Quadruped / legged四足 / 足式

Humanoids and other legged robots operating in complex environments must remember information that leaves their field of view and only becomes relevant much later. Reinforcement learning policies address this using memory networks such as LSTMs that are trained end-to-end with the policy to memorize such task-relevant aspects. Yet, such architectures often fail to preserve sufficient information over long horizons. In this work, we propose a network architecture based on Hadamard memory that specifically targets robot navigation. Our Local Spatial Matrix Memory (LSMM) enables RL agents to …

Legged robots for lunar exploration must be designed for low gravity, where reduced contact forces and long flight phases make leg morphology and controller choice interdependent. We study this for a planar monoped in lunar gravity ($1.625$ m/s$^2$) using a bi-level co-design framework: a differential evolution outer loop searches over link lengths, and each candidate is evaluated on a vertical jump by either a quadratic program based task-space controller (QP-TSC) or a direct-collocation based trajectory optimization. The two controllers yield different optimal link lengths, and trajectory …

Quadruped robots are increasingly deployed in hazardous environments such as disaster response and facility inspection, where external-camera monitoring is essential for safe operation. This setting is challenging because quadrupeds are articulated systems with time-varying leg joints, leg symmetry, and frequent self-occlusions, which make keypoint correspondence ambiguous. Moreover, no public benchmark exists, making quantitative comparison difficult. To address these challenges, we propose QuadPose, which estimates the full-body 18-DoF pose (6-DoF base pose + 12-DoF joint angles) from …

Humanoid locomotion in confined spaces requires continuous height adaptation across multiple locomotion modes, yet most existing approaches remain limited to height-adjustable bipedal walking. We present REACH, an RL-based hierarchical framework that enables a Unitree G1 humanoid to traverse height-constrained environments through variable-height bipedal walking and crawling. The learned policies regulate body height over complementary command ranges of 1.27--0.50m in bipedal locomotion and 0.50--0.20m in crawling, extending traversal beyond the clearance limits of crouched walking. To …

We present CPG-ENN, a trainable quadruped locomotion framework that combines explicit neural coordination with learned motion realization. A symmetry-based eight-neuron central pattern generator (CPG) supplies gait rhythms, while a pretrained, leg-shared execution neural network (ENN) maps rhythmic signals and trajectory parameters to joint-angle references without online inverse kinematics. A single feedback policy modulates six physically interpretable trajectory variables. The controller tracks planar velocity and yaw-rate commands across walk, trot, pace, bound, and pronk without …

While velocity-commanded RL policies are effective for controlling quadrupeds, they are a limited interface for humanoids that need to perform complex whole-body motions. Furthermore, RL tracking policies for whole-body motions typically have limited information about the desired future motion, preventing them from performing controlled deviations to achieve long-term task success; such information is particularly relevant when a controller must prepare for transitions between behaviors. We address these challenges using concise motion representations that can be generated by a high-level …

This paper proposes a smooth analytic gradient for frictional contact and applies it to policy learning and contact-implicit trajectory optimization for legged locomotion. The exact contact sensitivity is available in closed form but describes changes within the current contact mode, providing no first-order information toward neighboring contact modes. The proposed gradient replaces this sensitivity only in the backward pass, leaving the hard-contact forward solve unchanged and the realized rollout feasible. A central-path relaxation of the de Saxc\'e-corrected second-order-cone …

Agile quadruped navigation in dynamic environments demands trajectories that are both dynamically feasible and provably collision-free. Most real-time planners achieve tractability through a convex reduction that requires simplified kinematic models, discarding motion that the robot can readily execute, and certify safety only at discretization points, leaving open possible inter-sample collisions with moving obstacles. We present a real-time motion planning framework that retains the fully-actuated $SE(2)$ model of a quadruped, with its anisotropic, heading-coupled velocity bounds, and …

Cooperative transport with heterogeneous legged robots requires coordinating different motion capabilities while supporting an unfixed shared payload. We present HA-DiPO (Heterogeneous-Agent Diffusion Policy Optimization), a hierarchical multi-agent reinforcement learning framework under centralized training with decentralized execution (CTDE). The framework decouples team-level coordination from embodiment-specific motion control: at the high level, a centralized critic uses team-value estimates to jointly train independent coordination policies, aligning robot-specific action responses with …

We present RAIWAY, an in-house wheeled bipedal robot with 20-inch wheels, together with a contact-informed control approach for rolling locomotion across irregular and discontinuous terrain. Such locomotion is fundamentally contact-dominated, governed by local wheel--terrain interaction that is impractical to instrument directly and depends on more than terrain geometry alone. The proposed framework exploits the contact information available in simulation, distilling multi-contact events into a latent representation. At deployment, the controller infers this representation online from …

