Task Generalization with Stability Guarantees via Elastic Dynamical
  System Motion Policies
Tianyu Li Nadia Figueroa
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