RL for Legged Locomotion

RL: Reinforcement Learning

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15 papers in the last four weeks, against 2 the four weeks before. 0.1% of all new papers.

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Jun 5, 2026cs.RO

T-GMP: Terrain-conditioned Generative Motion Priors for Versatile and Natural Humanoid Locomotion

Achieving both anthropomorphic naturalness and robust terrain traversal remains a fundamental challenge in humanoid locomotion. Existing Reinforcement Learning (RL) approaches typically rely on fixed motion priors, limiting their adaptability to varying environments. We propose Terrain-conditioned Generative Motion Priors (T-GMP), a module that captures a terrain-conditioned latent motion manifold from a few expert state-terrain demonstrations using a Conditional Variational Autoencoder (CVAE). The learned priors enable smooth style transitions, facilitating a unified policy that adapts to terrain variations. We integrate T-GMP into an adversarial learning pipeline with our proposed Foothold Penalty, where a discriminator dynamically modulates naturalness constraints conditioned on local terrain features, guiding the generation of versatile and human-like motions. Experimental results demonstrate that our method outperforms existing baselines in traversal success rate and motion smoothness, while preserving biomimetically natural and physically coordinated motions.

Junhong Guo, Hao Hu, Chen Chen +6

Harbin Institute of Technology · Leju Robotics

Humanoid Robot Locomotion Robot Motion Generation Terrain-Aware Robot Locomotion RL for Legged Locomotion

Jun 4, 2026cs.RO

TAGA: Terrain-aware Active Gaze Learning for Generalizable Agile Humanoid Locomotion

Agile humanoid locomotion across diverse challenging terrain demands both wide perceptual coverage and precise local geometry understanding. Motivated by the way humans selectively look at relevant terrain during locomotion, we introduce TAGA, a Terrain-aware Active Gaze learning framework for Attention-based humanoid control. By fusing vision, proprioception, and motion commands, our framework guides the model to learn anticipatory cues and actively attend to specific areas of the height scan, selectively using these informative regions for the downstream network. This adaptively increases the information density of observations under tight onboard computational constraints, thus enabling fine-grained perceptive locomotion over larger-scale terrains. We find that such gaze behaviors can naturally emerge through reinforcement learning alone, without requiring additional supervision or explicit guidance, significantly improve training efficiency. As a result, the trained policy demonstrates robust and generalizable locomotion in simulation and on hardware, including reliable terrain-aware foothold selection, elevated-platform traversal, competitive sparse-foothold traversal, and the largest reported real-world gap traversal distance of 1.2m among perceptive humanoid locomotion systems, while maintaining stability under severe perceptual disturbances and environmental interference.

Peizhuo Li, Hongyi Li, Mingfeng Fan +9

MarmotLab, National University of Singapore · Center of X-Mechanics, Zhejiang University · South China University of Technology

Active Perception Humanoid Robot Locomotion Robot Policy Learning Terrain-Aware Robot Locomotion RL for Legged Locomotion

Jun 3, 2026cs.RO

HORIZON: Recoverability-Governed Curriculum for Physical-Domain Scaling

Scaling robust robot policies requires more than broader randomization, because physical-domain experience must remain organized and learnable throughout training. We study when a policy can benefit from harder physics and identify recoverability as a central constraint in on-policy physical-domain scaling. In on-policy training, new dynamics are useful only insofar as they remain close enough to the current policy to generate corrective on-policy data, rather than collapsing rollouts into unrecoverable failures. Using quadruped locomotion as a physically demanding benchmark for embodied generalization, we introduce HORIZON, a checkpointed frontier curriculum that expands physical domains only within the current policy's recoverable boundary. HORIZON uses rollback and boundary refinement to govern each expansion step, turning fixed randomization into a continual process of physical-domain growth. Experiments reveal three regularities of physical-domain expansion. First, direct domain widening is uneven across physical axes and often unlearnable without staged ordering. Second, domain composition is non-monotonic, and adding more domains beyond a compact core can dilute recoverable joint samples and reduce overall robustness. Third, offline distillation of isolated experts cannot substitute for the joint interaction generated by on-policy curriculum. Together, these results frame physical-domain generalization as a continual growth problem for embodied control, with recoverability as the organizing principle for on-policy expansion.

Chenhao Bai, Liqin Lu, Kaijun Wang +5

1Zhejiang University, State Key Lab of CAD & CG · 2Zhejiang University of Technology

Domain Randomization Curriculum RL RL for Legged Locomotion Robot Policy Generalization Robust RL

Jun 3, 2026cs.RO

CoRe-MoE: Contrastive Reweighted Mixture of Experts for Multi-Terrain Humanoid Locomotion with Gait Adaptation

Humans primarily rely on walking and running to traverse complex terrains. Similarly, humanoid robots should be able to smoothly transition between walking and running while maintaining natural and stable locomotion. However, unifying gait transition and multi-terrain adaptation within a single policy remains challenging due to gradient interference between tasks and the distribution shift caused by terrain variations. Although Mixture-of-Experts (MoE) architectures can mitigate multi-skill interference, direct joint training often fails to achieve clear expert specialization. To address these challenges, we propose CoRe-MoE, a two-stage reinforcement learning framework that decouples gait generation from terrain adaptation. In the first stage, a stable locomotion policy is learned to produce natural walking and running behaviors with smooth transitions. In the second stage, a terrain-aware MoE branch is introduced, and the gating network is trained with a contrastive objective to learn structured terrain representations and promote expert specialization. The final action is obtained through weighted fusion of the base gait policy and the terrain-aware branch, enabling the policy to preserve stable locomotion while adapting to complex terrains. Extensive simulation results demonstrate that the proposed method outperforms baseline approaches in terms of success rate, locomotion stability, and multi-terrain adaptability. Furthermore, zero-shot deployment on a Unitree G1 humanoid robot validates the effectiveness of our framework, achieving robust walking and running across stairs, slopes, steps, obstacles, and unstructured outdoor terrains while maintaining accurate foothold control and dynamic stability.

