Quadruped Locomotion

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Overview

Quadruped locomotion research develops ways for four-legged robots to walk, run, jump, climb, and move through unfamiliar environments. Common approaches include reinforcement and imitation learning, model-predictive and whole-body control, and perception systems that use cameras, depth, LiDAR, or foot sensors to guide movement. Researchers also study hardware such as compliant feet and active spines, alongside sim-to-real transfer, adaptation to payloads or damage, and safety and energy constraints. Policies are increasingly tested on real robots and challenging terrain, but reliable transfer remains difficult when contact, sensing, or robot dynamics differ from training conditions.

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121 papers22 papers in the last four weeks, up 29% on the four weeks before. 0.1% of all new papers.

Apr 5, 2026

RK-MPC: Residual Koopman Model Predictive Control for Quadruped Locomotion in Offroad Environments

This paper presents Residual Koopman MPC (RK-MPC), a Koopman-based, data-driven model predictive control framework for quadruped locomotion that improves prediction fidelity while preserving real-time tractability. RK-MPC augments a nominal template model with a compact linear residual predictor learned from data in lifted coordinates, enabling systematic correction of model mismatch induced by contact variability and terrain disturbances with provable bounds on multi-step prediction error. The learned residual model is embedded within a convex quadratic-program MPC formulation, yielding a receding-horizon controller that runs onboard at 500 Hz and retains the structure and constraint-handling advantages of optimization-based control. We evaluate RK-MPC in both Gazebo simulation and Unitree Go1 hardware experiments, demonstrating reliable blind locomotion across contact disturbances, multiple gait schedules, and challenging off-road terrains including grass, gravel, snow, and ice. We further compare against Koopman/EDMD baselines using alternative observable dictionaries, including monomial and SE(3)SE(3)-structured bases, and show that the residual correction improves multi-step prediction and closed-loop performance while reducing sensitivity to the choice of observables. Overall, RK-MPC provides a practical, hardware-validated pathway for data-driven predictive control of quadrupeds in unstructured environments. See https://sriram-2502.github.io/rk-mpc for implementation videos.

Sriram S. K. S. Narayanan, Umesh Vaidya

Department of Mechanical Engineering, Clemson University, Clemson, SC 29630, USA

Model Predictive ControlQuadruped LocomotionResidual Dynamics LearningKoopman Operator LearningTerrain-Aware Robot Locomotion
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Apr 3, 2026

Learning-Based Fault Detection for Legged Robots in Remote Dynamic Environments

Operations in hazardous environments put humans, animals, and machines at high risk for physically damaging consequences. In contrast to humans and animals, quadruped robots cannot naturally identify and adjust their locomotion to a severely debilitated limb. The ability to detect limb damage and adjust movement to a new physical morphology is the difference between survival and death for humans and animals. The same can be said for quadruped robots autonomously carrying out remote assignments in dynamic, complex settings. This work presents the development and implementation of an off-line learning-based method to detect single limb faults from proprioceptive sensor data in a quadrupedal robot. The aim of the fault detection technique is to provide the correct output for the controller to select the appropriate tripedal gait to use given the robot's current physical morphology.

Abriana Stewart-Height, Seema Jahagirdar, Nikolai Matni

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge MA 02139, USA · Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, 19104, USA

Robot Failure DetectionLegged RoboticsQuadruped LocomotionRobotic Perception
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Apr 3, 2026

Learning Task-Invariant Properties via Dreamer: Enabling Efficient Policy Transfer for Quadruped Robots

Achieving quadruped robot locomotion across diverse and dynamic terrains presents significant challenges, primarily due to the discrepancies between simulation environments and real-world conditions. Traditional sim-to-real transfer methods often rely on manual feature design or costly real-world fine-tuning. To address these limitations, this paper proposes the DreamTIP framework, which incorporates Task-Invariant Properties learning within the Dreamer world model architecture to enhance sim-to-real transfer capabilities. Guided by large language models, DreamTIP identifies and leverages Task-Invariant Properties, such as contact stability and terrain clearance, which exhibit robustness to dynamic variations and strong transferability across tasks. These properties are integrated into the world model as auxiliary prediction targets, enabling the policy to learn representations that are insensitive to underlying dynamic changes. Furthermore, an efficient adaptation strategy is designed, employing a mixed replay buffer and regularization constraints to rapidly calibrate to real-world dynamics while effectively mitigating representation collapse and catastrophic forgetting. Extensive experiments on complex terrains, including Stair, Climb, Tilt, and Crawl, demonstrate that DreamTIP significantly outperforms state-of-the-art baselines in both simulated and real-world environments. Our method achieves an average performance improvement of 28.1% across eight distinct simulated transfer tasks. In the real-world Climb task, the baseline method achieved only a 10\ success rate, whereas our method attained a 100% success rate. These results indicate that incorporating Task-Invariant Properties into Dreamer learning offers a novel solution for achieving robust and transferable robot locomotion.

