Humanoid Robot Locomotion

This paper proposes a novel alternative to existing sim-to-real methods for training control policies with simulated experiences. Unlike prior methods that typically rely on domain randomization over a fixed finite set of parameters, the proposed approach injects state-dependent perturbations into the input joint torque during forward simulation. These perturbations are designed to simulate a broader spectrum of reality gaps than standard parameter randomization without requiring additional training. By using neural networks as flexible perturbation generators, the proposed method can represent complex, state-dependent uncertainties, such as nonlinear actuator dynamics and contact compliance, that parametric randomization cannot capture. Experimental results demonstrate that the proposed approach enables humanoid locomotion policies to achieve superior robustness against complex, unseen reality gaps in both simulation and real-world deployment.

Training perceptive humanoid locomotion policies that traverse complex terrains with natural gaits remains an open challenge, typically demanding multi-stage training pipelines, adversarial objectives, or extensive real-world calibration. We present PRIOR, an efficient and reproducible framework built on Isaac Lab that achieves robust terrain traversal with human-like gaits through a simple yet effective design: (i) a parametric gait generator that supplies stable reference trajectories derived from motion capture without adversarial training, (ii) a GRU-based state estimator that infers terrain geometry directly from egocentric depth images via self-supervised heightmap reconstruction, and (iii) terrain-adaptive footstep rewards that guide foot placement toward traversable regions. Through systematic analysis of depth image resolution trade-offs, we identify configurations that maximize terrain fidelity under real-time constraints, substantially reducing perceptual overhead without degrading traversal performance. Comprehensive experiments across terrains of varying difficulty-including stairs, boxes, and gaps-demonstrate that each component yields complementary and essential performance gains, with the full framework achieving a 100% traversal success rate. We will open-source the complete PRIOR framework, including the training pipeline, parametric gait generator, and evaluation benchmarks, to serve as a reproducible foundation for humanoid locomotion research on Isaac Lab.

While generative models have become effective at producing human-like motions from text, transferring these motions to humanoid robots for physical execution remains challenging. Existing pipelines are often limited by retargeting, where kinematic quality is undermined by physical infeasibility, contact-transition errors, and the high cost of real-world dynamical data. We present a unified latent-driven framework that bridges natural language and whole-body humanoid locomotion through a retarget-free, physics-optimized pipeline. Rather than treating generation and control as separate stages, our key insight is to couple them bidirectionally under physical constraints.We introduce a Physical Plausibility Optimization (PP-Opt) module as the coupling interface. In the forward direction, PP-Opt refines a teacher-student distillation policy with a plausibility-centric reward to suppress artifacts such as floating, skating, and penetration. In the backward direction, it converts reward-optimized simulation rollouts into high-quality explicit motion data, which is used to fine-tune the motion generator toward a more physically plausible latent distribution. This bidirectional design forms a self-improving cycle: the generator learns a physically grounded latent space, while the controller learns to execute latent-conditioned behaviors with dynamical integrity.Extensive experiments on the Unitree G1 humanoid show that our bidirectional optimization improves tracking accuracy and success rates. Across IsaacLab and MuJoCo, the implicit latent-driven pipeline consistently outperforms conventional explicit retargeting baselines in both precision and stability. By coupling diffusion-based motion generation with physical plausibility optimization, our framework provides a practical path toward deployable text-guided humanoid intelligence.

Agile humanoid locomotion in complex 3D en- vironments requires balancing perceptual fidelity with com- putational efficiency, yet existing methods typically rely on rigid sensing configurations. We propose ADAPT (Adaptive dual-projection architecture for perceptive traversal), which represents the environment using a horizontal elevation map for terrain geometry and a vertical distance map for traversable- space constraints. ADAPT further treats its spatial sensing range as a learnable action, enabling the policy to expand its perceptual horizon during fast motion and contract it in cluttered scenes for finer local resolution. Compared with voxel-based baselines, ADAPT drastically reduces observation dimensionality and computational overhead while substantially accelerating training. Experimentally, it achieves successful zero-shot transfer to a Unitree G1 Humanoid and signifi- cantly outperforms fixed-range baselines, yielding highly robust traversal across diverse 3D environtmental challenges.

