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Trajectory Optimization on the SE(3) Tangent Space

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# Whole-Body Trajectory Optimization in the SE(3) Tangent Space

## Overview

Agile whole-body motion generation for legged and humanoid robots remains a fundamental challenge in robotics. This repository implements a trajectory optimization framework that formulates the robot's floating-base dynamics in the tangent space of SE(3), enabling efficient optimization using standard off the self NLP solvers (IPOPT) without requiring manifold-specific techniques.

The implementation supports whole-body dynamics, contact constraints and terrain modeling while leveraging analytical derivatives via the Pinocchio library.

See more at [https://lar.upatras.gr/projects/ibrics.html](https://lar.upatras.gr/projects/ibrics.html).

## Results

You can find a video summarizing the approach and results at [https://www.youtube.com/watch?v=zBJSsiUExCw](https://www.youtube.com/watch?v=zBJSsiUExCw).

The videos below showcase various motions that were generated using the implemented trajectory optimization solver. The code for each particular motion can be found under `src/examples/agile_exps/`.

### Jump
https://github.com/user-attachments/assets/47698c0f-a3dd-43d8-beb0-040ad7d6c012

### Backflip
https://github.com/user-attachments/assets/be5b7db3-2185-4c06-8226-fc28839872ab

### Handstand
https://github.com/user-attachments/assets/fab747f8-0eb0-4b04-819b-5b10ca46a669

### Hopscotch
https://github.com/user-attachments/assets/f579ce10-0d2a-4a95-9d9b-9fb9b3147b29

### Sideflip
https://github.com/user-attachments/assets/31e9e250-8758-4190-8677-22f8fd361e7c

### Walk
https://github.com/user-attachments/assets/eb647602-af8b-4d3d-903f-c3fedc6d0f09

## Maintainers

- Evangelos Tsiatsianas (University of Patras) - etsiatsianas@ac.upatras.gr
- Konstantinos Chatzilygeroudis (University of Patras) - costashatz@upatras.gr

## Publication & Citation

This trajectory optimization solver was developed as part of our research on floating-base space parameterizations for agile whole-body motion planning. The work has been published in (also available on [arXiv](https://arxiv.org/abs/2508.11520)):

**A Comparative Study of Floating-Base Space Parameterizations for Agile Whole-Body Motion Planning**  
*Evangelos Tsiatsianas, Chairi Kiourt, Konstantinos Chatzilygeroudis*  
IEEE-RAS International Conference on Humanoid Robots (Humanoids), 2025

If you use this code in a scientific publication, please use the following citation:

```bibtex
@inproceedings{tsiatsianas2025comparative,
      title={{A Comparative Study of Floating-Base Space Parameterizations for Agile Whole-Body Motion Planning}},
      author={Tsiatsianas, Evangelos and Kiourt, Chairi and Chatzilygeroudis, Konstantinos},
      booktitle={IEEE-RAS International Conference on Humanoid Robots (Humanoids)},
      year={2025}
    }
```

## Install on your system

### Installation
We recommend using [Conda](https://docs.conda.io/) for managing dependencies.

#### Create and activate the environment
- `conda create -p ./.conda/ python=3.13`
- `conda activate ./.conda`

#### Install dependencies
Use `conda install conda-forge::"package_name"` to install the following packages:
  - pinocchio
  - meshcat-python
  - cyipopt
  - example-robot-data
  - matplotlib

### Usage

- `conda activate .conda`
- `export PYTHONPATH=$(pwd)/src`
- `python src/examples/talos_trajopt.py --vis`

use `--vis` option to visualize the results with meshcat

## Projects using SE3_TrajOpt

- [AHMP](https://github.com/hucebot/ahmp): Motion Planning and Contact Discovery based on Mixed-Distribution Cross-Entropy Method.

## Acknowledgments

This work has been partially supported by project MIS 5154714 of the National Recovery and Resilience Plan Greece 2.0 funded by the European Union under the NextGenerationEU Program.

This work was conducted within the [Laboratory of Automation and Robotics](https://lar.ece.upatras.gr/) (LAR), Department of Electrical and Computer Engineering, and [Archimedes Research Unit](https://archimedesai.gr/en/), RC Athena, Greece.

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