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
this https URL

弹性动态系统（Elastic-DS）是一种新颖的基于动态系统的学习与泛化方法，将任务参数嵌入到基于高斯混合模型（GMM）和线性参数变化（LPV）动态系统的公式中，并通过弹性高斯混合模型与 Laplacian Editing 的转换重新估计 LPV-DS 策略。该方法在多个模拟和真实机器人实验中展示了其强大能力，并保留了合理的控制理论保证。