can handle multibody systems with a tree structure. Each link can be either rigid or flexible, and each joint can be actuated. Additionally, flexible links can be tendon-actuated, allowing for modeling of custom continuum-robot systems.

The simulation is based on the Lie-Group Variational Integrator proposed by Herrmann and Kotyczka and features superior numerical stability even for longer time-step choices. The same integrator also serves as the foundation of the optimal control approaches built in the toolbox.

• Efficient simulation of rigid and flexible-link dynamics
• Optimal control framework for trajectory planning
• Optional symbolic implementation using CasADi (for fast derivatives of the equations of motion for example)

The current implementation is available in MATLAB (verified in R2025b) in the Elara repository.

⚠️ Work in progress: We are planning some further improvements to increase accessibility. A full release is scheduled for July 2026

If you use the Elara toolbox in your research, please cite:

BibTeX:

@article{HK24,
  title = {Relative-Kinematic Formulation of Geometrically Exact Beam Dynamics Based on {{Lie}} Group Variational Integrators},
  author = {Herrmann, Maximilian and Kotyczka, Paul},
  year = 2024,
  month = dec,
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {432},
  pages = {117367},
  issn = {00457825},
  doi = {10.1016/j.cma.2024.117367},
}
@inproceedings{HPK26,
  title = {Discrete {{Geometric Modeling}} and {{Extended State Estimation}} of {{Continuum Robots}}},
  booktitle = {IFAC World Congress},
  author = {Herrmann, Maximilian and Pfeiffer, Leander and Kotyczka, Paul},
  year = 2026,
  address = {Busan},
  }

APA:

Herrmann, M., & Kotyczka, P. (2024). Relative-kinematic formulation of geometrically exact beam dynamics based on Lie group variational integrators. Computer Methods in Applied Mechanics and Engineering, 432, 117367. https://doi.org/10.1016/j.cma.2024.117367

Herrmann, M., Pfeiffer, L., & Kotyczka, P. (2026). Discrete Geometric Modeling and Extended State Estimation of Continuum Robots. IFAC World Congress.

This project is licensed under the MIT License - see LICENSE file for details.

• Maximilian Herrmann [TUM, Chair of Automatic Control]
• Leander Pfeiffer [TUM, Chair of Automatic Control]

For questions, issues, or feature requests:

• Open an issue on GitHub
• Contact: [maximilian.herrmann@tum.de, leander.pfeiffer@tum.de]