Quaternion DMP with Controllable Final Angular Velocity for Robot Skill Generalization

Dynamic Movement Primitives (DMPs) are widely used for learning and generalizing robot skills. However, standard quaternion DMPs, when modeling orientation trajectories, constrain only the final orientation and cannot freely specify the final angular velocity. This limitation restricts its application to dynamic tasks requiring precise boundary conditions, such as hitting or throwing. Although existing improved methods achieve velocity generalization to some extent, they often struggle to balance trajectory shape preservation with dynamic smoothness, frequently causing significant deviation from demonstrations or abrupt acceleration discontinuities. In this paper, we propose a novel robot skill generalization method that enables controllable final angular velocity for quaternion DMPs. Specifically, we construct a dynamic goal system driven by a quintic polynomial in Lie algebra space, analytically planning the target orientation’s evolution based on given multi-order boundary constraints. This mechanism not only achieves precise control over the final angular velocity but also inherently guarantees global C² continuous dynamics across primitive segments. Comparative simulations and real-world robot hitting experiments demonstrate that, compared to existing approaches, our proposed method effectively satisfies dynamic boundary constraints while exhibiting superior shape preservation, minimal trajectory deviation, and higher smoothness, thereby significantly improving skill generalization performance in complex dynamic tasks.