Learning Smooth Humanoid Locomotion through Lipschitz-Constrained Policies

IEEE International Conference on Intelligent Robots and Systems (IROS 2025)

Zixuan Chen* (1)    Xialin He* (2)    Yen-Jen Wang* (3)    Qiayuan Liao (3)    Yanjie Ze (4)    Zhongyu Li (3)    S. Shankar Sastry (3)    Jiajun Wu (4)    Koushil Sreenath (3)    Saurabh Gupta (2)    Xue Bin Peng (1, 5)

(1) Simon Fraser University    (2) UIUC 3UC Berkeley    (4) Stanford University    (5) NVIDIA

*Equal contribution.

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Abstract

Reinforcement learning combined with sim-to-real transfer offers a general framework for developing locomotion controllers for legged robots. To facilitate successful deployment in the real world, smoothing techniques, such as low-pass filters and smoothness rewards, are often employed to develop policies with smooth behaviors. However, because these techniques are non-differentiable and usually require tedious tuning of a large set of hyperparameters, they tend to require extensive manual tuning for each robotic platform. To address this challenge and establish a general technique for enforcing smooth behaviors, we propose a simple and effective method that imposes a Lipschitz constraint on a learned policy, which we refer to as Lipschitz-Constrained Policies (LCP). We show that the Lipschitz constraint can be implemented in the form of a gradient penalty, which provides a differentiable objective that can be easily incorporated with automatic differentiation frameworks. We demonstrate that LCP effectively replaces the need for smoothing rewards or low-pass filters and can be easily integrated into training frameworks for many distinct humanoid robots. We extensively evaluate LCP in both simulation and real-world humanoid robots, producing smooth and robust locomotion controllers.

Paper: [PDF]       Code: [GitHub]       Webpage: [Link]       Preprint: [arXiv]

Video

Bibtex

@article{
	chen2025lcp,
	title = {Learning Smooth Humanoid Locomotion through Lipschitz-Constrained Policies},
	author = {Zixuan Chen and Xialin He and Yen-Jen Wang and Qiayuan Liao and Yanjie Ze and Zhongyu Li and S. Shankar Sastry and Jiajun Wu and Koushil Sreenath and Saurabh Gupta and Xue Bin Peng},
	journal={2025 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)},
	year = {2025}
}