Vision-language-action (VLA) models are typically pretrained on broad, diverse datasets and subsequently fine-tuned on a comparatively small dataset tailored to a specific target robot. Such adaptation recipe is now widely established, achieving its most mature results on fixed-base arms due to their static base dynamics and consistent reference frame. Mounting the same arm on a quadruped extends the workspace to the entire floor, but fundamentally changes the embodiment: rather than controlling the arm in isolation, the policy must jointly coordinate base navigation, body posture, and …

Achieving effective locomotion on diverse terrestrial substrates can require subtle changes of limb kinematics. Biologically inspired legged robots (physical models of organisms) have shown impressive mobility on hard ground but suffer performance loss on unconsolidated granular materials like sand. Because comprehensive limb-ground interaction models are lacking, optimal gaits on complex yielding terrain have been determined empirically. To develop predictive models for legged devices and to provide hypotheses for biological locomotors, we systematically study the performance of SandBot, a …

Legged locomotion on flowing ground ({\em e.g.} granular media) is unlike locomotion on hard ground because feet experience both solid- and fluid-like forces during surface penetration. Recent bio-inspired legged robots display speed relative to body size on hard ground comparable to high performing organisms like cockroaches but suffer significant performance loss on flowing materials like sand. In laboratory experiments we study the performance (speed) of a small (2.3 kg) six-legged robot, SandBot, as it runs on a bed of granular media (1 mm poppy seeds). For an alternating tripod gait on …

Choosing among robot demonstration corpora is a ranking problem: an upstream diagnostic must preserve which candidates produce better downstream policies, not merely correlate with average performance. We study paired instruction dependence, the rate at which a demonstrator changes its first decision when only the goal changes. Across 136 independently seeded quadruped-navigation corpora, predictions developed on 56 corpora are evaluated prospectively on 80 held-out corpora. The audit is reliable and associated with downstream paired correctness, and lowers mean absolute prediction error when …

Legged robots can extend planetary exploration to rugged and discontinuous terrain that is inaccessible to conventional rovers. In lunar gravity, jumping further expands this mobility by enabling robots to cross obstacles and gaps that cannot be traversed by walking alone. We present a multistage reinforcement-learning approach that produces a single end-to-end control policy for commanded point-to-point jumping under lunar gravity. The resulting policy has a simple architecture and relies exclusively on mission-compatible onboard sensing, making its deployment on a real lunar mission …

Recently, multi-node inertial measurement unit (multi-IMU) systems have shown promise for robust odometry in legged robots. Multi-IMU fusion can improve legged robot odometry but requires accurate spatiotemporal calibration among the sensors. Existing multi-IMU calibration methods, designed for aerial or handheld platforms, face challenges on legged robots because routine locomotion may provide insufficient excitation, while foot slips, impacts, and vibrations introduce measurement disturbances. To address these challenges, we propose A2I-Calib++, a kinematics-driven anti-noise active …

Blind and visually impaired individuals face uncertainty when navigating unfamiliar areas. Whether a cane or a guide dog is used for navigation, this may prove to be challenging. To mitigate this challenge, we present the Context-Aware Navigation Explanation framework that explains guide dog movements for obstacle avoidance and navigation using a large language model. This system integrates perceptual context with planned future trajectories to generate natural-language explanations of robot movement. We deploy the system on a Unitree Go2 platform in indoor navigation scenarios and evaluate …

Bipedal humanoids can change their effective footprint by adjusting body yaw, enabling both narrow-passage traversal and socially aware yielding. This paper presents a posture-aware navigation framework centered on \emph{Adaptive Traversal Tubes} (ATT), \emph{Interval Velocity--Heading} (IVH) control, and a sidestep-enhanced AMP locomotion prior. ATT represents a behavior-feasible corridor width field along a reference path, unifying geometric clearance and social comfort into a continuous signal. IVH maps this width to a continuous frontal-to-sidestep posture schedule and omnidirectional …

Mobile legged robots offer unique advantages for on-site construction, including the ability to traverse unstructured terrain, climb stairs, and operate independently between spatially separated work zones. This paper presents a proof-of-concept system for autonomous brick stacking using a Boston Dynamics Spot quadrupedal robot equipped with a manipulator arm. The system operates between a supply area and an assembly area, using AprilTag fiducials for localization and autowalk missions for navigation. Target brick positions and orientations are specified in CAD software and exported directly …

The integration of dynamic legged locomotion and aerial mobility offers versatility that is deterred by challenges in payload distribution, actuation, and the contrasting requirements of both domains. In this paper, we present the design and operation of a multimodal quadrupedal aerial-legged robot. The presence of legged aerial systems also allows for thruster-assisted legged locomotion, which we make possible with a unified control framework using Control Contraction Metrics (CCM). We search for separate domain-specific contraction metrics for walking and flight independently offline and …