Kailun Huang, Zikang Xie, Yanzhe Xie +8

Hong Kong University of Science and Technology · Hong Kong University of Science and Technology (Guangzhou) · Guangdong University of Technology +3

Humanoid Robot Locomotion Mixture of Experts Terrain-Aware Robot Locomotion Robot Locomotion RL for Legged Locomotion

May 30, 2026cs.RO

Global-Local Attention Decomposition for Terrain Encoding in Humanoid Perceptive Locomotion

Although reinforcement learning has significantly advanced humanoid locomotion, perceptive policies still struggle on sparse-foothold terrain and constrained environments. Success in these scenarios requires both broad terrain awareness and precise foothold selection, two perceptual roles that conventional encoders often entangle. To address this challenge, we propose Global-Local Attention Decomposition (GLAD) for terrain encoding in humanoid locomotion. Realized by a coarse-to-fine encoder over a robot-centric elevation map, GLAD explicitly separates these objectives: a global attention branch utilizes attention pooling to summarize the surrounding terrain context, while a state-conditioned local attention branch sparsifies and encodes precise foothold-relevant geometry. This explicit attention decomposition prevents the dilution of fine-grained spatial cues while reducing training overhead. Experiments demonstrate that GLAD enables reliable locomotion over challenging gaps, stepping stones, and stairs. Furthermore, the learned policy exhibits emergent terrain-responsive behaviors, autonomously following narrow paths and avoiding obstacles under simple velocity commands without explicit navigation planners. In real-world deployment on a Unitree G1 humanoid robot using onboard LiDAR, the proposed method achieves robust zero-shot sim-to-real transfer across diverse sparse-foothold and obstacle-rich domains.

Shengcheng Fu, Yang Zhang, Zhanxiang Cao +4

Tongji University, Shanghai, China · Shanghai Jiao Tong University, Shanghai, China · Shanghai Innovation Institute, Shanghai, China +1

Legged Robotics Humanoid Robot Locomotion Terrain-Aware Robot Locomotion RL for Legged Locomotion Attention Mechanisms

May 29, 2026cs.RO

Learning Terrain-Aware Whole-Body Control for Perceptive Legged Loco-Manipulation

Legged manipulators integrate exceptional terrain adaptability along with mobile manipulation capabilities, which make them highly promising for deployment in human-centric environments. By coordinating the control of both legs and arms, a whole-body controller can significantly expand the operational workspace of legged manipulators. However, many existing whole-body controllers primarily depend on proprioception and do not incorporate the critical exteroception required for effective terrain topology perception. This limitation can hinder their ability to adapt to varying environmental conditions and navigate complex terrains effectively. In this paper, we introduce TA-WBC, a terrain-aware whole-body control framework for legged manipulators, which features a novel RL-based unified policy tailored to whole-body loco-manipulation tasks in various terrains. Specifically, we employ a \rev{hierarchical exteroceptive encoder} to extract terrain features, providing an essential basis for the robot to proactively adapt posture and footholds. Furthermore, to facilitate stable cross-terrain loco-manipulation, we propose a novel end-effector sampling method based on the foot contact plane, \rev{decoupling the manipulation target from base height, roll, and pitch variations}. Moreover, a dual-policy distillation module is introduced to integrate expansive whole-body motion with terrain adaptability without catastrophic forgetting. The simulation and real-world experiments validate the robustness of our proposed controller, which leads to a larger reachable space, less tracking error, and reduced unexpected stumbles. This unified policy highlights the promising capabilities of legged manipulators in performing loco-manipulation tasks across complex terrains.

Sikai Guo, Yudong Zhong, Guoyang Zhao +3

Robotics and Autonomous Systems Thrust, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou 511453, China

Legged Robotics Terrain-Aware Robot Locomotion RL for Legged Locomotion

May 27, 2026cs.RO

Visualizing Latent Phase Structures in Locomotion Policies: A Multi-Environment Study with Temporal Feature Extension

Deep reinforcement learning (DRL) has been shown to achieve high performance on locomotion control tasks in MuJoCo benchmarks such as HalfCheetah, Ant, and Walker2D. However, visualizing the motion structures internally obtained by a trained policy function implemented as a deep neural network remains challenging. It is known from biomechanics and related fields that locomotion control is realized through the repetition of motion phases such as the stance phase and swing phase. In this study, we propose a framework for uncovering latent motion phase structures from trajectories generated by locomotion control policies through interaction with the environment. The proposed method extends the clustering features from state observations alone to augmented features including actions, next states, and next actions, and introduces a method for determining the number of clusters that suppresses self-transitions. Applying the proposed method to three environments -- Ant-v5, HalfCheetah-v5, and Walker2D-v5 -- we successfully identified phase structures with clearer and more regular transition rules than those obtained by the existing method.

