# Smoothness as a Constraint for Stable Humanoid Locomotion

arXiv: https://arxiv.org/abs/2609.24552 · HTML: https://mlsanity.com/paper/2609.24552/

## 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 30 of its 35 references that are in the map.
- First posted on arXiv 21 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, 30 of 30)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning](https://mlsanity.com/paper/2109.11978/) (2021)
- [RMA: Rapid Motor Adaptation for Legged Robots](https://mlsanity.com/paper/2107.04034/) (2021)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [BeyondMimic: From Motion Tracking to Versatile Humanoid Control via Guided Diffusion](https://mlsanity.com/paper/2508.08241/) (2025)
- [IPO: Interior-point Policy Optimization under Constraints](https://mlsanity.com/paper/1910.09615/) (2019)
- [ASAP: Aligning Simulation and Real-World Physics for Learning Agile Humanoid Whole-Body Skills](https://mlsanity.com/paper/2502.01143/) (2025)
- [HOMIE: Humanoid Loco-Manipulation with Isomorphic Exoskeleton Cockpit](https://mlsanity.com/paper/2502.13013/) (2025)
- [Regularizing Action Policies for Smooth Control with Reinforcement Learning](https://mlsanity.com/paper/2012.06644/) (2020)
- [Mobile-TeleVision: Predictive Motion Priors for Humanoid Whole-Body Control](https://mlsanity.com/paper/2412.07773/) (2024)
- [Not Only Rewards But Also Constraints: Applications on Legged Robot Locomotion](https://mlsanity.com/paper/2308.12517/) (2023)
- [FALCON: Learning Force-Adaptive Humanoid Loco-Manipulation](https://mlsanity.com/paper/2505.06776/) (2025)
- [Learning Smooth Humanoid Locomotion through Lipschitz-Constrained Policies](https://mlsanity.com/paper/2410.11825/) (2024)
- [HuB: Learning Extreme Humanoid Balance](https://mlsanity.com/paper/2505.07294/) (2025)
- [Learning Humanoid Locomotion over Challenging Terrain](https://mlsanity.com/paper/2410.03654/) (2024)
- [CaT: Constraints as Terminations for Legged Locomotion Reinforcement Learning](https://mlsanity.com/paper/2403.18765/) (2024)
- [Learning and Deploying Robust Locomotion Policies with Minimal Dynamics Randomization](https://mlsanity.com/paper/2209.12878/) (2022)
- [SoftMimic: Learning Compliant Whole-body Control from Examples](https://mlsanity.com/paper/2510.17792/) (2025)
- [Hold My Beer: Learning Gentle Humanoid Locomotion and End-Effector Stabilization Control](https://mlsanity.com/paper/2505.24198/) (2025)
- [Gradient-based Regularization for Action Smoothness in Robotic Control with Reinforcement Learning](https://mlsanity.com/paper/2407.04315/) (2024)
- [Motion Priors Reimagined: Adapting Flat-Terrain Skills for Complex Quadruped Mobility](https://mlsanity.com/paper/2505.16084/) (2025)
- [SteadyTray: Learning Object Balancing Tasks in Humanoid Tray Transport via Residual Reinforcement Learning](https://mlsanity.com/paper/2603.10306/) (2026)
- [Chasing Stability: Humanoid Running via Control Lyapunov Function Guided Reinforcement Learning](https://mlsanity.com/paper/2509.19573/) (2025)
- [Spectral Normalization for Lipschitz-Constrained Policies on Learning Humanoid Locomotion](https://mlsanity.com/paper/2504.08246/) (2025)
- [Robust Humanoid Walking on Compliant and Uneven Terrain with Deep Reinforcement Learning](https://mlsanity.com/paper/2504.13619/) (2025)
- [Humanoid Robots at work: where are we ?](https://mlsanity.com/paper/2404.04249/) (2024)
- [Proactive Constrained Policy Optimization with Preemptive Penalty](https://mlsanity.com/paper/2508.01883/) (2025)
- [ECO: Energy-Constrained Optimization with Reinforcement Learning for Humanoid Walking](https://mlsanity.com/paper/2602.06445/) (2026)

## Abstract (arXiv)

Embodied AI systems, particularly humanoid robots deployed in real world scenarios require whole-body control policies that are both task-responsive and physically smooth. However, smoothness is not uniform across the body: lower body must remain sufficiently reactive, while the upper body must be tightly regulated to preserve stability. Existing reinforcement learning approaches typically impose smoothness through auxiliary terms in the reward function, which compete with task objectives, treating the body as uniform and provide no direct control over the physical quantities responsible for smooth behavior. We introduce DeCap (Decoupled Constraint-aware policy), a constrained reinforcement learning algorithm that decouples whole-body smoothness into separate upper- and lower-body constraint groups, each formulates smoothness as explicit constraints on physical motion limits. To improve constraint satisfaction near feasibility boundaries, DeCap incorporates a bounded barrier penalty that activates proactively as limits are approached and remains bounded at the constraint limit. On real-world humanoid whole-body control task, DeCap reduces upper-body action rate by 2.50x and acceleration by 2.18x relative to reward-based smoothness policies, while also improving lower-body smoothness and reducing transient motion. We demonstrate that a fixed set of smoothness constraints transfers across diverse terrains, alleviating the need of extensive reward tuning.