Reinforcement learning (RL) has demonstrated substantial potential for humanoid bipedal locomotion and the control of complex motions. To cope with oscillations and impacts induced by environmental interactions, compliant control is widely regarded as an effective remedy. However, the model-free nature of RL makes it difficult to impose task-specified and quantitatively verifiable compliance objectives, and classical model-based stiffness designs are not directly applicable. Lipschitz-Constrained Policies (LCP), which regularize the local sensitivity of a policy via gradient penalties, have recently been used to smooth humanoid motions. Nevertheless, existing LCP-based methods typically employ a single scalar Lipschitz budget and lack an explicit connection to physically meaningful compliance specifications in real-world systems. In this study, we propose an anisotropic Lipschitz-constrained policy (ALCP) that maps a task-space stiffness upper bound to a state-dependent Lipschitz-style constraint on the policy Jacobian. The resulting constraint is enforced during RL training via a hinge-squared spectral-norm penalty, preserving physical interpretability while enabling direction-dependent compliance. Experiments on humanoid robots show that ALCP improves locomotion stability and impact robustness, while reducing oscillations and energy usage.

Humanoid robots deployed in industrial environments are required to perform load-carrying transportation tasks that tightly couple locomotion and manipulation. However, achieving stable and robust locomotion under varying payloads and upper-body motions is challenging due to dynamic coupling and partial observability. This paper presents a load-aware locomotion framework for industrial humanoids based on a decoupled yet coordinated loco-manipulation architecture. Lower-body locomotion is controlled via a reinforcement learning policy producing residual joint actions on kinematically derived nominal configurations. A kinematics-based locomotion reference with a height-conditioned joint-space offset guides learning, while a history-based state estimator infers base linear velocity and height and encodes residual load- and manipulation-induced disturbances in a compact latent representation. The framework is trained entirely in simulation and deployed on a full-size humanoid robot without fine-tuning. Simulation and real-world experiments demonstrate faster training, accurate height tracking, and stable loco-manipulation. Project page: https://lequn-f.github.io/LALO/

Robots are increasingly expected to execute open ended natural language requests in human environments, which demands reliable long horizon execution under partial observability. This is especially challenging for humanoids because locomotion and manipulation are tightly coupled through stance, reachability, and balance. We present a humanoid agent framework that turns VLM plans into verifiable task programs and closes the loop with multi object 3D geometric supervision. A VLM planner compiles each instruction into a typed JSON sequence of subtasks with explicit predicate based preconditions and success conditions. Using SAM3 and RGB-D, we ground all task relevant entities in 3D, estimate object centroids and extents, and evaluate predicates over stable frames to obtain condition level diagnostics. The supervisor uses these diagnostics to verify subtask completion and to provide condition-level feedback for progression and replanning. We execute each subtask by coordinating humanoid locomotion and whole-body manipulation, selecting feasible motion primitives under reachability and balance constraints. Experiments on tabletop manipulation and long horizon humanoid loco manipulation tasks show improved robustness from multi object grounding, temporal stability, and recovery driven replanning.

Stabilizing unsecured payloads against the inherent oscillations of dynamic bipedal locomotion remains a critical engineering bottleneck for humanoids in unstructured environments. To solve this, we introduce ReST-RL, a hierarchical reinforcement learning architecture that explicitly decouples locomotion from payload stabilization, evaluated via the SteadyTray benchmark. Rather than relying on monolithic end-to-end learning, our framework integrates a robust base locomotion policy with a dynamic residual module engineered to actively cancel gait-induced perturbations at the end-effector. This architectural separation ensures steady tray transport without degrading the underlying bipedal stability. In simulation, the residual design significantly outperforms end-to-end baselines in gait smoothness and orientation accuracy, achieving a 96.9% success rate in variable velocity tracking and 74.5% robustness against external force disturbances. Successfully deployed on the Unitree G1 humanoid hardware, this modular approach demonstrates highly reliable zero-shot sim-to-real generalization across various objects and external force disturbances.