Daisuke Yasui, Toshitaka Matuki, Hiroshi Sato

Mathematics and Computer Science National Defense Academy of Japan Yokosuka, Japan

Temporal Action Segmentation Robot Locomotion RL for Legged Locomotion

May 27, 2026cs.RO

S-Cheetah: A Novel Quadrupedal Robot with a 3-DOF Active Spine Learning Agile Locomotion

The biological spine of quadrupeds enables sagittal flexion/extension, lateral bending, and axial rotation, playing a crucial role in highly agile and dexterous locomotion. While numerous studies have integrated active spinal joints into quadrupedal robots to enhance agility, most designs simplify control complexity by reducing spinal degrees of freedom (DOF), failing to achieve the spatial tri-axial rotation characteristic of biological spines. Consequently, replicating a multi-DOF biomimetic spine and effectively leveraging it to empower the agile locomotion of quadrupedal robots remains a significant research challenge. In this study, we present S-Cheetah, a quadrupedal robot featuring a 3-DOF bio-inspired serial active spine capable of biomimetic spatial tri-axial rotation. To empower the robot to fully utilize this active spine, we developed a specialized reinforcement learning framework to actively promote the engagement of the introduced spine and maximize the robot's locomotive capabilities by integrating an acceleration curriculum learning strategy with tailored reward functions, such as a gallop gait reward, a spine undulation reward, and a spine steering reward. Experimental results demonstrate that S-Cheetah can achieve a peak speed of 6.9 m/s using the rotary G2 gallop gait and an in-place turning rate of 7.2 rad/s. Besides, the system exhibits an emergent, feline-inspired aerial self-righting capability, allowing it to land stably on four feet from arbitrary orientations during free fall. Finally, through extensive evaluations across diverse locomotion tasks, we prove that the introduction of the proposed 3-DOF spine comprehensively enhances the locomotive agility of quadrupedal robots. Project website: himmy-robotics.github.io/scheetah

Zimu Li, Weibang Bai

School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China

Robotic Control RL for Legged Locomotion Quadruped Locomotion

May 26, 2026cs.RO

Learning to Balance Motor Thermal Safety and Quadrupedal Locomotion Performance with Residual Policy

Motor thermal management is often overlooked in the context of electrically-actuated robots, particularly legged robots, but motor overheating is a key factor that limits long-duration locomotion especially under payload conditions. This paper integrates a whole-body thermal model of a quadruped robot into the reinforcement learning pipeline to update motor temperatures, and proposes a two-stage training framework for motor thermal management. In this framework, a nominal policy is first pre-trained as a locomotion baseline capable of traversing diverse terrains. A residual policy is then trained on top of the nominal policy to provide corrective actions based on the robot's thermal state, ensuring high performance under low-temperature conditions and preventing motor overheating under high-temperature conditions. Simulation results demonstrate that the proposed policy achieves an effective balance between motor thermal safety and locomotion performance. Real-world experiments on a Unitree A1 quadruped robot further validate the approach: under a 3 kg payload, the robot achieves stable locomotion across multiple terrains for over 13 minutes, while the nominal policy alone leads to motor overheating in about 5 minutes.

Yuhang Wan, Weixian Lin, Letian Qian +5

School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

RL for Legged Locomotion Residual Policy Learning Quadruped Locomotion

May 24, 2026cs.RO

Bridging the Gap: Enabling Soft Actor Critic for High Performance Legged Locomotion

Proximal Policy Optimization (PPO) has become the de facto standard for training legged robots, thanks to its robustness and scalability in massively parallel simulation environments like IsaacLab. However, its on-policy nature makes it inherently sample-inefficient, preventing its use for continuous adaptation and fine-tuning on real hardware. Soft Actor-Critic (SAC), by contrast, is an off-policy algorithm that can reuse past experience, making it a natural candidate for sim-to-real transfer workflows where the same algorithm can be used both in simulation and for online learning on the real robot. Despite these advantages, SAC has consistently failed to match PPO's empirical performance in massively parallel training settings. This work identifies the root causes of this gap and introduces targeted modifications, covering policy initialization, timeout-aware critic targets, and multi-step return estimation, that enable SAC to train stably at scale. Evaluated across multiple legged robot platforms and diverse locomotion tasks, our approach closes the performance gap with PPO entirely.

Gianluca Sabatini, Chenhao Li, Marco Hutter

ETH Zurich, Switzerland

RL for Legged Locomotion Soft Actor-Critic Sample-Efficient RL Off-Policy RL

May 23, 2026cs.RO

Towards Low-Gravity Planetary Exploration using Reinforcement Learning for Walking, Jumping, and In-flight Attitude Control

This paper presents reinforcement learning (RL) policies for dynamic quadrupedal locomotion in planetary exploration scenarios. Building on a taskoptimized quadruped with a 5-bar leg design, we develop RL policies for walking, vertical jumping, forward jumping, and in-flight attitude control, explicitly tailored to the reduced gravity on Mars. These policies jointly enable such robots to overcome obstacles larger than themselves through coordinated jumping and precise in-flight reorientation for safe landings. We demonstrate Sim2Real transfer of the attitude control policy on the Olympus quadruped through single-axis reorientation tests, while all locomotion policies are validated in simulation. A complete Mars exploration mission scenario demonstrates coordinated policy deployment across challenging terrain. Experimental results show 90° attitude reorientation in 2.6 seconds, with simulations demonstrating 3.1 meter vertical jumps and 3.9 meter forward jumps under Martian gravity conditions. - Supplementary video: https://www.youtube.com/watch?v=qlSJ3P87A4A

Jørgen Anker Olsen, Kostas Alexis

The authors are with the Autonomous Robots Lab, NTNU, O.S. Bragstads Plass 2D, 7034, Trondheim, Norway.

