From Movement Primitives to Distance Fields to Dynamical Systems

📄 Paper | 🌐 Interactive Webpage

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A simple module to represent trajectories using quadratic splines, enabling smooth transitions from movement primitives to distance fields and dynamical systems—all with analytical gradients and PyTorch/JAX support.

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What is this?

This project provides a simple and lightweight implementation to convert a trajectory into:

• Movement Primitives (MP)
• Distance Fields (DF)
• Dynamical Systems (DS)

by representing it as a series of concatenated quadratic splines. Thanks to the analytical gradients, it's easy to compute distances and directions at any point around the trajectory.

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Key Features

• ✅ Minimal dependencies (built with PyTorch, no heavy libraries needed)
• ✅ Optional JAX implementation with matching API
• ✅ Fully vectorized and parallelizable
• ✅ Supports gradient-based learning, optimization, and control
• ✅ Efficient computation

Requirements

• pytorch
• numpy
• matplotlib
• jax (optional, for JAX version)

Project Structure

File	Description
data	Trajectories for testing
quadratic_spline.py	Core implementation of spline representation and gradient computation
quadratic_spline_jax.py	JAX version of the core spline implementation (API aligned with PyTorch version)
run_mp_df_ds.py	Example: Convert a quadratic spline into distance field, and dynamical system
run_mp_df_ds_jax.py	JAX example mirroring run_mp_df_ds.py
run_single_traj.py	Similar to above, but for a trajectory that represented using discrete points
run_multiple_traj.py	Combine and fuse multiple trajectories
run_LASA.py	Run experiments on the LASA dataset (requires pylasadataset)

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Citation

If you find this work useful in your research, please cite:

@article{Li25RAL,
    author={Li, Y. and Calinon, S.},
    title={From Movement Primitives to Distance Fields to Dynamical Systems},
    journal={{IEEE} Robotics and Automation Letters ({RA-L})},
    year={2025},
    volume={10}, 
    number={9},
    pages={9550--9556},
    doi={10.1109/LRA.2025.3595073}
}

This code is maintained by Yiming LI and licensed under the MIT License.

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