SU Decomposition

This repository contains a Python implementation of the SU-decomposition, which can be used to compute a coordinate-invariant local representation for rigid-body motion and force trajectories. This representation is referred to as the Dual-Upper-Triangular Invariant Representation (DUTIR).

The implementation is intended for trajectory analysis, identification, and generalization across coordinate systems. It provides tools for preprocessing trajectory data, computing screw trajectories, applying the SU-decomposition, and visualizing the resulting representations.

A detailed description of the method is provided in the corresponding paper:

A Coordinate-Invariant Local Representation of Motion and Force Trajectories for Identification and Generalization Across Coordinate Systems

A preprint is available on arXiv.

Installation

The project requires Python 3.10 or newer.

Clone the repository and install the required dependencies:

git clone https://github.com/arnoverduyn/SU_decomposition.git
cd SU_decomposition
pip install -r requirements.txt

The core implementation is located in src/sulib.

Repository structure

SU_decomposition/
├── data/
│   └── demos/
│       ├── contour_following/
│       ├── peg_on_hole_alignment/
│       ├── pouring/
│       └── pouring_objects/
│
├── figures/
│
├── notebooks/
│
├── scripts/
│   ├── example_SU_calculation_force.py
│   └── example_SU_calculation_motion.py
│
├── src/
│   └── sulib/
│       ├── _data_handling.py
│       ├── _plotting.py
│       ├── _preprocessing.py
│       ├── _robotics.py
│       └── su_decomp.py
│
├── tests/
│   └── test_su_decomp.py
│
├── pyproject.toml
├── requirements.txt
├── LICENSE
└── README.md

Package modules (public)

• sulib.su_decomp — core SU-decomposition and DUTIR computation.

Package modules (internal)

• sulib._robotics — robotics-related operations for rigid-body trajectories.
• sulib._preprocessing — trajectory preprocessing utilities.
• sulib._data_handling — loading and handling trajectory data.
• sulib._plotting — visualization utilities.

SU-decomposition

The function sulib.su_decomp.compute_dutir_from_screw_traj() takes screw trajectories as input. For motion, these screw trajectories correspond to twist trajectories. For force/torque data, they correspond to wrench trajectories.

For motion data provided as a pose trajectory, sulib.su_decomp.compute_dutir_from_pose_traj() first computes the corresponding twist trajectory and then computes the DUTIR from this twist trajectory.

Conceptually:

Rigid-body pose trajectory
          │
          ▼
    Twist trajectory                         Wrench trajectory
          │                                         │
          ▼                                         ▼
   SU-decomposition                          SU-decomposition
          │                                         │
          ▼                                         ▼
DUTIR of rigid-body motion               DUTIR of force/torque data

More generally, the SU-decomposition can be applied directly to either a twist or wrench trajectory:

Examples

The notebooks/ directory contains numerical examples and demonstrations.

Additional example scripts are provided in scripts/:

Reference

If you use this implementation in academic work, please cite the associated paper:

A Coordinate-Invariant Local Representation of Motion and Force Trajectories for Identification and Generalization Across Coordinate Systems

Preprint: arXiv:2604.10241

License

This project is distributed under the license specified in LICENSE.