SafeDMPs: Integrating Formal Safety with DMPs for Adaptive HRI

Abstract

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.

Figures (7)

• Figure 3: Hardware setup featuring the Franka Research 3 robot equipped for human-robot interaction tasks. Illustration of SafeDMPs for adaptive Human Robot Interaction (HRI) in response to dynamic interference.
• Figure 4: Proposed framework pipeline. (a) Demonstrations are recorded in end-effector space. (b) DMPs encode the nominal motion plan. (c) Spatio-Temporal Tubes (STTs) define a safe envelope around the DMP. (d) During execution, trajectory deformation is triggered when obstacles are encountered, and the system safely reroutes motion within the STT while ensuring convergence.
• Figure 5: Simulation setup featuring the Franka robot performing tasks within a workspace containing obstacles.
• Figure 6: Perturbation response across methods. The plots illustrate the evolution of the end-effector trajectory over time (top) and the corresponding $X$, $Y$, and $Z$ coordinates (bottom) under external disturbances.
• Figure 7: Obstacle avoidance across methods with static obstacles. The plots show the evolution of the end-effector trajectory when static obstacles are introduced during execution (top) and the corresponding $X$, $Y$, and $Z$ coordinates (bottom).