# Constraint-Grounded Reinforcement Learning for Variable Impedance Control in Contact-Rich Robotic Insertion

arXiv: https://arxiv.org/abs/2609.13516 · HTML: https://mlsanity.com/paper/2609.13516/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 26 of its 50 references that are in the map.
- First posted on arXiv 11 Sep 2026.

## 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, 26 of 26)

- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World](https://mlsanity.com/paper/1703.06907/) (2017)
- [Learning Dexterous In-Hand Manipulation](https://mlsanity.com/paper/1808.00177/) (2018)
- [Sim-to-Real Transfer of Robotic Control with Dynamics Randomization](https://mlsanity.com/paper/1710.06537/) (2017)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [Efficient Off-Policy Meta-Reinforcement Learning via Probabilistic Context Variables](https://mlsanity.com/paper/1903.08254/) (2019)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems](https://mlsanity.com/paper/1705.01292/) (2017)
- [Making Sense of Vision and Touch: Self-Supervised Learning of Multimodal Representations for Contact-Rich Tasks](https://mlsanity.com/paper/1810.10191/) (2018)
- [ObjectFolder 2.0: A Multisensory Object Dataset for Sim2Real Transfer](https://mlsanity.com/paper/2204.02389/) (2022)
- [Variable Impedance Control in End-Effector Space: An Action Space for Reinforcement Learning in Contact-Rich Tasks](https://mlsanity.com/paper/1906.08880/) (2019)
- [IndustReal: Transferring Contact-Rich Assembly Tasks from Simulation to Reality](https://mlsanity.com/paper/2305.17110/) (2023)
- [Reinforcement Learning on Variable Impedance Controller for High-Precision Robotic Assembly](https://mlsanity.com/paper/1903.01066/) (2019)
- [Meta-Reinforcement Learning for Robotic Industrial Insertion Tasks](https://mlsanity.com/paper/2004.14404/) (2020)
- [Robust Multi-Modal Policies for Industrial Assembly via Reinforcement Learning and Demonstrations: A Large-Scale Study](https://mlsanity.com/paper/2103.11512/) (2021)
- [Variable Compliance Control for Robotic Peg-in-Hole Assembly: A Deep Reinforcement Learning Approach](https://mlsanity.com/paper/2008.10224/) (2020)
- [A Survey of Robot Manipulation in Contact](https://mlsanity.com/paper/2112.01942/) (2021)
- [AutoMate: Specialist and Generalist Assembly Policies over Diverse Geometries](https://mlsanity.com/paper/2407.08028/) (2024)
- [FORGE: Force-Guided Exploration for Robust Contact-Rich Manipulation under Uncertainty](https://mlsanity.com/paper/2408.04587/) (2024)
- [Constraint-Conditioned Policy Optimization for Versatile Safe Reinforcement Learning](https://mlsanity.com/paper/2310.03718/) (2023)
- [Variable impedance control and learning -- A review](https://mlsanity.com/paper/2010.06246/) (2020)
- [Integrating LLMs and Digital Twins for Adaptive Multi-Robot Task Allocation in Construction](https://mlsanity.com/paper/2506.18178/) (2025)
- [From Perception to Symbolic Task Planning: Vision-Language Guided Human-Robot Collaborative Structured Assembly](https://mlsanity.com/paper/2601.00978/) (2026)
- [Learning Diffusion Policies for Robotic Manipulation of Timber Joinery under Fabrication Uncertainty](https://mlsanity.com/paper/2511.17774/) (2025)

## Built on by (most cited first, 1 of 1)

- [From Documented Strengths to Force Limits: Material-Informed Robotic Insertion for Construction Assembly](https://mlsanity.com/paper/2609.22609/) (2026)

## Abstract (arXiv)

In robotic insertion under uncertain contact, the axial force limit and the appropriate controller gain vary across tasks. As a result, a single fixed gain is unlikely to remain suitable across different task conditions, making conventional impedance controllers reliant on manual retuning. To eliminate manual retuning, we propose Constraint-Grounded Reinforcement Learning (CG-RL), a variable impedance framework for online gain adaptation. Conditioned on the force limit and contact feedback, the policy outputs a residual motion, an insertion rate, and a requested gain. The controller projects this gain into the admissible range without exposing the range itself to the policy. This separation allows a single policy to operate under different force limits without retraining or manual retuning. We evaluate CG-RL on simulated oblique insertion across five training seeds. CG-RL achieves an 85.8±7.7% (mean ± SD) success rate of insertions without violating the force limit, while keeping the applied gain within the admissible range. As a comparison, a fixed-gain baseline using the midpoint gain achieves a success rate of 50.1%. The policy adapts its insertion rate continuously to the specified force limit and further generalizes to more permissive force limits above the training range. In contrast, the same actor without force-limit input does not exhibit this adaptation. The applied gain is guaranteed to remain within the admissible range, while force-limit satisfaction is validated empirically rather than guaranteed formally.