We present the KinoDynamic Motion Retargeting (KDMR) framework, a novel approach for humanoid locomotion that models the retargeting process as a multi-contact, whole-body trajectory optimization problem. Conventional kinematics-based retargeting methods rely solely on spatial motion capture (MoCap) data, inevitably introducing physically inconsistent artifacts, such as foot sliding and ground penetration, that severely degrade the performance of downstream imitation learning policies. To bridge this gap, KDMR extends beyond pure kinematics by explicitly enforcing rigid-body dynamics and contact complementarity constraints. Further, by integrating ground reaction force (GRF) measurements alongside MoCap data, our method automatically detects heel-toe contact events to accurately replicate complex human-like contact patterns. We evaluate KDMR against the state-of-the-art baseline, GMR, across three key dimensions: 1) the dynamic feasibility and smoothness of the retargeted motions, 2) the accuracy of GRF tracking compared to raw source data, and 3) the training efficiency and final performance of downstream control policies trained via the BeyondMimic framework. Experimental results demonstrate that KDMR significantly outperforms purely kinematic methods, yielding dynamically viable reference trajectories that accelerate policy convergence and enhance overall locomotion stability. Our end-to-end pipeline will be open-sourced upon publication.

Distilling humanoid locomotion control from offline datasets into deployable policies remains a challenge, as existing methods rely on privileged full-body states that require complex and often unreliable state estimation. We present Sensor-Conditioned Diffusion Policies (SCDP) that enables humanoid locomotion using only onboard sensors, eliminating the need for explicit state estimation. SCDP decouples sensing from supervision through mixed-observation training: diffusion model conditions on sensor histories while being supervised to predict privileged future state-action trajectories, enforcing the model to infer the motion dynamics under partial observability. We further develop restricted denoising, context distribution alignment, and context-aware attention masking to encourage implicit state estimation within the model and to prevent train-deploy mismatch. We validate SCDP on velocity-commanded locomotion and motion reference tracking tasks. In simulation, SCDP achieves near-perfect success on velocity control (99-100%) and 93% tracking success in AMASS test set, performing comparable to privileged baselines while using only onboard sensors. Finally, we deploy the trained policy on a real G1 humanoid at 50 Hz, demonstrating robust real robot locomotion without external sensing or state estimation.

Humanoid robots, characterized by numerous degrees of freedom and a high center of gravity, are inherently unstable. Safe omnidirectional locomotion on stairs requires both omnidirectional terrain perception and reliable foothold selection. Existing methods often rely on forward-facing depth cameras, which create blind zones that restrict omnidirectional mobility. Furthermore, sparse post-contact unsafe stepping penalties lead to low learning efficiency and suboptimal strategies. To realize safe stair-traversal gaits, this paper introduces a single-stage training framework incorporating a dense unsafe stepping penalty that provides continuous feedback as the foot approaches a hazardous placement. To obtain stable and reliable elevation maps, we build a rolling point-cloud mapping system with spatiotemporal confidence decay and a self-protection zone mechanism, producing temporally consistent local maps. These maps are further refined by an Edge-Guided Asymmetric U-Net (EGAU), which mitigates reconstruction distortion caused by sparse LiDAR returns on stair risers. Simulation and real-robot experiments show that the proposed method achieves a near-100% safe stepping rate on stair terrains in simulation, while maintaining a remarkably high safe stepping rate in real-world deployments. Furthermore, it completes a continuous long-distance walking test on complex outdoor terrains, demonstrating reliable sim-to-real transfer and long-term stability.

