Dynamic Movement Primitives (DMP) have found remarkable applicability and success in various robotic tasks, which can be mainly attributed to their generalization, modulation and robustness properties. However, the spatial generalization of DMP can be problematic in some cases, leading to excessive overscaling and in turn large velocities and accelerations. While other DMP variants have been proposed in the literature to tackle this issue, they can also exhibit excessive overscaling as we show in this work. Moreover, incorporating intermediate points (via-points) for adjusting the DMP trajectory to account for the geometry of objects related to the task, or to avoid or push aside objects that obstruct a specific task, is not addressed by the current DMP literature. In this work we tackle these unresolved so far issues by proposing an improved online spatial generalization, that remedies the shortcomings of the classical DMP generalization, and moreover allows the incorporation of dynamic via-points. This is achieved by designing an online adaptation scheme for the DMP weights which is proved to minimize the distance from the demonstrated acceleration profile to retain the shape of the demonstration, subject to dynamic via-point and initial/final state constraints. Extensive comparative simulations with the classical and other DMP variants are conducted, while experimental results validate the practical usefulness and efficiency of the proposed method.

动态运动基元（DMP）在各种机器人任务中具有显着的适用性和成功，这主要归功于它们的泛化、调制和鲁棒性特性。然而，DMP 的空间泛化在某些情况下可能会出现问题，导致过度缩放，进而导致较大的速度和加速度。虽然文献中提出了其他 DMP 变体来解决此问题，但正如我们在这项工作中所示，它们也可能表现出过度的过度缩放。此外，当前的 DMP 文献没有解决合并中间点（通过点）来调整 DMP 轨迹以考虑与任务相关的对象的几何形状，或者避免或推开阻碍特定任务的对象。在这项工作中，我们通过提出改进的在线空间泛化来解决这些迄今为止尚未解决的问题，它弥补了经典 DMP 泛化的缺点，而且允许合并动态过点。这是通过为 DMP 权重设计在线自适应方案来实现的，事实证明，该方案可以最小化与演示加速度曲线的距离，以保持演示的形状，并受到动态经由点和初始/最终状态约束的影响。与经典和其他 DMP 变体进行了广泛的比较模拟，而实验结果验证了所提出方法的实际用途和效率。