Junyang Liang, Yuxuan Liu, Yabin Chang +5

Shenzhen University, Shenzhen, China · Peng Cheng Laboratory, Shenzhen, China

Sim-to-Real TransferRobot Policy AdaptationQuadruped LocomotionModel-Based RLInvariant Representation Learning
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Apr 3, 2026

Learning Locomotion on Complex Terrain for Quadrupedal Robots with Foot Position Maps and Stability Rewards

Quadrupedal locomotion over complex terrain has been a long-standing research topic in robotics. While recent reinforcement learning-based locomotion methods improve generalizability and foot-placement precision, they rely on implicit inference of foot positions from joint angles, lacking the explicit precision and stability guarantees of optimization-based approaches. To address this, we introduce a foot position map integrated into the heightmap, and a dynamic locomotion-stability reward within an attention-based framework to achieve locomotion on complex terrain. We validate our method extensively on terrains seen during training as well as out-of-domain (OOD) terrains. Our results demonstrate that the proposed method enables precise and stable movement, resulting in improved locomotion success rates on both in-domain and OOD terrains.

Matthew Hwang, Yubin Liu, Ryo Hakoda +1

University of Tokyo, Japan

Quadruped LocomotionTerrain-Aware Robot LocomotionRL for Legged LocomotionReinforcement Learning
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Mar 25, 2026

QuadFM: Foundational Text-Driven Quadruped Motion Dataset for Generation and Control

Despite significant advances in quadrupedal robotics, a critical gap persists in foundational motion resources that holistically integrate diverse locomotion, emotionally expressive behaviors, and rich language semantics-essential for agile, intuitive human-robot interaction. Current quadruped motion datasets are limited to a few mocap primitives (e.g., walk, trot, sit) and lack diverse behaviors with rich language grounding. To bridge this gap, we introduce Quadruped Foundational Motion (QuadFM) , the first large-scale, ultra-high-fidelity dataset designed for text-to-motion generation and general motion control. QuadFM contains 11,784 curated motion clips spanning locomotion, interactive, and emotion-expressive behaviors (e.g., dancing, stretching, peeing), each with three-layer annotation-fine-grained action labels, interaction scenarios, and natural language commands-totaling 35,352 descriptions to support language-conditioned understanding and command execution. We further propose Gen2Control RL, a unified framework that jointly trains a general motion controller and a text-to-motion generator, enabling efficient end-to-end inference on edge hardware. On a real quadruped robot with an NVIDIA Orin, our system achieves real-time motion synthesis (<500 ms latency). Simulation and real-world results show realistic, diverse motions while maintaining robust physical interaction. The dataset will be released at https://github.com/GaoLii/QuadFM.

Li Gao, Fuzhi Yang, Jianhui Chen +4

AMAP, Alibaba Group

Robot Motion GenerationLegged RoboticsQuadruped LocomotionLanguage-Conditioned Robot ControlRL for Robotics
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Mar 23, 2026

MEVIUS2: Practical Open-Source Quadruped Robot with Sheet Metal Welding and Multimodal Perception

Various quadruped robots have been developed to date, and thanks to reinforcement learning, they are now capable of traversing diverse types of rough terrain. In parallel, there is a growing trend of releasing these robot designs as open-source, enabling researchers to freely build and modify robots themselves. However, most existing open-source quadruped robots have been designed with 3D printing in mind, resulting in structurally fragile systems that do not scale well in size, leading to the construction of relatively small robots. Although a few open-source quadruped robots constructed with metal components exist, they still tend to be small in size and lack multimodal sensors for perception, making them less practical. In this study, we developed MEVIUS2, an open-source quadruped robot with a size comparable to Boston Dynamics' Spot, whose structural components can all be ordered through e-commerce services. By leveraging sheet metal welding and metal machining, we achieved a large, highly durable body structure while reducing the number of individual parts. Furthermore, by integrating sensors such as LiDARs and a high dynamic range camera, the robot is capable of detailed perception of its surroundings, making it more practical than previous open-source quadruped robots. We experimentally validated that MEVIUS2 can traverse various types of rough terrain and demonstrated its environmental perception capabilities. All hardware, software, and training environments can be obtained from Supplementary Materials or https://github.com/haraduka/mevius2.

Kento Kawaharazuka, Keita Yoneda, Shintaro Inoue +3

The authors are with the 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.

RoboticsLegged RoboticsQuadruped Locomotion
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Mar 19, 2026

ADMM-Based Distributed MPC with Control Barrier Functions for Safe Multi-Robot Quadrupedal Locomotion

This paper proposes a fully decentralized model predictive control (MPC) framework with control barrier function (CBF) constraints for safety-critical trajectory planning in multi-robot legged systems. The incorporation of CBF constraints introduces explicit inter-agent coupling, which prevents direct decomposition of the resulting optimal control problems. To address this challenge, we reformulate the centralized safety-critical MPC problem using a structured distributed optimization framework based on the alternating direction method of multipliers (ADMM). By introducing a novel node-edge splitting formulation with consensus constraints, the proposed approach decomposes the global problem into independent node-local and edge-local quadratic programs that can be solved in parallel using only neighbor-to-neighbor communication. This enables fully decentralized trajectory optimization with symmetric computational load across agents while preserving safety and dynamic feasibility. The proposed framework is integrated into a hierarchical locomotion control architecture for quadrupedal robots, combining high-level distributed trajectory planning, mid-level nonlinear MPC enforcing single rigid body dynamics, and low-level whole-body control enforcing full-order robot dynamics. The effectiveness of the proposed approach is demonstrated through hardware experiments on two Unitree Go2 quadrupedal robots and numerical simulations involving up to four robots navigating uncertain environments with rough terrain and external disturbances. The results show that the proposed distributed formulation achieves performance comparable to centralized MPC while reducing the average per-cycle planning time by up to 51% in the four-agent case, enabling efficient real-time decentralized implementation.

