Legged Robotics

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.

The performance of legged robots depends strongly on both mechanical design and control, motivating co-design approaches that jointly optimize these parameters. However, most existing co-design studies focus on link dimensions and transmission ratios while neglecting detailed actuator design, particularly motor and gearbox parameter optimization, and are largely limited to serial open-chain mechanisms. In this work, we present a co-design framework for a planar closed-chain five-bar monoped that jointly optimizes mechanical design, motor and gearbox parameters, and control parameters for dynamic jumping. The objective is to maximize jump distance while minimizing mechanical energy consumption. The framework employs a two-stage optimization approach, where actuator optimization generates a mapping from gear ratio to actuator mass, efficiency, and peak torque, which is then incorporated into CMA-ES-based co-design optimization of the robot design and control parameters. Simulation results demonstrate an improvement of approximately 30.4% in jump distance and an 11.5% reduction in mechanical energy consumption compared to a nominal design, highlighting the effectiveness of the proposed framework for high-performance and energy-efficient planar jumping.

Legged robots operate across a wide range of physical scales, but how their designs should be adapted as size changes remains unclear. Here, we tackle this question in two ways. First, we survey existing legged robots to provide a broad context for the key scaling variables, robot mass m and leg length L. We find the surprising result that bipedal robot mass generally scales with the length squared, L^2, rather than the isometric prediction L^3. Then, to reduce the variance in design choices, we focus on a pair of previously developed bipeds that share the same quasi-passive morphology but differ by a factor of six in leg length, use different feet and controllers, and achieve different relative speeds. We reconstruct both robots in a common 3-D simulation environment and scale each design over leg lengths from 0.02 to 1.2 meters under both mass models (mass is proportional to L^2 and is proportional to L^). The controlled comparison shows that velocity follows dynamic similarity, velocity is proportional to L^{1/2}, across designs and mass models, while the torque needed to sustain walking follows that tau is proportional to mL. Consequently, torque scales approximately with L^3 when m is proportional to L^2 and L^4 when mass is proportional to L^3. A 3-D foot-shape sweep further shows that foot dimensions that permit walking scale approximately linearly with leg length, but the speed-maximizing shape and the mechanism by which each robot moves do not transfer by scaling alone. Overall, the results provide practical insights for rescaling legged systems that leverage natural body dynamics.

Accurate state estimation and multi-modal perception are prerequisites for autonomous legged robots in complex, large-scale environments. To date, no large-scale public legged-robot dataset captures the real-world conditions needed to develop and benchmark algorithms for legged-robot state estimation, perception, and navigation. To address this, we introduce the GrandTour dataset, a multi-modal legged-robotics dataset collected across challenging outdoor and indoor environments, featuring an ANYbotics ANYmal-D quadruped equipped with the Boxi multi-modal sensor payload. GrandTour spans a broad range of environments and operational scenarios across distinct test sites, ranging from alpine scenery and forests to demolished buildings and urban areas, and covers a wide variation in scale, complexity, illumination, and weather conditions. The dataset provides time-synchronized sensor data from spinning LiDARs, multiple RGB cameras with complementary characteristics, proprioceptive sensors, and stereo depth cameras. Moreover, it includes high-precision ground-truth trajectories from satellite-based RTK-GNSS and a Leica Geosystems total station. This dataset supports research in SLAM, high-precision state estimation, and multi-modal learning, enabling rigorous evaluation and development of new approaches to sensor fusion in legged robotic systems. With its extensive scope, GrandTour represents the largest open-access legged-robotics dataset to date. The dataset is available at https://grand-tour.leggedrobotics.com on HuggingFace (ROS-independent), and in ROS formats, along with tools and demo resources.

Reliable odometry for legged robots without cameras or LiDAR remains challenging due to IMU drift and noisy joint velocity sensing. This paper presents a purely proprioceptive state estimator that uses only IMU and motor measurements to estimate body pose and velocity, with a unified formulation applicable to quadruped and wheel-legged robots and extensible to other legged morphologies. The key idea is to treat each reliable contact as a kinematic anchor: joint-torque--based foot wrench estimation selects stance contacts, and the corresponding footfall records provide intermittent world-frame constraints that suppress long-term drift. To prevent elevation drift during extended traversal, we introduce a lightweight height clustering and time-decay correction that snaps newly recorded footfall heights to previously observed support planes. For wheel-legged platforms, the recorded contact is further propagated by effective wheel rolling displacement with shank-motion compensation and a slope-aware rolling direction. To improve foot velocity observations under encoder quantization, we retain an inverse-kinematics cubature Kalman filter as an optional velocity-enhancement module that filters foot-end velocities from joint angles and velocities. The implementation further mitigates yaw drift through multi-contact geometric consistency, which is injected as a soft heading prior rather than as a hard reset of the attitude state. The method is evaluated on four quadruped platforms.

