  Learning from Demonstration (LfD) stands as an efficient framework for
imparting human-like skills to robots. Nevertheless, designing an LfD framework
capable of seamlessly imitating, generalizing, and reacting to disturbances for
long-horizon manipulation tasks in dynamic environments remains a challenge. To
tackle this challenge, we present Logic Dynamic Movement Primitives
(Logic-DMP), which combines Task and Motion Planning (TAMP) with an optimal
control formulation of DMP, allowing us to incorporate motion-level via-point
specifications and to handle task-level variations or disturbances in dynamic
environments. We conduct a comparative analysis of our proposed approach
against several baselines, evaluating its generalization ability and reactivity
across three long-horizon manipulation tasks. Our experiment demonstrates the
fast generalization and reactivity of Logic-DMP for handling task-level
variants and disturbances in long-horizon manipulation tasks.