This paper presents the hardware implementation of a quadratic program-based controller on Harpy: thruster-assisted bipedal robot to perform thruster-assisted trotting. This is inspired by wing-assisted locomotion observed in birds such as the chukar partridge, which employ thrust vectoring to manipulate the ground reaction force. The proposed controller formulates the thruster-assisted spring-loaded inverted pendulum dynamics as a condensed QP-based model predictive control problem, enabling simultaneous regulation of ground contact force and active thrust vectoring at 500 Hz. A decoupled …

Wheel kinematics can support odometry for quadrupedal wheel-legged robots when LiDAR geometry provides weak motion constraints. However, slip and contact loss make rolling predictions unreliable, and contact state alone cannot determine their reliability across motion directions. We propose a tightly coupled LiDAR-inertial-kinematic odometry framework that retains analytical rolling predictions and learns per-wheel, direction-dependent process covariances from proprioceptive history. The estimator maintains moving wheel-center states, allowing the learned uncertainty to regulate the influence …

Passive-wheel quadrupedal robots offer energy-efficient locomotion through leg-driven propulsion and momentum-driven gliding. However, navigation requires coordinating steering with intermittent propulsion and adapting push-glide timing to task demands. Velocity-tracking objectives may suppress the speed variations inherent in skating, discouraging efficient gliding. To address these challenges, we propose SkateNav, a unified skating-navigation framework based on reinforcement learning. A time-budgeted goal-reaching objective allows the policy to jointly learn steering, propulsion, and their …

Quadruped robots often switch gaits to traverse mixed terrain safely. Many practical supervisors enforce hardware constraints (e.g., dwell or guard intervals) using a transition handler. However, the switch decision itself is often driven by near-field thresholds, which can delay commitment when rough terrain is only detected shortly before contact in the local height map. We propose a lightweight height-map-only gait supervisor that unifies look-ahead and locomotion constraints in a single decision policy. A robot-centered height map is partitioned into near-, mid-, and far-field bands, each …

Quadruped locomotion requires coordinating body motion,contact forces, foothold placement, and gait timing. We present a hierarchical controller in which reinforcement learning adapts these structured locomotion references while a gait scheduler, reactive footstep planner, and whole-body impulse controller retain responsibility for high-frequency execution. The model-based backbone can sustain a nominal trot independently, allowing the policy to focus on when and how to modify an already functional locomotion controller. We train the complete hierarchy in a vectorized controller-in-the-loop …

Pedipulating a freestanding articulated object requires controlling its pose and internal configuration while maintaining balance. We demonstrate this capability by autonomously solving a giant Rubik's Cube with a quadruped using only its feet. The task demands repeated precise interactions, since unintended layer motion can invalidate subsequent operations. We develop an onboard RGB-D perception pipeline that estimates the cube's metric pose and its full color state from partial views acquired through locomotion and flipping. A planner converts the computed solve into robot-executable skill …

This work demonstrates the use of a fast simulation-based training framework to learn control policies using reinforcement learning. The hardware requirements are minimal and the simulation-learned policies transfer reliably to the real world. With this setup, we show that a quadruped robot can learn to traverse diverse real-world terrains reliably---including in a lunar-analog facility---after less than 20 minutes of training on a single consumer-grade GPU. These results provide a glimpse of a future where reinforcement learning is a crucial tool in developing more capable and robust space …

Long-range throwing on unstructured terrain is a key capability for mobile robots in delivery and retrieval tasks, but it requires high release velocity, coordinated whole-body motion, and robustness to terrain-induced disturbances. We present a whole-body kinetic-coordination framework for a wheeled-quadruped manipulator that combines kinetic-chain arm modeling with SQP-based trajectory optimization and a reference-guided reinforcement learning policy for coordinated base motion. The manipulator is first reduced to a kinetic-chain model and optimized under kinematic and dynamic constraints …

Legged robot control is not yet practical in non-inertial environments, where the ground and surroundings accelerate in the inertial Earth frame, mainly because of the unknown, time-varying, persistent perturbations caused by environmental motion, compounded by the associated hybrid robotic dynamics. We formulate the problem of robot walking control as unknown-disturbance rejection for hybrid linear systems subject to hybrid sinusoidal disturbances (i.e., a linear combination of sinusoidal components with instantaneous phase jumps at discrete events). First, necessary and sufficient …

Every robot already carries high-resolution contact sensors: its own joints. Legged robots and humanoids exploit them to walk, run, and track whole-body motions without vision, but there the contacts are large and forceful. Is joint sensing also enough for precise, contact-rich assembly, where the robot must find a millimeter-scale opening, mesh gear teeth, or catch a thread through light contact? We study this question by training blind assembly policies that observe only a short history of joint positions, velocities, and their own actions, without visual, force, torque, or tactile sensing. …