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.

Deployment of legged robots for navigating challenging terrains (e.g., stairs, slopes, and unstructured environments) has gained increasing preference over wheel-based platforms. In such scenarios, accurate odometry estimation is a preliminary requirement for stable locomotion, localization, and mapping. Traditional proprioceptive approaches, which rely on leg kinematics sensor modalities and inertial sensing, suffer from irrepressible vertical drift caused by frequent contact impacts, foot slippage, and vibrations, particularly affected by inaccurate roll and pitch estimation. Existing methods incorporate exteroceptive sensors such as LiDAR or cameras. Further enhancement has been introduced by leveraging gravity vector estimation to add additional observations on roll and pitch, thereby increasing the accuracy of vertical pose estimation. However, these approaches tend to degrade in feature-sparse or repetitive scenes and are prone to errors from double-integrated IMU acceleration. To address these challenges, we propose GaRLILEO, a novel gravity-aligned continuous-time radar-leg-inertial odometry framework. GaRLILEO decouples velocity from the IMU by building a continuous-time ego-velocity spline from SoC radar Doppler and leg kinematics information, enabling seamless sensor fusion which mitigates odometry distortion. In addition, GaRLILEO can reliably capture accurate gravity vectors leveraging a novel soft S2-constrained gravity factor, improving vertical pose accuracy without relying on LiDAR or cameras. Evaluated on a self-collected real-world dataset with diverse indoor-outdoor trajectories, GaRLILEO demonstrates state-of-the-art accuracy, particularly in vertical odometry estimation on stairs and slopes. We open-source both our dataset and algorithm to foster further research in legged robot odometry and SLAM. https://garlileo.github.io/GaRLILEO

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

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

We present the design and implementation of HASTA (Hopper with Adjustable Stiffness for Terrain Adaptation), a vertical hopping robot with real-time tunable leg stiffness, aimed at optimizing energy efficiency across various ground profiles (a pair of ground stiffness and damping conditions). By adjusting leg stiffness, we aim to maximize apex hopping height, a key metric for energy-efficient vertical hopping. We hypothesize that softer legs perform better on soft, damped ground by minimizing penetration and energy loss, while stiffer legs excel on hard, less damped ground by reducing limb deformation and energy dissipation. Through experimental tests and simulations, we find the best leg stiffness within our selection for each combination of ground stiffness and damping, enabling the robot to achieve maximum steady-state hopping height with a constant energy input. These results support our hypothesis that tunable stiffness improves energy-efficient locomotion in controlled experimental conditions. In addition, the simulation provides insights that could aid in the future development of controllers for selecting leg stiffness.

Robust and accurate proprioceptive state estimation of the main body is crucial for legged robots to execute tasks in extreme environments where exteroceptive sensors, such as LiDARs and cameras, may become unreliable. In this paper, we propose DogLegs, a state estimation system for legged robots that fuses the measurements from a body-mounted inertial measurement unit (Body-IMU), joint encoders, and multiple leg-mounted IMUs (Leg-IMU) using an extended Kalman filter (EKF). The filter system contains the error states of all IMU frames. The Leg-IMUs are used to detect foot contact, thereby providing zero-velocity measurements to update the state of the Leg-IMU frames. Additionally, we compute the relative position constraints between the Body-IMU and Leg-IMUs by the leg kinematics and use them to update the main body state and reduce the error drift of the individual IMU frames. Field experimental results have shown that our proposed DogLegs system achieves better state estimation accuracy compared to the traditional leg odometry method (using only Body-IMU and joint encoders) across various terrains. We make our code and datasets publicly available to benefit the research community (https://github.com/YibinWu/DogLegs).

This paper presents the Kinetics Observer, a novel proprioceptive state estimator for legged robots designed to provide the feedback required for versatile locomotion and physical interaction with the environment, with enhanced robustness to contact slippage. Its core contribution is a tight coupling between whole-body kinematics and external wrenches through a contact dynamics model, enabling the consistent fusion of leg kinematics, IMU, and wrench sensor measurements for real-time joint estimation of centroidal kinematics, contact rest poses, contact wrenches, and disturbance wrenches. By exploiting contact wrench measurements as correction terms, the proposed observer increases sensing redundancy, which provides observability of contact slippage relative to the centroid frame and enhanced robustness to modeling and sensor errors. The approach is experimentally evaluated on two humanoid robots across three scenarios totaling thirteen walking sequences, including long-distance walking with repeated contact changes, locomotion over slippery obstacles, and non-coplanar multicontact motion.