Learning motion policies from expert demonstrations is an essential paradigm in modern robotics. While end-to-end models aim for broad generalization, they require large datasets and computationally heavy inference. Conversely, learning dynamical systems (DS) provides fast, reactive, and provably stable control from very few demonstrations. However, existing DS learning methods typically model isolated tasks and struggle to reuse demonstrations for novel behaviors. In this work, we formalize the problem of combining isolated demonstrations within a shared workspace to enable generalization to unseen tasks. The Gaussian Graph is introduced, which reinterprets spatial components of learned motion primitives as discrete vertices with connections to one another. This formulation allows us to bridge continuous control with discrete graph search. We propose two frameworks leveraging this graph: Stitching, for constructing time-invariant DSs, and Chaining, giving a sequence-based DS for complex motions while retaining convergence guarantees. Simulations and real-robot experiments show that these methods successfully generalize to new tasks where baseline methods fail.

翻译：从专家演示中学习运动策略是现代机器人学的重要范式。端到端模型虽追求广泛泛化能力，但需要大规模数据集且推理计算负担重。相反，从少量演示中学习动态系统（DS）能提供快速、响应式且可证明稳定的控制。然而，现有DS学习方法通常针对孤立任务建模，难以将演示复用于新行为。本研究将共享工作空间中孤立演示的组合问题形式化，以实现对未见任务的泛化。我们提出高斯图方法，将习得运动基元的空间分量重新解释为彼此连接的离散顶点。该形式化框架使我们能够将连续控制与离散图搜索相衔接。基于此图结构，我们提出两种框架：用于构建时不变动态系统的"缝合"框架，以及为复杂运动提供序列化动态系统同时保持收敛性保证的"链式"框架。仿真与真实机器人实验表明，这些方法能成功泛化至基线方法失效的新任务场景。