Yicheng Zeng, Ruturaj S. Sambhus, Basit Muhammad Imran +3

Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA · The University of Texas at El Paso, El Paso, TX 79968, USA

Model Predictive ControlMulti-Robot Motion PlanningMulti-Robot CoordinationQuadruped Locomotion
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Mar 19, 2026

Efficient and Versatile Quadrupedal Skating: Optimal Co-design via Reinforcement Learning and Bayesian Optimization

In this paper, we present a hardware-control co-design approach that enables efficient and versatile roller skating on quadrupedal robots equipped with passive wheels. Passive-wheel skating reduces leg inertia and improves energy efficiency, particularly at high speeds. However, the absence of direct wheel actuation tightly couples mechanical design and control. To unlock the full potential of this modality, we formulate a bilevel optimization framework: an upper-level Bayesian Optimization searches the mechanical design space, while a lower-level Reinforcement Learning trains a motor control policy for each candidate design. The resulting design-policy pairs not only outperform human-engineered baselines, but also exhibit versatile behaviors such as hockey stop (rapid braking by turning sideways to maximize friction) and self-aligning motion (automatic reorientation to improve energy efficiency in the direction of travel), offering the first system-level study of dynamic skating motion on quadrupedal robots.

Hanwen Wang, Zhenlong Fang, Josiah Hanna +1

Hanwen Wang, Zhenlong Fang, and Josiah Hanna are with the University of Wisconsin - Madison. · Xiaobin Xiong was with the University of Wisconsin - Madison, and now with the Shanghai Innovation Institute (SII).

Robot Morphology-Control Co-DesignQuadruped LocomotionEnergy-Efficient Robot Locomotion
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Mar 17, 2026

LIMBERO: A Limbed Climbing Exploration Robot Toward Traveling on Rocky Cliffs

In lunar and planetary exploration, legged robots have attracted significant attention as an alternative to conventional wheeled robots, which struggle to traverse rough and uneven terrain. To enable locomotion over highly irregular and steeply inclined surfaces, limbed climbing robots equipped with grippers on their feet have emerged as a promising solution. In this paper, we present LIMBERO, a 10 kg-class quadrupedal climbing robot that employs spine-type grippers for stable locomotion and climbing on rugged and steep terrain. We first introduce a novel gripper design featuring coupled finger-closing and spine-hooking motions, tightly actuated by a single motor, which achieves exceptional grasping performance (>150 N) despite its lightweight design (525 g). Furthermore, we develop an efficient algorithm to visualize a geometry-based graspability index on continuous rough terrain. Finally, we integrate these components into LIMBERO and demonstrate its ability to ascend steep rocky surfaces under a 1 G gravity condition, a performance not previously achieved yet for limbed climbing robots of this scale.

Kentaro Uno, Masazumi Imai, Kazuki Takada +7

The authors are with the Space Robotics Lab. (SRL) in Department of Aerospace Engineering, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan. · The author is with the National Institute of Applied Sciences of Toulouse, 31400 Toulouse, France.

Robot LocomotionQuadruped LocomotionRobotic Grasping
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Mar 16, 2026

KiRAS: Keyframe Guided Self-Imitation for Robust and Adaptive Skill Learning in Quadruped Robots

With advances in reinforcement learning and imitation learning, quadruped robots can acquire diverse skills within a single policy by imitating multiple skill-specific datasets. However, the lack of datasets on complex terrains limits the ability of such multi-skill policies to generalize effectively in unstructured environments. Inspired by animation, we adopt keyframes as minimal and universal skill representations, relaxing dataset constraints and enabling the integration of terrain adaptability with skill diversity. We propose Keyframe Guided Self-Imitation for Robust and Adaptive Skill Learning (KiRAS), an end-to-end framework for acquiring and transitioning between diverse skill primitives on complex terrains. KiRAS first learns diverse skills on flat terrain through keyframe-guided self-imitation, eliminating the need for expert datasets; then continues training the same policy network on rough terrains to enhance robustness. To eliminate catastrophic forgetting, a proficiency-based Skill Initialization Technique is introduced. Experiments on Solo-8 and Unitree Go1 robots show that KiRAS enables robust skill acquisition and smooth transitions across challenging terrains. This framework demonstrates its potential as a lightweight platform for multi-skill generation and dataset collection. It further enables flexible skill transitions that enhance locomotion on challenging terrains.

Xiaoyi Wei, Peng Zhai, Jiaxin Tu +5

College of Intelligent Robotics and Advanced Manufacturing, Fudan University, China. · Power China Huadong Engineering Corporation Limited, China.

