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

翻译：基于演示学习的动力学系统方法允许从少量轨迹中学习具有稳定性和收敛保证的反应式运动策略。然而，当前的动力学系统学习技术缺乏泛化到新任务实例的灵活性，因为它们忽略了本质上改变底层轨迹的显式任务参数。本文提出弹性动力学系统——一种新颖的动力学系统学习与泛化方法，它将任务参数嵌入到基于高斯混合模型的线性参数变化动力学系统框架中。该方法的核心是弹性高斯混合模型，一种约束在SE(3)任务相关坐标框架上的高斯混合模型。给定新的任务实例/上下文，通过拉普拉斯编辑对弹性高斯混合模型进行变换，并用于重新估计线性参数变化动力学系统策略。弹性动力学系统本质上具有组合性，可用于构建灵活的多步骤任务。我们在大量仿真与真实机器人实验中展示了其优势，同时保留了控制理论中所需的保证。补充视频见 https://sites.google.com/view/elastic-ds