# Variable Stiffness for Robust Locomotion through Reinforcement Learning

arXiv: https://arxiv.org/abs/2502.09436 · HTML: https://mlsanity.com/paper/2502.09436/

## 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 12 of its 17 references that are in the map.
- First posted on arXiv 13 Feb 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, 12 of 12)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning](https://mlsanity.com/paper/2109.11978/) (2021)
- [Rapid Locomotion via Reinforcement Learning](https://mlsanity.com/paper/2205.02824/) (2022)
- [DreamWaQ: Learning Robust Quadrupedal Locomotion With Implicit Terrain Imagination via Deep Reinforcement Learning](https://mlsanity.com/paper/2301.10602/) (2023)
- [Dynamics Randomization Revisited:A Case Study for Quadrupedal Locomotion](https://mlsanity.com/paper/2011.02404/) (2020)
- [Highly Dynamic Quadruped Locomotion via Whole-Body Impulse Control and Model Predictive Control](https://mlsanity.com/paper/1909.06586/) (2019)
- [GenLoco: Generalized Locomotion Controllers for Quadrupedal Robots](https://mlsanity.com/paper/2209.05309/) (2022)
- [Learning Torque Control for Quadrupedal Locomotion](https://mlsanity.com/paper/2203.05194/) (2022)
- [Torque-based Deep Reinforcement Learning for Task-and-Robot Agnostic Learning on Bipedal Robots Using Sim-to-Real Transfer](https://mlsanity.com/paper/2304.09434/) (2023)
- [Learning Variable Impedance Control for Contact Sensitive Tasks](https://mlsanity.com/paper/1907.07500/) (2019)
- [A Compact Variable Stiffness Actuator for Agile Legged Locomotion](https://mlsanity.com/paper/2308.13988/) (2023)

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

- [CoTaP: Compliant Task Pipeline and Reinforcement Learning of Its Controller with Compliance Modulation](https://mlsanity.com/paper/2509.25443/) (2025)

## Abstract (arXiv)

Reinforcement-learned locomotion enables legged robots to perform highly dynamic motions but often accompanies time-consuming manual tuning of joint stiffness. This paper introduces a novel control paradigm that integrates variable stiffness into the action space alongside joint positions, enabling grouped stiffness control such as per-joint stiffness (PJS), per-leg stiffness (PLS) and hybrid joint-leg stiffness (HJLS). We show that variable stiffness policies, with grouping in per-leg stiffness (PLS), outperform position-based control in velocity tracking and push recovery. In contrast, HJLS excels in energy efficiency. Despite the fact that our policy is trained on flat floor only, our method showcases robust walking behaviour on diverse outdoor terrains, indicating robust sim-to-real transfer. Our approach simplifies design by eliminating per-joint stiffness tuning while keeping competitive results with various metrics.