Robot Skill LearningQuadruped LocomotionImitation LearningTerrain-Aware Robot LocomotionContinual Robot Learning
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Mar 14, 2026

TransCurriculum: Multi-Dimensional Curriculum Learning for Fast & Stable Locomotion

High-speed legged locomotion struggles with stability and transfer losses at higher command velocities during deployment. One reason is that most curricula vary difficulty along single axis, for example increase the range of command velocities, terrain difficulty, or domain parameters (e.g. friction or payload mass) using either fixed update rule or instantaneous rewards while ignoring how the history of robot training has evolved. We propose TransCurriculum, a transformer-based multi-dimensional curriculum learning approach for agile quadrupedal locomotion. TransCurriculum adapts to 3 axes, velocity command targets, terrain difficulty, and domain randomization parameters (friction and payload mass). Rather than feeding task reward history directly into the low-level control policy, our formulation exploits it at the curriculum level. A transformer-based teacher retrieves the sequence of rewards and uses it to predict future rewards, success rate, and learning progress to guide expansion of this multidimensional curriculum towards high performing task bins. Finally we validate our approach on the Unitree Go1 robot in simulation (Isaac Gym) and deploy it zero-shot on Go1 hardware. Our TransCurriculum policy achieves a maximum velocity of 6.3 m/s in simulation and outperforms prior curriculum baselines. We tested our TransCurriculum trained policy on terrains (carpets, slopes, tiles, concrete), achieving a forward velocity of 4.1 m/s on carpet surpassing the fastest curriculum methods by 18.8% and achieves maximum zero-shot value among all tested methods. Our multi-dimensional curriculum also reduces the transfer loss to 18% from 27% for command only curriculum, demonstrating the benefits of joint training over velocity, terrain and domain randomization dimension while keeping the task success rate of 80-90% on rigid indoor and outdoor surfaces.

Prakhar Mishra, Amir Hossain Raj, Xuesu Xiao +1

University of Maryland, College Park, MD, USA. · George Mason University, Fairfax, VA, USA.

RL for Legged LocomotionCurriculum LearningQuadruped LocomotionSim-to-Real TransferTerrain-Aware Robot Locomotion
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Mar 13, 2026

Prepare to Turn: Learning Anticipatory Maneuvering for Fast Sequential Quadrupedal Navigation

Fast quadrupedal navigation requires preparing for the next turn while approaching the current goal. Policies trained to reach and remain at a single target can instead produce stop-and-go motion when applied to sequential goals, compromising its agility potential. We introduce PrepTurn, a reinforcement learning framework for anticipatory maneuvering in sequential local navigation. PrepTurn maps the current and next pose goals directly to joint actions, using the upcoming goal to inform how the robot should approaches the current one. Its persistent-credit reward encourages timely completion of the whole sequence by continuing to reward reached goals while moving on and preparing subsequent maneuvers, and an automatic curriculum that gradually increases goal difficulty is critical for learning stable turning behaviors. Together, these components enable the policy to coordinate approach speed and reorientation across goal transitions without prescribed trajectories or arrival times. Simulation and onboard Unitree Go2 experiments demonstrate fast, efficient sequential traversal with high completion and reduced stop-and-go motion. We further show that when the goal-reaching tolerances are more relaxed, the policy learns to exploit the freedom allowed by the task with emergent behaviors, such as turning to the next goal in advance and cutting corners within the permitted regions behaviors, to traverse goal sequences more efficiently.

Zunzhi You, Yunke Wang, Haolan Guo +1

All authors are with School of Computer Science, University of Sydney.

Robot Policy LearningRobot NavigationRL for Legged LocomotionQuadruped LocomotionQuadruped Robot Navigation
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Mar 12, 2026

Energy Prediction on Sloping Ground for Quadruped Robots

Energy management is a fundamental challenge for legged robots in outdoor environments. Endurance directly constrains mission success, while efficient resource use reduces ecological impact. This paper investigates how terrain slope and heading orientation influence the energetic cost of quadruped locomotion. We introduce a simple energy model that relies solely on standard onboard sensors, avoids specialized instrumentation, and remains applicable in previously unexplored environments. The model is identified from field runs on a commercial quadruped and expressed as a compact function of slope angle and heading. Field validation on natural terrain shows near-linear trends of force-equivalent cost with slope angle, consistently higher lateral costs, and additive behavior across trajectory segments, supporting path-level energy prediction for planning-oriented evaluation.

Mohamed Ounally, Cyrille Pierre, Johann Laconte

Université Clermont Auvergne, INRAE, UR TSCF, 63000, Clermont-Ferrand, France

Energy-Efficient Robot LocomotionQuadruped LocomotionTerrain-Aware Robot Locomotion
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Mar 12, 2026

MiNI-Q: A Miniature, Wire-Free Quadruped with Unbounded, Independently Actuated Leg Joints

Physical joint limits are common in legged robots and can restrict workspace, constrain gait design, and increase the risk of hardware damage. This paper introduces MiNI-Q^2, a miniature, wire-free quadruped robot with independently actuated, mechanically unbounded 2-DOF leg joints. We present the mechanical design, kinematic analysis, and experimental validation of the proposed robot. The leg mechanism enables both oscillatory gaits and rotary locomotion while allowing the robot to fold to a minimum height of 2.5 cm. Experimentally, MiNI-Q achieves speeds up to 0.46 m/s and demonstrates low-clearance crawling, stair climbing, inverted locomotion, jumping, and backflipping. The wire-free architecture extends our previous Q8bot design, improving assembly reliability at miniature scale. All mechanical and electrical design files are released open source to support reproducibility and further research.

Daniel Koh, Suraj Shah, Yufeng Wu +1

Department of Mechanical and Aerospace Engineering, UCLA, Los Angeles, CA 90095, USA.

