{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/learning-smooth-humanoid-locomotion-through","title":"Learning Smooth Humanoid Locomotion through Lipschitz-Constrained Policies","arxiv_id":"2410.11825","date":"2024-10-15","proceeding":null,"authors":["Zixuan Chen","Xialin He","Yen-Jen Wang","Qiayuan Liao","Yanjie Ze","Zhongyu Li","S. Shankar Sastry","Jiajun Wu","Koushil Sreenath","Saurabh Gupta","Xue Bin Peng"],"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. All simulation and deployment code, along with complete checkpoints, is available on our project page: https://lipschitz-constrained-policy.github.io.","url_abs":"https://arxiv.org/abs/2410.11825v3","url_pdf":"https://arxiv.org/pdf/2410.11825v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"learning-smooth-humanoid-locomotion-through","repo_url":"https://github.com/zixuan417/smooth-humanoid-locomotion","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2410.11825","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}