Robotic Control Space Robotics Robot Locomotion RL for Legged Locomotion Quadruped Locomotion

May 19, 2026cs.RO

ARC-RL: A Reinforcement Learning Playground Inspired by ARC Raiders

Reinforcement learning for legged locomotion has matured into a stack of multi-component reward functions and physics-engine benchmarks whose morphologies are uniformly derived from real commercial hardware. Game NPCs, however, are bound by stylistic constraints absent from sim-to-real robotics and routinely take the form of creatures with no real-robot counterpart. We introduce ARC-RL, a suite of four MuJoCo continuous-control environments featuring robotic morphologies inspired by the bestiary of ARC Raiders: the 18-DoF tall hexapod Queen, the 12-DoF armoured hexapod Bastion, the 18-DoF compact hexapod Tick, and the 12-DoF quadruped Leaper. All four robots share a unified observation template, action convention, simulation cadence, and a single closed-form multi-component reward function whose only per-morphology variation lives in a small set of weights and parameters. The reward fuses a velocity-tracking tent, a healthy survive bonus, a phase-locked gait-compliance bonus/cost pair, action regularisers, three safety penalties, and a posture anchor; no motion-capture data enters the reward at any point. We additionally provide hand-crafted Central Pattern Generator demonstrators per morphology, which serve both as fixed expert references and as sources of prior data for offline-to-online training. On this playground, we conduct a controlled empirical study comparing standard online algorithms (SAC, SPEQ, SOPE-EO) and methods augmented with prior data (SACfD, SPEQ-O2O, SOPE), and characterise how each paradigm copes with the playground's morphological diversity and animation-style stylistic constraints. Source code is available at https://github.com/CarloRomeo427/ARC_RL.git.

Carlo Romeo, Andrew D. Bagdanov

Media Integration and Communication Center – University of Florence

RL Benchmarks Robotics Simulation RL for Legged Locomotion Reward Design for RL Offline-To-Online RL

May 18, 2026cs.RO

Unified Walking, Running, and Recovery for Humanoids via State-Dependent Adversarial Motion Priors

We propose a unified reinforcement learning framework that enables a single policy to perform walking, running, and fall recovery on the Unitree G1 humanoid robot, validated on physical hardware without any explicit mode-switching command at deployment. The framework extends Adversarial Motion Priors (AMP) by replacing the conventional global reference distribution with a state-dependent gate that routes each training transition to one of two discriminators: a dedicated recovery discriminator and a velocity-conditioned locomotion discriminator that jointly covers walking and running. The gate is defined by a single fixed threshold on projected gravity: the recovery discriminator is activated when body tilt exceeds approximately

37^\circ

from vertical (

|g_z+1|>0.6

); otherwise the locomotion discriminator is used, with the normalized commanded velocity serving as a condition that selects the appropriate reference trajectory between walk and run clips. Only three LAFAN1 reference clips are required to regularize the complete behavior set. At deployment, a single frozen ONNX policy executes at 50,Hz with no runtime mode logic; hardware experiments demonstrate successful recovery from both prone and supine falls and smooth walk-to-run transitions under the same controller.

Yidan Lu, Yichao Zhong, Liu Zhao +2

The University of Hong Kong, Hong Kong SAR, China.

Humanoid Robot Locomotion Robot Failure Recovery RL for Legged Locomotion Policy Learning Humanoid Robotics

May 15, 2026cs.RO

Terrain Consistent Reference-Guided RL for Humanoid Navigation Autonomy

We present a method for training reference-guided, perceptive reinforcement learning locomotion policies for humanoid robots in which reference trajectories are modulated in training to be consistent with terrain geometry. Aiming to deploy our method with standard navigation autonomy infrastructure, we synthesize SE(2)-controllable reference trajectories inside the RL training loop, projecting desired footsteps onto valid footholds and adjusting swing-foot and center-of-mass trajectories to match the terrain. The resulting policy exposes a clean SE(2) velocity interface compatible with standard navigation planners. In simulation, environmentally-conditioned references significantly improve reference tracking performance compared to environment agnostic references. On hardware, we integrate the policy with an MPC + control barrier function planner and demonstrate long-horizon (>70m) closed-loop autonomous navigation on the Unitree G1 through outdoor environments containing rough terrain and consecutive flights of stairs, with all sensing and computation onboard.

William D. Compton, Zachary Olkin, Aaron D. Ames

Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA 91125

Humanoid Robot Locomotion Reinforcement Learning Robot Navigation Terrain-Aware Robot Locomotion Robot Locomotion RL for Legged Locomotion

May 13, 2026cs.RO

Robot Squid Game: Quadrupedal Locomotion for Traversing Narrow Tunnels

Quadruped robots demonstrate exceptional potential for navigating complex terrain in critical applications such as search and rescue missions and infrastructure inspection However autonomous traversal of confined 3D environments including tunnels caves and collapsed structures remains a significant challenge Existing methods often struggle with rigid gait patterns limited adaptability to diverse geometries and reliance on oversimplified environmental assumptions This paper introduces a Reinforcement Learning RL framework that combines procedural environment generation with policy distillation to enable robust locomotion across various tunnel configurations Our approach leverages a teacher student training paradigm where specialized expert policies trained on procedurally generated tunnel geometries transfer their knowledge to a unified student policy This strategy eliminates the need for complex reward shaping in end-to-end RL training simplifying the process by breaking down complicated tasks into smaller more manageable components that are easier for the robot to learn By synthesizing diverse tunnel structures during training and distilling navigation strategies into a generalizable policy our method achieves consistent traversal across complex spatial constraints where conventional approaches fail We demonstrate through both simulation and real world experiments that our method enables quadruped robots to successfully traverse challenging confined tunnel environments

