Legged Robots

This paper presents the kinematic and dynamic modeling, trajectory generation, and stability analysis of an 8-degree-of-freedom (DOF) biped robot walking on flat and inclined terrain. Denavit-Hartenberg (DH) parameters and homogeneous transformations are used to derive the forward kinematics, while closed-form inverse kinematics maps the desired hip and swing-foot Cartesian trajectories, generated with cubic splines, to joint angles. Joint torques are computed using the Newton-Euler iterative algorithm, and dynamic stability is evaluated using the zero moment point (ZMP) criterion. A genetic algorithm (GA) optimizes the hip height, maximum swing-foot lift, and frontal-plane tilt angle by minimizing the work done by the joints subject to a ZMP feasibility penalty. Simulation results in MATLAB show that the nominal 8-DOF model remains ZMP-stable for step completion times down to 0.5 s and for slope inclinations up to 22.5 degrees with the given foot geometry. Beyond these limits, the ZMP leaves the support polygon, and either the foot dimensions or the trajectory parameters must be modified. The results also show that ZMP stability is governed by the mass distribution among the links rather than the total mass of the robot.

Herbicide-based weed control is increasingly unsustainable due to rising weed resistance and the adverse environmental impacts of chemical use. While mechanical weed control avoids these drawbacks, it is typically implemented using large machines that cause soil compaction. We propose a novel alternative based on small mobile robots for mechanical weeding. Compared with existing automated mechanical weeding approaches, the proposed method offers reduced soil compaction, simpler automation, and improved scalability. Our solution involves a Boston Dynamics Spot quadruped robot equipped with a custom weed removal tool featuring a milling bit at its end. The tool is rigidly attached to the robot and uses the degrees of freedom of the robot base by actuating the legs, while keeping the feet stationary. We develop a software architecture that enables autonomous weed removal and integrate this system with all other required components. We analyze the accuracy and efficiency of the current proof of concept both in an indoor and outdoor environment and provide recommendations for future work to make the system more accurate and efficient.

Mechanical intelligence, loosely defined as the reduction in control burden afforded by a robot's physical form, has become a prominent concept in robotics, with instantiations in bioinspired robotics, soft robotics, robotic swarms, and many other areas. However, rigorous theoretical understanding and quantitative measures of mechanical intelligence have lagged behind the engineering systems that the community has developed. In this work, using modern legged robots as a benchmark and exemplar, we propose several information-theoretic metrics for quantifying mechanical intelligence. By viewing body dynamics as both a computational process and a communication channel, we show that several prior insights in legged-robot engineering can be described using information theory, and we quantify how bits are processed by mechanical modes and across robot coordinates. Specifically, we examine the trade-off between explicitly incorporating compliance through series-elastic actuation and using so-called proprioceptive, low-gear-ratio transmissions, and we explore how these mechanisms interact with control policies during locomotion. We develop these results on systems of increasing complexity: a simplified linear model of a robot-leg transmission, a nonlinear single-leg simulation, and simulated quadruped robots controlled by a learned policy while navigating challenging terrain. These results lay the groundwork for broader study of robot mechanisms and their role in embodied computation.

Semantic exploration in confined environments requires both environment mapping and detailed observation of target objects. For ground robots, limited sensor vertical fields of view and restricted standoff distances can leave upper object surfaces unobserved from planar viewpoints. Body tilting can improve coverage, but additional observations and posture transitions increase mission time. To address this trade-off, we present POSE, a pose-aware semantic exploration system that exploits a legged robot's intrinsic body pitch and roll with omnidirectional camera-LiDAR perception. The proposed pose-aware viewpoint sampling module selects body postures from partial object maps according to expected coverage gain, while aim-aligned execution reduces unnecessary body reorientation. Further, we introduce an object-centric viewpoint pruning strategy assisted by a vision-language model (VLM), which uses persistent observation history and bird's-eye-view (BEV) maps to reduce redundant inspection visits. The resulting semantic viewpoints are combined with geometric exploration viewpoints in a global exploration planner. Simulations show that POSE improves final target-surface coverage by 8-10 percentage points over the planar planning baseline while reducing exploration time by 17-32%, and achieves the highest mean object coverage AUC among the evaluated baselines. Real-world experiments with a legged robot carrying an omnidirectional camera-LiDAR suite in a machine shop further demonstrate the system's applicability. These results support adaptive body-posture planning for improving the coverage-efficiency trade-off in legged robot semantic exploration. We plan to release the code for community benefit in the future.

