HJ-SafeDMP: Hamilton-Jacobi Reachability-Guided Dynamic Movement Primitives for Provably Safe Robot Motion

2026-06-27

AI Summary

This work addresses the lack of formal safety guarantees in Dynamic Movement Primitives (DMPs) for safety-critical applications and the computational intractability of traditional Hamilton–Jacobi reachability analysis for real-time deployment. The authors propose a novel framework that integrates DMPs with a learned safety value function: a Control Barrier Value Function (CBVF) is trained offline using expectile regression to avoid out-of-distribution queries, and conformal prediction is employed to provide probabilistic safety guarantees with finite-sample validity. At runtime, a closed-form safety controller modulates the DMP output without requiring online optimization. Experiments on a 7-degree-of-freedom robotic arm demonstrate that the method achieves several orders of magnitude faster execution than optimization-based baselines while preserving the robustness and adaptability of DMPs and offering provable safety assurances.

Abstract

Robots deployed in safety-critical environments must execute motions that are simultaneously robust to disturbances and provably safe from collisions. Dynamic Movement Primitives (DMPs) offer inherent stability, temporal flexibility, and efficient trajectory generalization from single demonstrations, but they lack formal safety certificates. Conversely, Hamilton-Jacobi (HJ) Reachability analysis provides a principled framework for computing worst-case safety margins and forward-invariant safe sets, but classical grid-based methods suffer from the curse of dimensionality and are impractical for real-time control. This paper introduces HJ-SafeDMP, a framework that integrates DMPs with learned HJ Reachability-based safety value functions to achieve provably safe, robust, and computationally efficient robot motion. We learn a Control Barrier Value Function (CBVF) from offline demonstration data using a model-free, finite-difference HJ recursion and deploy it as a real-time safety filter via a closed-form control law that modulates the DMP output. Unlike optimization-based CBF-QP approaches, our method achieves safety filtering without online quadratic program solves, preserving the computational efficiency of DMPs. We further incorporate an expectile-based offline learning objective that avoids querying out-of-distribution actions, and a conformal prediction calibration step that provides finite-sample probabilistic safety coverage. Experimental evaluation on a 7-DOF robot manipulator demonstrates that HJ-SafeDMP achieves formal safety guarantees with orders-of-magnitude faster execution than optimization-based baselines, while maintaining the robustness and adaptability of DMPs for human-robot interaction.

Problem

• Safe robot motion
• Dynamic Movement Primitives
• Hamilton-Jacobi Reachability
• Formal safety guarantees
• Real-time control

Innovation

• Hamilton-Jacobi Reachability
• Dynamic Movement Primitives
• Control Barrier Value Function
• Conformal Prediction
• Real-time Safety Filtering