The prevailing paradigm of perceptive humanoid locomotion relies heavily on active depth sensors. However, this depth-centric approach fundamentally discards the rich semantic and dense appearance cues of the visual world, severing low-level control from the high-level reasoning essential for general embodied intelligence. While monocular RGB offers a ubiquitous, information-dense alternative, end-to-end reinforcement learning from raw 2D pixels suffers from extreme sample inefficiency and catastrophic sim-to-real collapse due to the inherent loss of geometric scale. To break this deadlock, we propose GeoLoco, a purely RGB-driven locomotion framework that conceptualizes monocular images as high-dimensional 3D latent representations by harnessing the powerful geometric priors of a frozen, scale-aware Visual Foundation Model (VFM). Rather than naive feature concatenation, we design a proprioceptive-query multi-head cross-attention mechanism that dynamically attends to task-critical topological features conditioned on the robot's real-time gait phase. Crucially, to prevent the policy from overfitting to superficial textures, we introduce a dual-head auxiliary learning scheme. This explicit regularization forces the high-dimensional latent space to strictly align with the physical terrain geometry, ensuring robust zero-shot sim-to-real transfer. Trained exclusively in simulation, GeoLoco achieves robust zero-shot transfer to the Unitree G1 humanoid and successfully negotiates challenging terrains.

Walking over disconnected footholds requires selecting landing regions while adapting step timing to the robot's motion. We present a perceptive model predictive planner that combines discrete region selection, foot placement, and current-step duration in a mixed-integer quadratic program using step-to-step Divergent Component of Motion (DCM) dynamics. Onboard depth data are fused into a probabilistic heightmap in the stance foot frame. Convex steppable regions are extracted and shrunk by margins that increase with estimated height uncertainty. Linear constraints impose capturability-based bounds on DCM evolution and limit swing-foot retargeting using the remaining commanded swing time. Within-step replanning updates the initial DCM from measurements to respond to model mismatch and disturbances. We evaluate the framework on Digit in simulation over randomized footholds and on hardware over separated plates, with mean planner solve times of 11.4ms and 4.0ms, respectively.

Recent advances in humanoid locomotion have enabled dynamic behaviors such as dancing, martial arts, and parkour, yet these capabilities are predominantly demonstrated in open, flat, and obstacle-free settings. In contrast, real-world environments such as homes, offices, and public spaces, are densely cluttered, three-dimensional, and geometrically constrained, requiring scene-aware whole-body coordination, precise balance control, and reasoning over spatial constraints imposed by furniture and household objects. However, humanoid locomotion in cluttered 3D environments remains underexplored, and no public dataset systematically couples full-body human locomotion with the scene geometry that shapes it. To address this gap, we present Moving Through Clutter (MTC), an opensource Virtual Reality (VR) based data collection and evaluation framework for scene-aware humanoid locomotion in cluttered environments. Our system procedurally generates scenes with controllable clutter levels and captures embodiment-consistent, whole-body human motion through immersive VR navigation, which is then automatically retargeted to a humanoid robot model. We further introduce benchmarks that quantify environment clutter level and locomotion performance, including stability and collision safety. Using this framework, we compile a dataset of 348 trajectories across 145 diverse 3D cluttered scenes. The dataset provides a foundation for studying geometry-induced adaptation in humanoid locomotion and developing scene-aware planning and control methods.

While recent advances have demonstrated strong performance in individual humanoid skills such as upright locomotion, fall recovery and whole-body coordination, learning a single policy that masters all these skills remains challenging due to the diverse dynamics and conflicting control objectives involved. To address this, we introduce X-Loco, a framework for training a vision-based generalist humanoid locomotion policy. X-Loco trains multiple oracle specialist policies and adopts a synergetic policy distillation with a case-adaptive specialist selection mechanism, which dynamically leverages multiple specialist policies to guide a vision-based student policy. This design enables the student to acquire a broad spectrum of locomotion skills, ranging from fall recovery to terrain traversal and whole-body coordination skills. To the best of our knowledge, X-Loco is the first framework to demonstrate vision-based humanoid locomotion that jointly integrates upright locomotion, whole-body coordination and fall recovery, while operating solely under velocity commands without relying on reference motions. Experimental results show that X-Loco achieves superior performance, demonstrated by tasks such as fall recovery and terrain traversal. Ablation studies further highlight that our framework effectively leverages specialist expertise and enhances learning efficiency.