Legged RoboticsRoboticsQuadruped Locomotion
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Mar 10, 2026

Towards Terrain-Aware Safe Locomotion for Quadrupedal Robots Using Proprioceptive Sensing

Achieving safe quadrupedal locomotion in real-world environments has attracted much attention in recent years. When walking over uneven terrain, achieving reliable estimation and realising safety-critical control based on the obtained information is still an open question. To address this challenge, especially for low-cost robots equipped solely with proprioceptive sensors (e.g., IMUs, joint encoders, and contact force sensors), this work first presents an estimation framework that generates a 2.5-D terrain map and extracts support plane parameters, which are then integrated into contact and state estimation. Then, we integrate this estimation framework into a safety-critical control pipeline by formulating control barrier functions that provide rigorous safety guarantees. Experiments demonstrate that the proposed terrain estimation method provides smooth terrain representations. Moreover, the coupled estimation framework of terrain, state, and contact reduces the mean absolute error of base position estimation by 64.8%, decreases the estimation variance by 47.2%, and improves the robustness of contact estimation compared to a decoupled framework. The terrain-informed CBFs integrate historical terrain information and current proprioceptive measurements to ensure global safety by keeping the robot out of hazardous areas and local safety by preventing body-terrain collision, relying solely on proprioceptive sensing.

Peiyu Yang, Jiatao Ding, Wei Pan +2

Dynamic Legged Systems, Istituto Italiano di Tecnologia (IIT), Italy · Department of Industrial Engineering, University of Trento, Italy · Department of Computer Science, University of Manchester, UK +2

Terrain-Aware Robot LocomotionQuadruped LocomotionRobot State EstimationControl Barrier Functions
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Mar 9, 2026

Predictive Control with Indirect Adaptive Laws for Payload Transportation by Quadrupedal Robots

This paper formally develops a novel hierarchical planning and control framework for robust payload transportation by quadrupedal robots, integrating a model predictive control (MPC) algorithm with a gradient-descent-based adaptive updating law. At the framework's high level, an indirect adaptive law estimates the unknown parameters of the reduced-order (template) locomotion model under varying payloads. These estimated parameters feed into an MPC algorithm for real-time trajectory planning, incorporating a convex stability criterion within the MPC constraints to ensure the stability of the template model's estimation error. The optimal reduced-order trajectories generated by the high-level adaptive MPC (AMPC) are then passed to a low-level nonlinear whole-body controller (WBC) for tracking. Extensive numerical investigations validate the framework's capabilities, showcasing the robot's proficiency in transporting unmodeled, unknown static payloads up to 109% in experiments on flat terrains and 91% on rough experimental terrains. The robot also successfully manages dynamic payloads with 73% of its mass on rough terrains. Performance comparisons with a normal MPC and an L1 MPC indicate a significant improvement. Furthermore, comprehensive hardware experiments conducted in indoor and outdoor environments confirm the method's efficacy on rough terrains despite uncertainties such as payload variations, push disturbances, and obstacles.

Leila Amanzadeh, Taizoon Chunawala, Randall T. Fawcett +2

Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA · Exponent Inc., Phoenix, AZ 85027, USA

Adaptive MPCRoboticsModel Predictive ControlQuadruped Locomotion
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Mar 9, 2026

Dual-Horizon Hybrid Internal Model for Low-Gravity Quadrupedal Jumping with Hardware-in-the-Loop Validation

Locomotion under reduced gravity is commonly realized through jumping, yet continuous pronking in lunar gravity remains challenging due to prolonged flight phases and sparse ground contact. The extended aerial duration increases landing impact sensitivity and makes stable attitude regulation over rough planetary terrain difficult. Existing approaches primarily address single jumps on flat surfaces and lack both continuous-terrain solutions and realistic hardware validation. This work presents a Dual-Horizon Hybrid Internal Model for continuous quadrupedal jumping under lunar gravity using proprioceptive sensing only. Two temporal encoders capture complementary time scales: a short-horizon branch models rapid vertical dynamics with explicit vertical velocity estimation, while a long-horizon branch models horizontal motion trends and center-of-mass height evolution across the jump cycle. The fused representation enables stable and continuous jumping under extended aerial phases characteristic of lunar gravity. To provide hardware-in-the-loop validation, we develop the MATRIX (Mixed-reality Adaptive Testbed for Robotic Integrated eXploration) platform, a digital-twin-driven system that offloads gravity through a pulley-counterweight mechanism and maps Unreal Engine lunar terrain to a motion platform and treadmill in real time. Using MATRIX, we demonstrate continuous jumping of a quadruped robot under lunar-gravity emulation across cratered lunar-like terrain.

Haozhe Xu, Yifei Zhao, Wenhao Feng +6

Robot LocomotionQuadruped LocomotionRobot Dynamics LearningTerrain-Aware Robot Locomotion
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Mar 7, 2026

Learning Quadruped Walking from Seconds of Demonstration

Quadruped locomotion provides a natural setting for understanding when model-free learning can outperform model-based control design, by exploiting data patterns to bypass the difficulty of optimizing over discrete contacts and the combinatorial explosion of mode changes. We give a principled analysis of why imitation learning with quadrupeds can be inherently effective in a small data regime, based on the structure of its limit cycles, Poincaré return maps, and local numerical properties of neural networks. The understanding motivates a new imitation learning method that regulates the alignment between variations in a latent space and those over the output actions. Hardware experiments confirm that a few seconds of demonstration is sufficient to train various locomotion policies from scratch entirely offline with reasonable robustness.