Amir Hossain Raj, Dibyendu Das, Xuesu Xiao

Department of Computer Science, George Mason University

Legged Robotics RL for Legged Locomotion Quadruped Locomotion

May 11, 2026cs.RO

EFGCL: Learning Dynamic Motion through Spotting-Inspired External Force Guided Curriculum Learning

Learning dynamic whole-body motions for legged robots through reinforcement learning (RL) remains challenging due to the high risk of failure, which makes efficient exploration difficult and often leads to unstable learning. In this paper, we propose External Force Guided Curriculum Learning (EFGCL), a guided RL approach based on the principle of physical guidance, in which external assistive forces are introduced during training. Inspired by spotting in artistic gymnastics, EFGCL enables agents to physically experience successful motion executions without relying on task-specific reward shaping or reference trajectories. Experiments on a quadrupedal robot performing Jump, Backflip, and Lateral-Flip tasks demonstrate that EFGCL accelerates learning of the Jump task by approximately a factor of two and enables the acquisition of complex whole body motions that conventional RL methods fail to learn. We further show that the learned policies can be deployed on real robot, reproducing motions consistent with those observed in simulation. These results indicate that physically guided exploration, which allows agents to experience success early in training, is an effective and general strategy for improving learning efficiency in dynamic whole-body motion tasks.

Keita Yoneda, Kento Kawaharazuka, Kei Okada

Department of Mechano-Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan · AI Center, Graduate School of Information Science and Technology, The University of Tokyo, Japan

Reinforcement Learning Whole-Body Control RL for Legged Locomotion Curriculum Learning

May 11, 2026cs.RO

Explicit Stair Geometry Conditioning for Robust Humanoid Locomotion

Robust humanoid stair climbing remains challenging due to geometric discontinuities, sensitivity to step height variations, and perception uncertainty in real-world environments. Existing learning-based locomotion policies often rely on implicit terrain representations or blind proprioceptive feedback, limiting their ability to generalize across varying stair geometries and to anticipate required gait adjustments. This paper proposes an explicit stair geometry conditioning framework for robust humanoid stair climbing. Instead of encoding terrain as high-dimensional latent features, we extract a compact set of interpretable geometric parameters, including step height, step depth, and current yaw angle relative to the robot heading. These explicit stair parameters directly condition a Proximal Policy Optimization (PPO)-based locomotion policy, enabling proactive modulation of swing-foot clearance and stride characteristics according to stair structure. Simulation experiments demonstrate improved generalization across unseen stair heights beyond the training distribution. Real-world experiments on the Unitree G1 humanoid validate reliable indoor and outdoor stair traversal. In challenging outdoor scenarios, the robot successfully ascends 33 consecutive steps without failure, demonstrating robustness and practical deployability.

Jianguo Zhang, Wentai Xu, Shusheng Ye +5

Shenzhen Institute of Artificial Intelligence and Robotics for Society. · Mohamed bin Zayed University of Artificial Intelligence (MBZUAI). · School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen.

Humanoid Robot Locomotion Robot Locomotion RL for Legged Locomotion

May 9, 2026cs.RO

Constraint-Aware Diffusion Priors for High-Fidelity and Versatile Quadruped Locomotion

Reinforcement learning combined with imitation learning has significantly advanced biomimetic quadrupedal locomotion. However, scaling these frameworks to massive, multi-source datasets exposes fundamental bottlenecks. First, traditional GAN-based discriminators are prone to mode collapse, struggling to capture diverse motion distributions from uncurated datasets. Second, existing kinematic priors suffer from out-of-distribution (OOD) tracking conflicts, leading to severe unintended heading drifts during complex maneuvers. Furthermore, deploying unconstrained priors to physical hardware poses critical safety risks by disregarding actuator dynamics. To overcome these challenges, we propose Diff-CAST (Diffusion-guided Constraint-Aware Symmetric Tracking), a novel motion prior framework leveraging the multi-modal distribution modeling capabilities of diffusion models for stylistic rewards. Diff-CAST effectively replaces traditional GAN discriminators, unlocking robust data scaling on heterogeneous collections. To ensure high-fidelity intent execution and reliable real-world deployment, we introduce a comprehensive Sim2Real architecture integrating Symmetric Augmented Command Conditioning (SACC) for drift-free tracking, and Constrained RL for hardware safety. Experiments on a quadruped demonstrate that Diff-CAST mitigates mode collapse, enables seamless transitions between diverse skills, and ensures robust, hardware-compliant locomotion.

Jianhui Chen, Ruixin Zhan, Liu Liu +2

Amap, Alibaba Group

Sim-to-Real Transfer Constrained RL Robot Motion Generation RL for Legged Locomotion Robot Imitation Learning Quadruped Locomotion

May 3, 2026eess.SY

Stability of Control Lyapunov Function Guided Reinforcement Learning

Reinforcement learning (RL) has become the de facto method for achieving locomotion on humanoid robots in practice, yet stability analysis of the corresponding control policies is lacking. Recent work has attempted to merge control theoretic ideas with reinforcement learning through control guided learning. A notable example of this is the use of a control Lyapunov function (CLF) to synthesize the reinforcement learning rewards, a technique known as CLF-RL, which has shown practical success. This paper investigates the stability properties of optimal controllers using CLF-RL with the goal of bridging experimentally observed stability with theoretical guarantees. The RL problem is viewed as an optimal control problem and exponential stability is proven in both continuous and discrete time using both core CLF reward terms and the additional terms used in practice. The theoretical bounds are numerically verified on systems such as the double integrator and cart-pole. Finally, the CLF guided rewards are implemented for a walking humanoid robot to generate stable periodic orbits.