For effective deployment in real-world environments, humanoid robots must autonomously navigate a diverse range of complex terrains with abrupt transitions. While the Vanilla mixture of experts (MoE) framework is theoretically capable of modeling diverse terrain features, in practice, the gating network exhibits nearly uniform expert activations across different terrains, weakening the expert specialization and limiting the model's expressive power. To address this limitation, we introduce CMoE, a novel single-stage reinforcement learning framework that integrates contrastive learning to refine expert activation distributions. By imposing contrastive constraints, CMoE maximizes the consistency of expert activations within the same terrain while minimizing their similarity across different terrains, thereby encouraging experts to specialize in distinct terrain types. We validated our approach on the Unitree G1 humanoid robot through a series of challenging experiments. Results demonstrate that CMoE enables the robot to traverse continuous steps up to 20 cm high and gaps up to 80 cm wide, while achieving robust and natural gait across diverse mixed terrains, surpassing the limits of existing methods. To support further research and foster community development, we release our code publicly.

Footstep planning involves a challenging combinatorial search. Traditional A* approaches require discretising reachability constraints, while Mixed-Integer Programming (MIP) supports continuous formulations but quickly becomes intractable, especially when rotations are included. We present CASSR, a novel framework that recursively propagates convex, continuous formulations of a robot's kinematic constraints within an A* search. Combined with a new cost-to-go heuristic based on the EPA algorithm, CASSR efficiently plans contact sequences of up to 30 footsteps in under 125 ms. Experiments on biped locomotion tasks demonstrate that CASSR outperforms traditional discretised A* by up to a factor of 100, while also surpassing a commercial MIP solver. These results show that CASSR enables fast, reliable, and real-time footstep planning for biped robots.

It remains challenging to achieve human-like locomotion in legged robots due to fundamental discrepancies between biological and mechanical structures. Although imitation learning has emerged as a promising approach for generating natural robotic movements, simply replicating joint angle trajectories fails to capture the underlying principles of human motion. This study proposes a Gait Divergence Analysis Framework (GDAF), a unified biomechanical evaluation framework that systematically quantifies kinematic and kinetic discrepancies between humans and bipedal robots. We apply GDAF to systematically compare human and humanoid locomotion across 28 walking speeds. To enable reproducible analysis, we collect and release a speed-continuous humanoid locomotion dataset from a state-of-the-art humanoid controller. We further provide an open-source implementation of GDAF, including analysis, visualization, and MuJoCo-based tools, enabling quantitative, interpretable, and reproducible biomechanical analysis of humanoid locomotion. Results demonstrate that despite visually human-like motion generated by modern humanoid controllers, significant biomechanical divergence persists across speeds. Robots exhibit systematic deviations in gait symmetry, energy distribution, and joint coordination, indicating that substantial room remains for improving the biomechanical fidelity and energetic efficiency of humanoid locomotion. This work provides a quantitative benchmark for evaluating humanoid locomotion and offers data and versatile tools to support the development of more human-like and energetically efficient locomotion controllers. The data and code will be made publicly available upon acceptance of the paper.