Ruipeng Zhang, Hongzhan Yu, Ya-Chien Chang +3

University of California, San Diego

Robot Imitation LearningData-Efficient Robot LearningQuadruped LocomotionDynamical Systems
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Mar 6, 2026

Task-Level Decisions to Gait Level Control: A Hierarchical Policy Approach for Quadruped Navigation

Real-world quadruped navigation is constrained by a scale mismatch between high-level navigation decisions and low-level gait execution, as well as by instabilities under out-of-distribution environmental changes. Such variations challenge sim-to-real transfer and can trigger falls when policies lack explicit interfaces for adaptation. In this paper, we present a hierarchical policy architecture for quadrupedal navigation, termed Task-level Decision to Gait Control (TDGC). A low-level policy, trained with reinforcement learning in simulation, delivers gait-conditioned locomotion and maps task requirements to a compact set of controllable behavior parameters, enabling robust mode generation and smooth switching. A high-level policy makes task-centric decisions from sparse semantic or geometric terrain cues and translates them into low-level targets, forming a traceable decision pipeline without dense maps or high-resolution terrain reconstruction. Different from end-to-end approaches, our architecture provides explicit interfaces for deployment-time tuning, fault diagnosis, and policy refinement. We introduce a structured curriculum with performance-driven progression that expands environmental difficulty and disturbance ranges. Experiments show higher task success rates on mixed terrains and out-of-distribution tests.

Sijia Li, Haoyu Wang, Shenghai Yuan +2

Quadruped Robot NavigationRobot NavigationQuadruped LocomotionTerrain-Aware Robot LocomotionHierarchical RLSim-to-Real Transfer
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Mar 4, 2026

Swimming Under Constraints: A Safe Reinforcement Learning Framework for Quadrupedal Bio-Inspired Propulsion

Bio-inspired aquatic propulsion offers high thrust and maneuverability but is prone to destabilizing forces such as lift fluctuations, which are further amplified by six-degree-of-freedom (6-DoF) fluid coupling. We formulate quadrupedal swimming as a constrained optimization problem that maximizes forward thrust while minimizing destabilizing fluctuations. Our proposed framework, Accelerated Constrained Proximal Policy Optimization with a PID-regulated Lagrange multiplier (ACPPO-PID), enforces constraints with a PID-regulated Lagrange multiplier, accelerates learning via conditional asymmetric clipping, and stabilizes updates through cycle-wise geometric aggregation. Initialized with imitation learning and refined through on-hardware towing-tank experiments, ACPPO-PID produces control policies that transfer effectively to quadrupedal free-swimming trials. Results demonstrate improved thrust efficiency, reduced destabilizing forces, and faster convergence compared with state-of-the-art baselines, underscoring the importance of constraint-aware safe RL for robust and generalizable bio-inspired locomotion in complex fluid environments.

Xinyu Cui, Fei Han, Hang Xu +9

FSI lab, Westlake University, Hangzhou, 310030, China. · Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China. · School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 100049, China +3

Constrained RLUnderwater RoboticsProximal Policy OptimizationQuadruped Locomotion
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Mar 2, 2026

Learning Thermal-Aware Locomotion Policies for an Electrically-Actuated Quadruped Robot

Electrically-actuated quadrupedal robots possess high mobility on complex terrains, but their motors tend to accumulate heat under high-torque cyclic loads, potentially triggering overheat protection and limiting long-duration tasks. This work proposes a thermal-aware control method that incorporates motor temperatures into reinforcement learning locomotion policies and introduces thermal-constraint rewards to prevent temperature exceedance. Real-world experiments on the Unitree A1 demonstrate that, under a fixed 3 kg payload, the baseline policy triggers overheat protection and stops within approximately 7 minutes, whereas the proposed method can operate continuously for over 27 minutes without thermal interruptions while maintaining comparable command-tracking performance, thereby enhancing sustainable operational capability.

Letian Qian, Yuhang Wan, Shuhan Wang +1

State Key Laboratory of Intelligent Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China

Robot LocomotionQuadruped LocomotionRL for Legged LocomotionConstrained RL
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Mar 1, 2026

A Deployable Bio-inspired Compliant Leg Design for Enhanced Leaping in Quadruped Robots

Quadruped robots are becoming increasingly essential for various applications, including industrial inspection and catastrophe search and rescue. These scenarios require robots to possess enhanced agility and obstacle-navigation skills. Nonetheless, the performance of current platforms is often constrained by insufficient peak motor power, limiting their ability to perform explosive jumps. To address this challenge, this paper proposes a bio-inspired method that emulates the energy-storage mechanism found in froghopper legs. We designed a Deployable Compliant Leg (DCL) utilizing a specialized 3D-printed elastic material, Polyether block amide (PEBA), featuring a lightweight internal lattice structure. This structure functions analogously to biological tendons, storing elastic energy during the robot's squatting phase and rapidly releasing it to augment motor output during the leap. The proposed mechanical design significantly enhances the robot's vertical jumping capability. Through finite element analysis (FEA) and experimental validation, we demonstrate a relative performance improvement of 17.1% in vertical jumping height.

Yiyang Chen, Yuxin Liu, Jinzheng Zhou +4

Department of Mechatronics and Robotics, Xi’an Jiaotong-Liverpool University, Suzhou 215123, China. · Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Champaign, Illinois, United States.

