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Dynamical System (DS) based Learning from Demonstration (LfD) allows learningof reactive motion policies with stability and convergence guarantees from afew trajectories. Yet, current DS learning techniques lack the flexibility togeneralize to new task instances as they ignore explicit task parameters thatinherently change the underlying trajectories. In this work, we proposeElastic-DS, a novel DS learning, and generalization approach that embeds taskparameters into the Gaussian Mixture Model (GMM) based Linear Parameter Varying(LPV) DS formulation. Central to our approach is the Elastic-GMM, a GMMconstrained to SE(3) task-relevant frames. Given a new task instance/context,the Elastic-GMM is transformed with Laplacian Editing and used to re-estimatethe LPV-DS policy. Elastic-DS is compositional in nature and can be used toconstruct flexible multi-step tasks. We showcase its strength on a myriad ofsimulated and real-robot experiments while preserving desirablecontrol-theoretic guarantees. Supplementary videos can be found athttps://sites.google.com/view/elastic-ds

Task Generalization with Stability Guarantees via Elastic Dynamical System Motion Policies