While recent advances in humanoid locomotion have achieved stable walking on varied terrains, capturing the agility and adaptivity of highly dynamic human motions remains an open challenge. In particular, agile parkour in complex environments demands not only low-level robustness, but also human-like motion expressiveness, long-horizon skill composition, and perception-driven decision-making. In this paper, we present Perceptive Humanoid Parkour (PHP), a modular framework that enables humanoid robots to autonomously perform long-horizon, vision-based parkour across challenging obstacle courses. Our approach first leverages motion matching, formulated as nearest-neighbor search in a feature space, to compose retargeted atomic human skills into long-horizon kinematic trajectories. This framework enables the flexible composition and smooth transition of complex skill chains while preserving the elegance and fluidity of dynamic human motions. Next, we train motion-tracking reinforcement learning (RL) expert policies for these composed motions, and distill them into a single depth-based, multi-skill student policy, using a combination of DAgger and RL. Crucially, the combination of perception and skill composition enables autonomous, context-aware decision-making: using only onboard depth sensing and a discrete 2D velocity command, the robot selects and executes whether to step over, climb onto, vault or roll off obstacles of varying geometries and heights. We validate our framework with extensive real-world experiments on a Unitree G1 humanoid robot, demonstrating highly dynamic parkour skills such as climbing tall obstacles up to 1.25m (96% robot height), as well as long-horizon multi-obstacle traversal with closed-loop adaptation to real-time obstacle perturbations.

Achieving highly dynamic parkour with humanoid robots on complex terrains unseen during the pre-training stage remains a challenge in robotics. Although general locomotion policies demonstrate capabilities across broad terrain distributions, they often struggle with arbitrary and highly challenging environments. To overcome this limitation, we propose a real-to-sim-to-real framework for rapid test-time training (TTT): environment-specific policy fine-tuning in simulation before deployment on a newly encountered terrain. We adopt a two-stage end-to-end learning paradigm: a policy is first pre-trained on diverse procedurally generated terrains, followed by rapid fine-tuning on high-fidelity meshes reconstructed from real-world captures. Specifically, we develop an efficient, feed-forward, and high-fidelity geometry reconstruction pipeline using RGB-D inputs, ensuring both speed and quality during test-time training. We demonstrate that TTT-Parkour empowers humanoid robots to master complex obstacles, including wedges, stakes, boxes, trapezoids, and narrow beams. The entire pipeline, including capture, reconstruction, and test-time training, takes approximately 10 minutes for most tested terrains. Experiments show improved traversal on the tested terrains after fine-tuning, with direct sim-to-real deployment and no further policy updates on the robot.

Achieving robust humanoid locomotion in complex, unstructured environments requires transitioning from reactive proprioception to proactive perception. However, integrating exteroception remains a significant challenge: existing approaches often fail to achieve high-speed, stable locomotion across diverse, unstructured terrains. In this work, we present Hiking in the Wild, an extensible, end-to-end perceptive legged parkour framework designed for robust humanoid hiking. Our approach maps depth inputs and proprioception directly to joint actions, without relying on external localization and mapping. To ensure safety and training stability, we introduce two key mechanisms: a foothold safety mechanism combining extensible Terrain Edge Detection with Foot Volume Points to reduce catastrophic slippage on edges, and a Flat Patch Sampling strategy that mitigates reward hacking by generating feasible navigation targets. Extensive experiments on the Unitree G1 humanoid robot demonstrate that our policy enables robust traversal of complex terrains at speeds up to 2.5 m/s.

Although recent years have seen significant progress of humanoid robots in walking and running, the frequent foot strikes with ground during these locomotion gaits inevitably generate high instantaneous impact forces, which leads to exacerbated joint wear and poor energy utilization. Roller skating, as a sport with substantial biomechanical value, can achieve fast and continuous sliding through rational utilization of body inertia, featuring minimal kinetic energy loss. Therefore, this study proposes a novel humanoid robot with each foot equipped with a row of four passive wheels for roller skating. A deep reinforcement learning control framework is also developed for the swizzle gait with the reward function design based on the intrinsic characteristics of roller skating. The learned policy is first analyzed in simulation and then deployed on the physical robot to demonstrate the smoothness and efficiency of the swizzle gait over traditional bipedal walking gait in terms of Impact Intensity and Cost of Transport during locomotion. A reduction of $75.86\%$ and $63.34\%$ of these two metrics indicate roller skating as a superior locomotion mode for enhanced energy efficiency and joint longevity.