Zachary Olkin, William D. Compton, Aaron D. Ames

The authors are with the Department of Control and Dynamical Systems at the California Institute of Technology.

RL Control Lyapunov Stability RL for Legged Locomotion Optimal Control

May 2, 2026cs.RO

Dynamics Aware Quadrupedal Locomotion via Intrinsic Dynamics Head

Quadrupedal locomotion plays a critical role in enabling agile, versatile movement across complex terrains. Understanding and estimating the underlying physical dynamics are essential for achieving efficient and stable quadrupedal locomotion. We propose a novel training framework for quadrupedal locomotion that enables the Control Policy to understand and reason about physical dynamics. In simulation, we concurrently train an Intrinsic Dynamics (ID) Head that learns state-to-torque dynamics alongside the Control Policy, and we define a dynamics reward enabled by the ID Head that encourages the Policy toward more predictable dynamical behavior. We also provide a mechanism to tune the learned dynamics in the resulting Policy by controlling the training coefficients of the ID Head. Our simulation experiments show that this mechanism drives convergence to better optima across a wide range of standard quadrupedal locomotion rewards, yielding more efficient and smoother policies. Our real-robot experiments demonstrate sim-to-real transfer of these improvements, with significant gains in torque efficiency (16.8%), action rate (18.6%), and mechanical power (12.8%), while improving safe torque occupancy by 6.4%.

Aman Arora, Nalini Ratha

Department of Computer Science, University at Buffalo, The State University of New York, Buffalo, USA

Robot Dynamics Learning RL for Legged Locomotion Inverse Dynamics Quadruped Locomotion Robot Learning

Apr 26, 2026cs.RO

Unleashing the Agility of Wheeled-Legged Robots for High-Dynamic Reflexive Obstacle Evasion

Wheeled-legged robots combine the efficiency of rolling with the adaptability of legged locomotion, offering unique agility for dynamic environments. However, enabling rapid reflexive evasion remains challenging due to the coexistence of heterogeneous wheel-leg dynamics, hybrid locomotion modes, and non-holonomic constraints. In this work, we investigate how wheeled-legged robots can exploit their hybrid morphology for high-dynamic obstacle avoidance. We propose AWARE, a hierarchical reinforcement learning framework that decomposes avoidance into navigation-avoidance and reflexive-evasion regimes coordinated by a threat-conditioned high-level policy. By learning specialized low-level experts, AWARE autonomously discovers distinct rolling-, stepping-, and hybrid-dominated evasive behaviors, including forward lunges and lateral dodges. Simulation experiments across different reaction times and approach directions, together with real-robot evaluations on the M20 platform, demonstrate improved evasion capability and effective online transition between locomotion regimes. These results highlight the potential of exploiting hybrid wheel-leg actuation for agile and reactive mobility in dynamic environments. Paper homepage: https://aware-ral-2026.github.io/.

Yongen Zhao, Zihao Xu, Wenzhi Lu +4

Beijing Zhongguancun Academy, Beijing, China · School of Mechanical Engineering, Tianjin University, Tianjin, China · School of Computing, National University of Singapore, Singapore +1

Hierarchical RL Robot Locomotion RL for Legged Locomotion Dynamic Obstacle Avoidance

Apr 26, 2026cs.RO

QuietWalk: Physics-Informed Reinforcement Learning for Ground Reaction Force-Aware Humanoid Locomotion Under Diverse Footwear

Humanoid robots operating in human-centered environments (e.g., homes, hospitals, and offices) must mitigate foot--ground impact transients, as impact-induced vibration and noise degrade user experience and repeated impacts accelerate hardware wear. However, existing low-noise locomotion training often relies on kinematic proxy objectives or fragile force sensors, and footwear-induced changes in contact dynamics introduce distribution shifts that hinder policy generalization.We present QuietWalk, a physics-informed reinforcement learning framework for ground-reaction-force-aware humanoid locomotion under diverse footwear conditions. QuietWalk employs an inverse-dynamics-constrained physics-informed neural network (PINN) to estimate per-foot vertical ground reaction forces (GRFs) from proprioceptive signals, and integrates the frozen predictor into the RL training loop to penalize predicted impact forces without requiring force sensors at deployment.On a held-out real-robot dataset, enforcing inverse-dynamics consistency reduces vertical GRF prediction errors by 82%-86% compared with a purely supervised predictor and improves the coefficient of determination from 0.39/0.67 to 0.99/0.99 for the left/right feet. On hardware at 1.2 m/s (barefoot; averaged over four floor materials), QuietWalk reduces mean A-weighted noise level by 7.17 dB and peak noise level by 4.98 dB under a consistent recording setup. Cross-footwear experiments (barefoot, skate shoes, athletic sneakers, and high heels) across multiple surfaces further demonstrate robust adaptation to footwear-induced contact variations.

