Task Generalization with Stability Guarantees via Elastic Dynamical System Motion Policies

TL;DR

Elastic-DS is a novel dynamical system learning method that incorporates task parameters into the model, enabling flexible generalization to new task instances while maintaining stability guarantees, demonstrated through various robot experiments.

Contribution

The paper introduces Elastic-DS, a new approach embedding task parameters into DS models for improved generalization, using Elastic-GMM constrained to task-relevant frames.

Findings

Successfully generalizes to new task instances

Maintains stability and convergence guarantees

Effective in simulated and real-robot experiments

Abstract

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. Supplementary videos can be found at https://sites.google.com/view/elastic-ds