Dynamical System (DS) based Learning from Demonstration (LfD) allows learning of reactive motion policies with stability and convergence guarantees from a few trajectories. Yet, current DS learning techniques lack the flexibility to generalize to new task instances as they ignore explicit task parameters that inherently change the underlying trajectories. In this work, we propose Elastic-DS, a novel DS learning and generalization approach that embeds task parameters into the Gaussian Mixture Model (GMM) based Linear Parameter Varying (LPV) DS formulation. Central to our approach is the Elastic-GMM, a GMM constrained to SE(3) task-relevant frames. Given a new task instance/context, the Elastic-GMM is transformed with Laplacian Editing and used to re-estimate the LPV-DS policy. Elastic-DS is compositional in nature and can be used to construct flexible multi-step tasks. We showcase its strength on a myriad of simulated and real-robot experiments while preserving desirable control-theoretic guarantees.

A 1-min spotlight video introducing Elastic-DS

The video has a series of robot experiments showing the ability of Elastic-DS to learn from a single demonstration and generalize to different task instances with converging guarantees. The last two videos show the compositional ability of Elastic-DS.

A robot experiment in the bookshelf task showcases the ability to recover from large disturbances and the property of converging guaranteed. It is able to generate a new motion policy that adapts to a new bookshelf instance (the opening faces upward) without new demonstrations.

Given a single demonstration, our approach, Elastic-DS, can generalize to new task configurations while other approaches require more demonstrations to adapt.

@article{li2023task,

    title={Task Generalization with Stability Guarantees via Elastic Dynamical System Motion Policies}, 

    author={Tianyu Li and Nadia Figueroa},

    year={2023},

    eprint={2309.01884},

    archivePrefix={arXiv},

    primaryClass={cs.RO}

}