Quadruped / legged四足 / 足式

Legged robots equipped with manipulators have shown significant potential in the fields of daily life and industry in complex environments. However, existing methods mainly focus on global navigation or manipulation independently, while overlooking the last-mile navigation problem, where the robot must jointly determine the base placement, approach direction, and grasp execution to achieve reliable object grasping, and different manipulation stages require distinct control behaviors. To address these challenges, we propose Last-Mile Grasp-Navigation (LMGN), a unified policy learning model for …

This paper presents the kinematic modeling and singularity analysis of a three-degree-of-freedom, double four-bar closed-loop quadruped leg mechanism. This leg is essential for transitioning between the two operational modes; therefore, it is examined in both joint and task spaces, leading to the development of its Jacobian matrix, which is vital for designing the gaits required for terrestrial mode and mid-air aerial reconfiguration (for aerial mode). Various gaits are devised for the system's motion in the MATLAB simulation, and their practical implementation on the single-leg test rig is …

Wiping, sanding, and inspection robots press a sliding tool on a surface with controlled force. Controlling that force needs the surface normal, which is unknown on real-world, unmapped surfaces. Surface-normal estimators can help estimate the surface normal, but they either need a friction model or assume that the instantaneous tool velocity lies along the surface; however, walking violates this assumption. We propose SCRUB, a contact-based surface-frame estimator, which lets an armless quadruped slide a body-mounted tool along near-vertical surfaces in the absence of known, axis-aligned, or …

This letter presents a trajectory planner for humanoid robots to perform dynamic motions on complex, parameterizable terrains using a contact-implicit whole-body optimization framework. The planner generates feasible movements without predefined contact sequences, considering the robot's full dynamics and kinematics. To plan bipedal locomotion on steps, ramps, and other terrains, we propose a mathematical model to approximate ground geometry with a smooth surface. The rigid interaction between the robot and the ground is modeled via novel contact constraints, extending the domain of …

By harnessing the inherent commonsense capabilities of pretrained Large Language Models (LLMs) and Vision-Language Models (VLMs), current Vision-Language Action(VLA) models for legged robots excel at interpreting language-based navigation commands but lack the physical grounding and explicit safety assurance required for real-world operation. Therefore, this paper aims to cage Legged-Vision-Language Navigation (VLN) through a safety architecture that provides physical grounding and ensures navigation safety. The key idea is not to abandon the powerful capabilities of end-to-end VLA planning, …

Treating morphology and control as separate design problems has constrained the efficiency and adaptability of quadrupedal robots, while current co-design approaches are often constrained by restricted design spaces. We overcome this limit by introducing Dogger, a bio-inspired quadruped with modular three-segment legs, four-bar linkages and adjustable passive knee compliance. A two-stage framework combining reinforcement learning and Bayesian optimization is developed: the morphology-conditioned control policy is trained across designs and then held fixed during task-specific design …

Unsupervised environment design (UED) methods such as PLR, ACCEL, SFL and PAIRED are compared mostly on 2D mazes, grid worlds and BipedalWalker, while terrain curricula for legged robots are hand-designed and evaluated against a few baselines. We present a benchmark that runs fourteen UED, domain-randomisation and robotics curricula under one protocol on five 3D quadrupeds in MuJoCo MJX: the closed-chain W01-TEK and the open-chain Unitree Go1 and Go2, Google Barkour vB and Boston Dynamics Spot. Levels are vectors of eight interpretable terrain parameters, and all curricula drive the same PPO …

Robotic navigation typically assumes a collision-free route to the goal exists; in cluttered environments with movable obstacles, however, reaching the goal may require physical interaction. Classical solutions encode these behaviors through geometric rules and task-specific logic, while learning-based approaches often constrain the decision space to low-dimensional motion commands or predefined action sets. We instead consider a broader decision space, jointly selecting the skill, relevant object, and geometric target. Our language-conditioned task planner, fine-tuned with LoRA on synthetic …

Legged robots have demonstrated advanced capabilities across a wide range of real-world tasks, yet much of this progress concerns the robot controlling only itself. Once the robot is coupled to an external object -- particularly an underactuated one -- the dynamics of the combined assembly become more complex. Towing a wagon is a common practical scenario, where coupled dynamics make reliable navigation challenging. This difficulty is amplified in confined spaces, where collision-free navigation requires finding a narrow set of feasible paths under strict real-time constraints. To address …

Combining wheeled and legged locomotion within a single robotic platform offers the potential to harness the advantages of both systems. The development of such hybrid systems remains an active area of research. While legged robots exhibit remarkable adaptability for traversing uneven and rugged terrains, their relatively low speed limits their practicality in indoor environments. Conversely, wheeled robots demonstrate higher efficiency on flat surfaces but often encounter difficulties when navigating obstacles such as steps. This paper introduces OmniQuad, a novel hybrid robot that …

Quadrupedal manipulators can extend their workspace through whole-body interaction, but task-planning agents' capabilities remain limited by their available controllers. We present ELEVATE, a framework that uses persistent failures during task-program refinement to identify and acquire missing whole-body control capabilities. When these failures suggest a missing physical capability, a coding agent formulates and iteratively refines a reinforcement-learning problem, specifying behavior-specific rewards, curricula, and termination conditions. Validated controllers are added to the capability …

Humans navigate their environment based on their vision system, anticipating how the ground will respond before committing to a step. Self-supervised learning could provide legged robots the same ability, but the supervisory signal is typically chosen on intuition, and its effect on what the model learns is rarely examined. We present Terrain-Aware COntact Supervision (TACOS), which proposes a meaningful and consistent footstep instability score, based on the residual of a factor graph in legged state estimation. It projects the continuous score into preceding images to supervise a dense …

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 …