Humans intuitively move to sound, but current humanoid robots lack expressive improvisational capabilities, confined to predefined motions or sparse commands. Generating motion from audio and then retargeting it to robots relies on explicit motion reconstruction, leading to cascaded errors, high latency, and disjointed acoustic-actuation mapping. We propose RoboPerform, the first unified audio-to-locomotion framework that can directly generate music-driven dance and speech-driven co-speech gestures from audio. Guided by the core principle of "motion = content + style", the framework treats audio as implicit style signals and eliminates the need for explicit motion reconstruction. RoboPerform integrates a ResMoE teacher policy for adapting to diverse motion patterns and a diffusion-based student policy for audio style injection. This retargeting-free design ensures low latency and high fidelity. Experimental validation shows that RoboPerform achieves promising results in physical plausibility and audio alignment, successfully transforming robots into responsive performers capable of reacting to audio.

Motion imitation is a promising approach for humanoid locomotion, enabling agents to acquire humanlike behaviors. Existing methods typically rely on high-quality motion capture datasets such as AMASS, but these are scarce and expensive, limiting scalability and diversity. Recent studies attempt to scale data collection by converting large-scale internet videos, exemplified by Humanoid-X. However, they often suffer from physical artifacts such as floating, penetration, and foot skating, which hinder stable imitation. To address this, we introduce PHUMA, a Physically Reliable HUMAnoid locomotion dataset produced by a two-stage pipeline combining physics-aware curation and physics-constrained retargeting, aggregating both motion capture and internet video into a physically reliable, 73-hour corpus. On motion tracking benchmarks, PHUMA-trained policies achieve higher success rates than those trained on AMASS and Humanoid-X, and successfully transfer zero-shot to a real Unitree G1. The code is available at https://davian-robotics.github.io/PHUMA.

Traversing narrow paths is challenging for humanoid robots due to the sparse and safety-critical footholds required. Purely template-based or end-to-end reinforcement learning-based methods suffer from such harsh terrains. This paper proposes a two stage training framework for such narrow path traversing tasks, coupling a template-based foothold planner with a low-level foothold tracker from Stage-I training and a lightweight perception aided foothold modifier from Stage-II training. With the curriculum setup from flat ground to narrow paths across stages, the resulted controller in turn learns to robustly track and safely modify foothold targets to ensure precise foot placement over narrow paths. This framework preserves the interpretability from the physics-based template and takes advantage of the generalization capability from reinforcement learning, resulting in easy sim-to-real transfer. The learned policies outperform purely template-based or reinforcement learning-based baselines in terms of success rate, centerline adherence and safety margins. Validation on a Unitree G1 humanoid robot yields successful traversal of a 0.2m wide and 3m long beam for 20 trials without any failure.

Push recovery during locomotion will facilitate the deployment of humanoid robots in human-centered environments. In this paper, we present a unified framework for walking control and push recovery for humanoid robots, leveraging the arms for push recovery while dynamically walking. The key innovation is to use the environment, such as walls, to facilitate push recovery by combining Single Rigid Body model predictive control (SRB-MPC) with Hybrid Linear Inverted Pendulum (HLIP) dynamics to enable robust locomotion, push detection, and recovery by utilizing the robot's arms to brace against such walls and dynamically adjusting the desired contact forces and stepping patterns. Extensive simulation results on a humanoid robot demonstrate improved perturbation rejection and tracking performance compared to HLIP alone, with the robot able to recover from pushes up to 100N for 0.2s while walking at commanded speeds up to 0.5m/s. Robustness is further validated in scenarios with angled walls and multi-directional pushes.