# Safe and Optimal Variable Impedance Control via Certified Reinforcement Learning

arXiv: https://arxiv.org/abs/2511.16330 · HTML: https://mlsanity.com/paper/2511.16330/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 5 of its 18 references that are in the map.
- First posted on arXiv 20 Nov 2025.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 5 of 5)

- [Grounding DINO: Marrying DINO with Grounded Pre-Training for Open-Set Object Detection](https://mlsanity.com/paper/2303.05499/) (2023)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Dynamic Movement Primitives in Robotics: A Tutorial Survey](https://mlsanity.com/paper/2102.03861/) (2021)
- [RMPflow: A Computational Graph for Automatic Motion Policy Generation](https://mlsanity.com/paper/1811.07049/) (2018)

## Abstract (arXiv)

Reinforcement learning (RL) offers a powerful approach for robots to learn complex, collaborative skills by combining Dynamic Movement Primitives (DMPs) for motion and Variable Impedance Control (VIC) for compliant interaction. However, this model-free paradigm often risks instability and unsafe exploration due to the time-varying nature of impedance gains. This work introduces Certified Gaussian Manifold Sampling (C-GMS), a novel trajectory-centric RL framework that learns combined DMP and VIC policies while guaranteeing Lyapunov stability and actuator feasibility by construction. Our approach reframes policy exploration as sampling from a mathematically defined manifold of stable gain schedules. This ensures every policy rollout is guaranteed to be stable and physically realizable, thereby eliminating the need for reward penalties or post-hoc validation. Furthermore, we provide a theoretical guarantee that our approach ensures bounded tracking error even in the presence of bounded model errors and deployment-time uncertainties. We demonstrate the effectiveness of C-GMS in simulation and verify its efficacy on a real robot, paving the way for reliable autonomous interaction in complex environments.