Bioinspired RoboticsRoboticsQuadruped LocomotionSoft Robotics
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Feb 25, 2026

Jumping Control for a Quadrupedal Wheeled-Legged Robot via NMPC and DE Optimization

Quadrupedal wheeled-legged robots combine the advantages of legged and wheeled locomotion to achieve superior mobility, but executing dynamic jumps remains a significant challenge due to the additional degrees of freedom introduced by wheeled legs. This paper develops a mini-sized wheeled-legged robot for agile motion and presents a novel motion control framework that integrates the Nonlinear Model Predictive Control (NMPC) for locomotion and the Differential Evolution (DE) based trajectory optimization for jumping in quadrupedal wheeled-legged robots. The proposed controller utilizes wheel motion and locomotion to enhance jumping performance, achieving versatile maneuvers such as vertical jumping, forward jumping, and backflips. Extensive simulations and real-world experiments validate the effectiveness of the framework, demonstrating a forward jump over a 0.12 m obstacle and a vertical jump reaching 0.5 m.

Xuanqi Zeng, Lingwei Zhang, Linzhu Yue +4

Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong

Robot LocomotionQuadruped Locomotion
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Feb 18, 2026

Dynamic Modeling and MPC for Locomotion of Tendon-Driven Soft Quadruped

SLOT (Soft Legged Omnidirectional Tetrapod), a tendon-driven soft quadruped robot with 3D-printed TPU legs, is presented to study physics-informed modeling and control of compliant legged locomotion using only four actuators. Each leg is modeled as a deformable continuum using discrete Cosserat rod theory, enabling the capture of large bending deformations, distributed elasticity, tendon actuation, and ground contact interactions. A modular whole-body modeling framework is introduced, in which compliant leg dynamics are represented through physically consistent reaction forces applied to a rigid torso, providing a scalable interface between continuum soft limbs and rigid-body locomotion dynamics. This formulation allows efficient whole-body simulation and real-time control without sacrificing physical fidelity. The proposed model is embedded into a convex model predictive control framework that optimizes ground reaction forces over a 0.495 s prediction horizon and maps them to tendon actuation through a physics-informed force-angle relationship. The resulting controller achieves asymptotic stability under diverse perturbations. The framework is experimentally validated on a physical prototype during crawling and walking gaits, achieving high accuracy with less than 5 mm RMSE in center of mass trajectories. These results demonstrate a generalizable approach for integrating continuum soft legs into model-based locomotion control, advancing scalable and reusable modeling and control methods for soft quadruped robots.

Saumya Karan, Neerav Maram, Suraj Borate +1

IIT Gandhinagar, Department of Electrical Engineering, Gujarat, India · Sreenidhi Institute of Science and Technology, Department of Electronics and Computer Engineering, Telangana, India

Quadruped LocomotionSoft RoboticsContinuum Robot ControlModel Predictive Control
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Feb 16, 2026

Learning Transferability: A Two-Stage Reinforcement Learning Approach for Enhancing Quadruped Robots' Performance in U-Shaped Stair Climbing

Quadruped robots are employed in various scenarios in building construction. However, autonomous stair climbing across different indoor staircases remains a major challenge for robot dogs to complete building construction tasks. In this project, we employed a two-stage end-to-end deep reinforcement learning (RL) approach to optimize a robot's performance on U-shaped stairs. The training robot-dog modality, Unitree Go2, was first trained to climb stairs on Isaac Lab's pyramid-stair terrain, and then to climb a U-shaped indoor staircase using the learned policies. This project explores end-to-end RL methods that enable robot dogs to autonomously climb stairs. The results showed (1) the successful goal reached for robot dogs climbing U-shaped stairs with a stall penalty, and (2) the transferability from the policy trained on U-shaped stairs to deployment on straight, L-shaped, and spiral stair terrains, and transferability from other stair models to deployment on U-shaped terrain.

Baixiao Huang, Baiyu Huang, Yu Hou

Independent Researcher, 7200 Bollinger Rd, Apt 516, CA 95129. · Independent Researcher, 16506 82nd Pl NE, Kenmore, WA, 98028. · Western New England University, Department of Construction Management, 1215 Wilbraham Rd, Springfield, MA 01119 (corresponding author).

RL for Legged LocomotionQuadruped LocomotionRobot Policy Generalization
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Jan 22, 2026

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 RoboticsTerrain-Aware Robot LocomotionRL for Legged LocomotionRobotic PerceptionQuadruped Locomotion
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Oct 12, 2025

Gain Tuning Is Not What You Need: Reward Gain Adaptation for Constrained Locomotion Learning

Existing robot locomotion learning techniques rely heavily on the offline selection of proper reward weighting gains and cannot guarantee constraint satisfaction (i.e., constraint violation) during training. Thus, this work aims to address both issues by proposing Reward-Oriented Gains via Embodied Regulation (ROGER), which adapts reward-weighting gains online based on penalties received throughout the embodied interaction process. The ratio between the positive reward (primary reward) and negative reward (penalty) gains is automatically reduced as the learning approaches the constraint thresholds to avoid violation. Conversely, the ratio is increased when learning is in safe states to prioritize performance. With a 60-kg quadruped robot, ROGER achieved near-zero constraint violation throughout multiple learning trials. It also achieved up to 50% more primary reward than the equivalent state-of-the-art techniques. In MuJoCo continuous locomotion benchmarks, including a single-leg hopper, ROGER exhibited comparable or up to 100% higher performance and 60% less torque usage and orientation deviation compared to those trained with the default reward function. Finally, real-world locomotion learning of a physical quadruped robot was achieved from scratch within one hour without any falls. Therefore, this work contributes to constraint-satisfying real-world continual robot locomotion learning and simplifies reward weighting gain tuning, potentially facilitating the development of physical robots and those that learn in the real world.

