# CLF-RL: Control Lyapunov Function Guided Reinforcement Learning

arXiv: https://arxiv.org/abs/2508.09354 · HTML: https://mlsanity.com/paper/2508.09354/

## Key facts

- Cited by 5 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 15 of its 33 references that are in the map.
- First posted on arXiv 12 Aug 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, 15 of 15)

- [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)
- [Orbit: A Unified Simulation Framework for Interactive Robot Learning Environments](https://mlsanity.com/paper/2301.04195/) (2023)
- [Reinforcement Learning for Robust Parameterized Locomotion Control of Bipedal Robots](https://mlsanity.com/paper/2103.14295/) (2021)
- [Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Control](https://mlsanity.com/paper/2401.16889/) (2024)
- [Humanoid Parkour Learning](https://mlsanity.com/paper/2406.10759/) (2024)
- [Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functions](https://mlsanity.com/paper/2004.07584/) (2020)
- [Opt2Skill: Imitating Dynamically-feasible Whole-Body Trajectories for Versatile Humanoid Loco-Manipulation](https://mlsanity.com/paper/2409.20514/) (2024)
- [Lyapunov Design for Robust and Efficient Robotic Reinforcement Learning](https://mlsanity.com/paper/2208.06721/) (2022)
- [Learning Spring Mass Locomotion: Guiding Policies with a Reduced-Order Model](https://mlsanity.com/paper/2010.11234/) (2020)
- [Benchmarking Potential Based Rewards for Learning Humanoid Locomotion](https://mlsanity.com/paper/2307.10142/) (2023)
- [Integrating Model-Based Footstep Planning with Model-Free Reinforcement Learning for Dynamic Legged Locomotion](https://mlsanity.com/paper/2408.02662/) (2024)
- [3D Underactuated Bipedal Walking via H-LIP based Gait Synthesis and Stepping Stabilization](https://mlsanity.com/paper/2101.09588/) (2021)
- [Optimizing Bipedal Maneuvers of Single Rigid-Body Models for Reinforcement Learning](https://mlsanity.com/paper/2207.04163/) (2022)

## Built on by (most cited first, 5 of 5)

- [Chasing Stability: Humanoid Running via Control Lyapunov Function Guided Reinforcement Learning](https://mlsanity.com/paper/2509.19573/) (2025)
- [MARCH: Model-Assisted Reinforcement Learning for the Perceptive Control of Humanoids over Sparse Footholds](https://mlsanity.com/paper/2606.10288/) (2026)
- [Stability of Control Lyapunov Function Guided Reinforcement Learning](https://mlsanity.com/paper/2605.01978/) (2026)
- [Terrain Consistent Reference-Guided RL for Humanoid Navigation Autonomy](https://mlsanity.com/paper/2605.15517/) (2026)
- [ResSafe: Learning Safety Filtering with Residual Reinforcement Learning for Humanoids](https://mlsanity.com/paper/2609.15988/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) has shown promise in generating robust locomotion policies for bipedal robots, but often suffers from tedious reward design and sensitivity to poorly shaped objectives. In this work, we propose a structured reward shaping framework that leverages model-based trajectory generation and control Lyapunov functions (CLFs) to guide policy learning. We explore two model-based planners for generating reference trajectories: a reduced-order linear inverted pendulum (LIP) model for velocity-conditioned motion planning, and a precomputed gait library based on hybrid zero dynamics (HZD) using full-order dynamics. These planners define desired end-effector and joint trajectories, which are used to construct CLF-based rewards that penalize tracking error and encourage rapid convergence. This formulation provides meaningful intermediate rewards, and is straightforward to implement once a reference is available. Both the reference trajectories and CLF shaping are used only during training, resulting in a lightweight policy at deployment. We validate our method both in simulation and through extensive real-world experiments on a Unitree G1 robot. CLF-RL demonstrates significantly improved robustness relative to the baseline RL policy and better performance than a classic tracking reward RL formulation.