Hanze Hu, Luying Feng, Silu Chen +6

Humanoid Robot Locomotion Robot Locomotion RL for Legged Locomotion Physics-Informed ML Physics-Informed RL Robust RL

Apr 23, 2026cs.RO

X2-N: A Transformable Wheel-legged Humanoid Robot with Dual-mode Locomotion and Manipulation

Wheel-legged robots combine the efficiency of wheeled locomotion with the versatility of legged systems, enabling rapid traversal over both continuous and discrete terrains. However, conventional designs typically employ fixed wheels as feet and limited degrees of freedom (DoFs) at the hips, resulting in reduced stability and mobility during legged locomotion compared to humanoids with flat feet. In addition, most existing platforms lack a full upper body with arms, which limits their ability to perform dexterous manipulation tasks. In this letter, we present X2-N, a high-DoF transformable robot with dual-mode locomotion and manipulation. X2-N can operate in both humanoid and wheel-legged forms and transform seamlessly between them through joint reconfiguration. We further propose a reinforcement learning (RL)-based whole-body control framework tailored to this morphology, enabling unified control across hybrid locomotion, transformation, and manipulation. We validate X2-N in a range of challenging locomotion and manipulation tasks, including dynamic skating-like motion, stair climbing and package delivery. Results demonstrate high locomotion efficiency, strong terrain adaptability, and stable loco-manipulation performance of X2-N, highlighting its potential for real-world deployment.

Yan Ning, Xingzhou Chen, Delong Li +6

Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology, Hong Kong, China. · X-lab Department, Agibot Innovation Company, Shanghai, China.

Legged Robotics Humanoid Loco-Manipulation Humanoid Robot Locomotion Robot Locomotion RL for Legged Locomotion

Apr 21, 2026cs.RO

Reinforcement Learning Enabled Adaptive Multi-Task Control for Bipedal Soccer Robots

Developing bipedal football robots in dynamiccombat environments presents challenges related to motionstability and deep coupling of multiple tasks, as well ascontrol switching issues between different states such as up-right walking and fall recovery. To address these problems,this paper proposes a modular reinforcement learning (RL)framework for achieving adaptive multi-task control. Firstly,this framework combines an open-loop feedforward oscilla-tor with a reinforcement learning-based feedback residualstrategy, effectively separating the generation of basic gaitsfrom complex football actions. Secondly, a posture-driven statemachine is introduced, clearly switching between the ballseeking and kicking network (BSKN) and the fall recoverynetwork (FRN), fundamentally preventing state interference.The FRN is efficiently trained through a progressive forceattenuation curriculum learning strategy. The architecture wasverified in Unity simulations of bipedal robots, demonstratingexcellent spatial adaptability-reliably finding and kicking theball even in restricted corner scenarios-and rapid autonomousfall recovery (with an average recovery time of 0.715 seconds).This ensures seamless and stable operation in complex multi-task environments.

Yulai Zhang, Yinrong Zhang, Ting Wu +1

School of Future Technology, Shanghai University, Shanghai, China

Legged Robotics Humanoid Robot Control Robotics RL for Legged Locomotion Multi-Task RL

Apr 21, 2026cs.RO

Multi-Gait Learning for Humanoid Robots Using Reinforcement Learning with Selective Adversarial Motion Prior

Learning diverse locomotion skills for humanoid robots in a unified reinforcement learning framework remains challenging due to the conflicting requirements of stability and dynamic expressiveness across different gaits. We present a multi-gait learning approach that enables a humanoid robot to master five distinct gaits -- walking, goose-stepping, running, stair climbing, and jumping -- using a consistent policy structure, action space, and reward formulation. The key contribution is a selective Adversarial Motion Prior (AMP) strategy: AMP is applied to periodic, stability-critical gaits (walking, goose-stepping, stair climbing) where it accelerates convergence and suppresses erratic behavior, while being deliberately omitted for highly dynamic gaits (running, jumping) where its regularization would over-constrain the motion. Policies are trained via PPO with domain randomization in simulation and deployed on a physical 12-DOF humanoid robot through zero-shot sim-to-real transfer. Quantitative comparisons demonstrate that selective AMP outperforms a uniform AMP policy across all five gaits, achieving faster convergence, lower tracking error, and higher success rates on stability-focused gaits without sacrificing the agility required for dynamic ones.

Yuanye Wu, Keyi Wang, Linqi Ye +1

School of Future Technology, Shanghai University, Shanghai, 200444, China · National and Local Co-Built Humanoid Robotics Innovation Center, 201203 Shanghai, China

Humanoid Robot Locomotion Robot Locomotion RL for Legged Locomotion

Apr 19, 2026cs.RO

Learning Whole-Body Humanoid Locomotion via Motion Generation and Motion Tracking

Whole-body humanoid locomotion is challenging due to high-dimensional control, morphological instability, and the need for real-time adaptation to various terrains using onboard perception. Directly applying reinforcement learning (RL) with reward shaping to humanoid locomotion often leads to lower-body-dominated behaviors, whereas imitation-based RL can learn more coordinated whole-body skills but is typically limited to replaying reference motions without a mechanism to adapt them online from perception for terrain-aware locomotion. To address this gap, we propose a whole-body humanoid locomotion framework that combines skills learned from reference motions with terrain-aware adaptation. We first train a diffusion model on retargeted human motions for real-time prediction of terrain-aware reference motions. Concurrently, we train a whole-body reference tracker with RL using this motion data. To improve robustness under imperfectly generated references, we further fine-tune the tracker with a frozen motion generator in a closed-loop setting. The resulting system supports directional goal-reaching control with terrain-aware whole-body adaptation, and can be deployed on a Unitree G1 humanoid robot with onboard perception and computation. The hardware experiments demonstrate successful traversal over boxes, hurdles, stairs, and mixed terrain combinations. Quantitative results further show the benefits of incorporating online motion generation and fine-tuning the motion tracker for improved generalization and robustness.