Arthicha Srisuchinnawong, Poramate Manoonpong

Vidyasirimedhi Institute of Science and Technology, Rayong, Thailand. · The University of Southern Denmark, Odense, Denmark.

Constrained RLRL for Legged LocomotionReward Design for RLQuadruped Locomotion
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Oct 8, 2025

Sampling Strategies for Robust Universal Quadrupedal Locomotion Policies

This work focuses on sampling strategies of configuration variations for generating robust universal locomotion policies for quadrupedal robots. We investigate the effects of sampling physical robot parameters and joint proportional-derivative gains to enable training a single reinforcement learning policy that generalizes to multiple parameter configurations. Three fundamental joint gain sampling strategies are compared: parameter sampling with (1) linear and polynomial function mappings of mass-to-gains, (2) performance-based adaptive filtering, and (3) uniform random sampling. We improve the robustness of the policy by biasing the configurations using nominal priors and reference models. All training was conducted using the RaiSim simulation environment, tested in simulation on a range of diverse quadrupeds, and zero-shot deployed onto hardware using the ANYmal quadruped robot. Compared to multiple baseline implementations, our results demonstrate the need for significant joint controller gains randomization for robust closing of the sim-to-real gap.

David Rytz, Kim Tien Ly, Ioannis Havoutis

1Dynamic Robot Systems, Oxford Robotics Institute, University of Oxford

Domain RandomizationSim-to-Real TransferRobot Policy GeneralizationRobust RLQuadruped Locomotion
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Oct 2, 2025

SPARC: Spine with Prismatic And Revolute Compliance for Faster Quadrupedal Bounding

Quadruped mammals coordinate sagittal spinal bending with axial extension and compression during dynamic locomotion. Yet most robotic quadrupeds use rigid trunks, passively compliant spines with fixed properties, or actively controlled spines that track prescribed trajectories. Whether actively regulated spinal compliance can support faster dynamic locomotion remains unclear. We present SPARC, a compact 1.26-kg, 3-DoF sagittal-plane spine that combines revolute and prismatic motion with independently tunable task-space stiffness and damping. A floating-base impedance controller renders the desired task-space compliance, and benchtop tests show that the fitted axial stiffness matches commanded values within 1.5%. We integrate SPARC into an 8-DoF quadruped and evaluate it across 97 bounding trials under three spine configurations: impedance-controlled SPARC, the same SPARC module held near a fixed pose using position control, and a lightweight rigid spine. Impedance-controlled SPARC reaches 1.029 m/s, compared with 0.769 m/s for position-controlled SPARC and 0.673 m/s for the rigid spine. Impedance-controlled SPARC reaches higher speeds with larger axial motion and greater mechanical power exchange, while at matched speed it has a higher electrical cost of transport than the rigid spine, revealing an energetic trade-off. Code and hardware are available at: https://github.com/YueWang996/sparc

Yue Wang, Yanran Xu

School of Electronic and Computer Science, University of Southampton, United Kingdom

Legged RoboticsImpedance ControlCompliant Legged LocomotionQuadruped Locomotion
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Sep 22, 2025

GeCCo -- a Generalist Contact-Conditioned Policy for Loco-Manipulation Skills on Legged Robots

Most modern approaches to quadruped locomotion focus on using Deep Reinforcement Learning (DRL) to learn policies from scratch, in an end-to-end manner. Such methods often fail to scale, as every new problem or application requires time-consuming and iterative reward definition and tuning. We present Generalist Contact-Conditioned Policy (GeCCo) --- a low-level policy trained with Deep Reinforcement Learning that is capable of tracking arbitrary contact points with a quadruped robot. We shift from task-specific end-to-end learning to a modular hierarchy in which a single planner-agnostic, contact-conditioned tracking policy serves as a robust interface between planning and control. By maintaining stable contact execution under dynamic uncertainty and planner mismatch, the policy enables high-level planners (e.g., handcrafted, learned, or optimization-based) to be composed and swapped without retraining. We demonstrate the scalability and robustness of our method by evaluating on a wide range of locomotion and manipulation tasks in a common framework and under a single generalist policy. These include a variety of gaits, traversing complex terrains (e.g., stairs and slopes) as well as previously unseen stepping-stones and narrow beams, and interacting with objects (e.g., pressing a button, pushing a barrel). Our framework acquires new behaviors more efficiently, simply by combining a task-specific high-level contact planner and the pre-trained generalist policy. Project website: https://vassil-atn.github.io/gecco.github.io

Vassil Atanassov, Wanming Yu, Siddhant Gangapurwala +2

Dynamic Robot Systems Group, Oxford Robotics Institute, University of Oxford · Sony AI · Dyson Institute of Engineering and Technology

Robotic ControlLegged RoboticsRobot Policy LearningRobot Skill LearningRobotic ManipulationRL for Legged Locomotion+1
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