Robots operating in human-centric environments must be both robust to disturbances and provably safe from collisions. Achieving these properties simultaneously and efficiently remains a central challenge. While Dynamic Movement Primitives (DMPs) offer inherent stability and generalization from single demonstrations, they lack formal safety guarantees. Conversely, formal methods like Control Barrier Functions (CBFs) provide provable safety but often rely on computationally expensive, real-time optimization, hindering their use in high-frequency control. This paper introduces SafeDMPs, a novel framework that resolves this trade-off. We integrate the closed-form efficiency and dynamic robustness of DMPs with a provably safe, non-optimization-based control law derived from Spatio-Temporal Tubes (STTs). This synergy allows us to generate motions that are not only robust to perturbations and adaptable to new goals, but also guaranteed to avoid static and dynamic obstacles. Our approach achieves a closed-form solution for a problem that traditionally requires online optimization. Experimental results on a 7-DOF robot manipulator demonstrate that SafeDMPs is orders of magnitude faster and more accurate than optimization-based baselines, making it an ideal solution for real-time, safe, and collaborative robotics.

翻译：在人类中心环境中运行的机器人必须兼具扰动鲁棒性和可证明的碰撞安全性，同时高效实现这两个特性仍是核心挑战。动态运动基元（DMPs）虽具备单次示教下的固有稳定性与泛化能力，但缺乏形式化安全保证。相反，控制障碍函数（CBFs）等形式化方法虽可提供可证明的安全性，却常依赖计算昂贵的实时优化，制约其在高频控制中的应用。本文提出SafeDMPs这一全新框架以解决此权衡问题。我们将DMP的闭式高效性与动态鲁棒性，与基于时空管（STTs）的可证明安全无优化控制律相结合。这种协同作用使得生成的运动不仅能够抵抗扰动、适应新目标，还可以保证避让静态与动态障碍物。本方法为传统需在线优化的问题提供了闭式解。在七自由度机器人操作臂上的实验结果表明，SafeDMPs比基于优化的基线方法快数个数量级且精度更高，成为实时安全协作机器人的理想方案。