Zewei Zhang, Kehan Wen, Michael Xu +7

Robotic Systems Lab, ETH Zurich · EPFL · Simon Fraser University +2

Robot Trajectory Tracking Humanoid Robot Locomotion Terrain-Aware Robot Locomotion Robot Locomotion RL for Legged Locomotion Robot Imitation Learning+2

Apr 16, 2026cs.RO

Switch: Learning Agile Skills Switching for Humanoid Robots

Recent advancements in whole-body control through deep reinforcement learning have enabled humanoid robots to achieve remarkable progress in real-world chal lenging locomotion skills. However, existing approaches often struggle with flexible transitions between distinct skills, cre ating safety concerns and practical limitations. To address this challenge, we introduce a hierarchical multi-skill system, Switch, enabling seamless skill transitions at any moment. Our approach comprises three key components: (1) a Skill Graph (SG) that establishes potential cross-skill transitions based on kinematic similarity within multi-skill motion data, (2) a whole-body tracking policy trained on this skill graph through deep reinforcement learning, and (3) an online skill scheduler to drive the tracking policy for robust skill execution and smooth transitions. For skill switching or significant tracking deviations, the scheduler performs online graph search to find the optimal feasible path, which ensures efficient, stable, and real-time execution of diverse locomotion skills. Comprehensive experiments demonstrate that Switch empowers humanoid to execute agile skill transitions with high success rates while maintaining strong motion imitation performance.

Yuen-Fui Lau, Qihan Zhao, Yinhuai Wang +4

The Hong Kong University of Science and Technology

Humanoid Robot Locomotion Humanoid Robot Control RL for Legged Locomotion

Apr 16, 2026cs.RO

Model-Based Reinforcement Learning Exploits Passive Body Dynamics for High-Performance Biped Robot Locomotion

Embodiment is a significant keyword in recent machine learning fields. This study focused on the passive nature of the body of a biped robot to generate walking and running locomotion using model-based deep reinforcement learning. We constructed two models in a simulator, one with passive elements (e.g., springs) and the other, which is similar to general humanoids, without passive elements. The training of the model with passive elements was highly affected by the attractor of the system. This lead that although the trajectories quickly converged to limit cycles, it took a long time to obtain large rewards. However, thanks to the attractor-driven learning, the acquired locomotion was robust and energy-efficient. The results revealed that robots with passive elements could efficiently acquire high-performance locomotion by utilizing stable limit cycles generated through dynamic interaction between the body and ground. This study demonstrates the importance of implementing passive properties in the body for future embodied AI.

Tomoya Kamimura, Haruka Washiyama, Akihito Sano

Department of Mechanical Science and Bioengineering, Graduate School of Engineering and Science, The University of Osaka, Toyonaka, Japan. · Department of ElectricalTechnology,and MechanicalAichi,Engineering,Japan. Nagoya Institute of

Robot Locomotion RL for Legged Locomotion Model-Based RL

Mar 13, 2026cs.RO

SmoothTurn: Learning to Turn Smoothly for Agile Navigation with Quadrupedal Robots

Quadrupedal robots show great potential for valuable real-world applications such as fire rescue and industrial inspection. Such applications often require urgency and the ability to navigate agilely, which in turn demands the capability to change directions smoothly while running in high speed. Existing approaches for agile navigation typically learn a single-goal reaching policy by encouraging the robot to stay at the target position after reaching there. As a result, when the policy is used to reach sequential goals that require changing directions, it cannot anticipate upcoming maneuvers or maintain momentum across the switch of goals, thereby preventing the robot from fully exploiting its agility potential. In this work, we formulate the task as sequential local navigation, extending the single-goal-conditioned local navigation formulation in prior work. We then introduce SmoothTurn, a learning-based control framework that learns to turn smoothly while running rapidly for agile sequential local navigation. The framework adopts a novel sequential goal-reaching reward, an expanded observation space with a lookahead window for future goals, and an automatic goal curriculum that progressively expands the difficulty of sampled goal sequences based on the goal-reaching performance. The trained policy can be directly deployed on real quadrupedal robots with onboard sensors and computation. Both simulation and real-world empirical results show that SmoothTurn learns an agile locomotion policy that performs smooth turning across goals, with emergent behaviors such as controlling momentum when switching goals, facing towards the future goal in advance, and planning efficient paths.

Zunzhi You, Yunke Wang, Haolan Guo +1

School of Computer Science, University of Sydney

Robot Policy Learning Robot Navigation RL for Legged Locomotion Quadruped Locomotion

Jan 22, 2026cs.RO

PUMA: Perception-driven Unified Foothold Prior for Mobility Augmented Quadruped Parkour

Parkour tasks for quadrupeds have emerged as a promising benchmark for agile locomotion. While human athletes can effectively perceive environmental characteristics to select appropriate footholds for obstacle traversal, endowing legged robots with similar perceptual reasoning remains a significant challenge. Existing methods often rely on hierarchical controllers that follow pre-computed footholds, thereby constraining the robot's real-time adaptability and the exploratory potential of reinforcement learning. To overcome these challenges, we present PUMA, an end-to-end learning framework that integrates visual perception and foothold priors into a single-stage training process. This approach leverages terrain features to estimate egocentric polar foothold priors, composed of relative distance and heading, guiding the robot in active posture adaptation for parkour tasks. Extensive experiments conducted in simulation and real-world environments across various discrete complex terrains, demonstrate PUMA's exceptional agility and robustness in challenging scenarios.

Liang Wang, Kanzhong Yao, Yang Liu +4

Institute of Cyber-Systems and Control, Zhejiang University, 310027, China · Institute of Artificial Intelligence (TeleAI), China Telecom.

Legged Robotics Terrain-Aware Robot Locomotion RL for Legged Locomotion Robotic Perception Quadruped Locomotion