Legged robots equipped with manipulators offer promising capabilities for loco-manipulation tasks in unstructured environments. However, achieving task-consistent end-effector behavior during locomotion remains challenging due to terrain-induced disturbances and the strong coupling between locomotion and manipulation, particularly for small-scale quadruped platforms. A reinforcement-learning based whole-body control framework is proposed for quadruped loco-manipulation on complex terrain. The proposed framework combines a hybrid task representation with task-prioritized whole-body learning to …

Quadruped parkour policies handle canonical obstacles well, but their training curricula often miss the irregular, compound geometry of industrial and disaster-response sites, where agile locomotion matters most. Such environments pose a hard generalization problem: even training directly on reconstructed geometry from the target site does not reliably yield policies that traverse it. Hand-designed curricula span only a few terrain families, and recent LLM-generated curricula offer little control over which policy weaknesses they target. We propose FCTS, a failure-conditioned terrain …

A wind-derived heading can guide a robot towards an odour source even after the wind reverses, but its reliability depends on the plume's transport history. On a quadruped initially facing the source, holding the initial heading reached it in every reversing-wind trial, whereas comparison controllers never settled there. An exact geometric condition links heading correctness to net odour transport, and simulations separate sensing error from departures from nominal flow. Where the alternating wind directions are too close for reversal alone to produce wrong-side headings, the wrong-side rate …

Executing heavy-duty physical manipulation in unpredictable environments remains a major challenge for quadrupedal robots lacking dedicated manipulators. This paper presents SOMA, a hierarchical reinforcement learning framework for whole-body non-prehensile manipulation of multi-object stacks using a quadruped robot. Unlike traditional methods restricted to two-dimensional planar pushing, SOMA integrates explicit robot base-height control, unlocking full three-dimensional pushing strategies. This capability enables the quadruped to manipulate complex payload stacks as a unified system while …

Differentiable reinforcement learning shows strong promise for robot policy learning, but its application to legged locomotion has remained limited to blind walking or simulated 2D tasks. Extending it to end-to-end visual obstacle avoidance is challenging because hard collision constraints and early termination upon contact corrupt first-order gradients, trapping optimizers in local minima. We present E2DRL, which addresses this with a soft differentiable obstacle-interaction formulation: penetration penalties across multiple body keypoints with velocity-conditioned stop-gradient shaping to …

Reinforcement learning has enabled robust locomotion for legged robots, but learned policies are typically tied to a specific robot morphology and require additional engineering when the number of legs, actuators, or mechanical properties change. We present PolyMorph, a morphology-conditioned framework that learns a single locomotion policy for heterogeneous legged robots. PolyMorph converts each robot's URDF into joint-link modules and combines a recurrent encoder, graph-based Transformer, and per-joint decoder to generate actions across variable leg counts and joint configurations. To …

Quadruped robots performing outdoor deliveries must interpret complex scenes, anticipate changes, and navigate in socially compliant ways. Robot demonstrations are costly to collect at the scale needed for generalization. Egocentric web videos offer abundant human navigation experience, but differences in viewpoint and motion make this experience difficult to transfer to robots. We introduce DR-VLA, a Mixture-of-Transformers framework that transfers human navigation experience through a domain-invariant scene representation (DISR). The framework combines vision-language understanding and …

We present a real-time framework for expressive legged locomotion that enables independent control over velocity and style. Unlike existing data-driven controllers, which typically require explicit style labels for training, our method efficiently leverages large-scale unstructured motion data and generalizes to unseen styles. We disentangle style from functional locomotion through a tailored sampling strategy used to train a style encoder whose output conditions an autoregressive diffusion model. During inference, the user provides a style reference clip and a joystick velocity command. The …

Wheel-legged robots operating in outdoor spaces shared with humans require accurate perception, socially compliant navigation, future-scene reasoning, and scene reconstruction. However, existing datasets typically support these capabilities in isolation and rarely provide dense spatial and behavior-level supervision on real wheel-legged platforms. We introduce LynxScenes, a large-scale real-world dataset and benchmark collected with a LYNX M20 wheel-legged robot. It contains approximately 100K 30-s navigation clips spanning 833.6 h and 3,294.7 km, with 3.0M annotated frames. The synchronized …

Robust proprioceptive state estimation is crucial for legged robots, particularly in challenging environments where exteroceptive sensors are unreliable. While traditional leg odometry typically relies on a single body-mounted inertial measurement unit (IMU) fused with leg kinematics via an extended Kalman filter (EKF), such methods are vulnerable to linearization errors and hard-contact assumptions, leading to severe drift during slippage or dynamic locomotion.In this paper, we propose LAG-IO, a factor graph-based multi-IMU state estimation framework that tightly couples measurements from a …