World models can anticipate the consequences of navigation actions, but predicted action sequences may become invalid during execution, especially when wheel-legged robots encounter dynamic obstacles or change locomotion modes. We propose WAVE-Go, an image-goal navigation framework that separates world-action prediction from interruptible command execution. Its executor adaptively selects an action prefix and cancels pending commands when updated observations invalidate execution. A conditional-risk formulation specifies prefix selection under an estimated cumulative failure budget, while posture and locomotion-mode transitions require clearance, stability, and task-evidence checks. In the reported navigation evaluation, WAVE-Go achieves 74.1% in-distribution success and 63.3% dynamic out-of-distribution success, exceeding the strongest baseline by 4.7 and 7.7 percentage points, respectively, while reducing collisions from 4.4 to 2.9 per 100 m. Compared with interruptible fixed four-command execution, WAVE-Go raises success by 4.0 percentage points while reducing replanning frequency by 51.2% and collision rate by 6.5%. Execution ablations also show that runtime interruption improves success, collision rate, and reaction latency at the cost of additional replanning. These results support adaptive, interruptible execution as a means of balancing navigation performance and planning overhead. Code is available at https://github.com/vigorlee/wave-go.

Legged robots have demonstrated a remarkable ability to traverse various terrains, yet generating effective loco-manipulation behaviors remains challenging. A key difficulty is that object and terrain parameters are typically unknown to the robot, and mismatches between these parameters and their simulated counterparts introduce a sim-to-real gap that degrades control performance. Classical system identification (Sys-ID) methods often assume differentiable dynamics, an assumption that does not hold for contact-rich legged systems. Sampling-based Sys-ID avoids this restriction by directly matching simulated and recorded state trajectories through massively parallel rollouts, but existing approaches are typically applied offline and do not adapt as environmental conditions change. We present Adaptive-MHE an online sampling-based Sys-ID framework, based on moving horizon estimation (MHE), that estimates the physical parameters of objects and terrain in the environment (e.g., mass, friction) and couples this estimate with a sampling-based model predictive controller, enabling adaptive loco-manipulation in changing and uncertain environments. In simulation and hardware experiments, our framework consistently outperforms baselines and matches the performance of a controller with access to ground-truth parameters.

Legged robots offer a variety of automation applications in real-world scenarios. But areas that are difficult to traverse, like slopes, caves, or scaffolding, still pose a great challenge for traversal. To tackle this problem, we propose an optimized algorithm for evaluating the full actuatable wrench polytope for arbitrary contact scenarios. With our improved analysis algorithm, the torques for each joint of the robot can be calculated within a control frequency of 49 Hz. The achieved speedup allows for deployment within a regular control loop for actuating robot poses for different contact scenarios. We evaluated our stability controller extensively in simulation scenarios and validated its applicability by deploying it on actual walking robot hardware. The proposed controller achieved stability in very complex scenarios that are currently not achievable by any other controller.

Visual monitoring of flapping-wing vehicles requires distinguishing individual wingbeats from motion strength and average frequency. This paper presents a controlled MuJoCo evaluation of wingbeat counting from signed optical flow observed by virtual cameras mounted on Crazyflie vehicles. Three flapping-wing models were recorded at optical distances of 1.5 and 3.0 m, producing 1,440 clips from 240 paired scene configurations with a scene-level 3:1 training-test split. A common spatial convolutional encoder was combined with a causal temporal convolutional network, a recurrent leaky integrate-and-fire spiking network, or causal self-attention. Each model predicted phase and activity, followed by the same directed-crossing event counter. The six existing convolutional models were retained, and all twelve new models were frozen before their test predictions were generated. Exact-count accuracies at 1.5 m were 96.67%, 95.00%, and 96.67%, respectively; at 3.0 m they were 94.44%, 92.22%, and 95.00%. All paired scene-bootstrap intervals for differences in exact-count accuracy included zero. Seven far-distance spiking-model clips had correct totals despite event-timing mismatches, demonstrating why total-count and event-level measurements must be reported together. The results support the feasibility of causal optical-flow counting in the tested setting and identify boundary-sensitive errors. They do not establish an architecture ranking across repeated training, real-flight robustness, or hardware efficiency.

The honeybee waggle dance motivates a communication mechanism in which one agent's movement conveys spatial information that guides other agents' actions. This paper presents a MuJoCo system that extends the point-to-point motion communication setting of MoCom to one performer and multiple observers. A performer broadcasts a six-bit navigation payload using four flight primitives and explicit null signals. Each of one to five observers processes its own onboard RGB images, extracts optical-flow trajectories, recognizes symbols, parses the message, and starts navigation only after confirming its own complete frame. Reception states and execution triggers are separate across observers, while simulation control and safety checks use shared ground truth. With stationary observers, 25 Hz image input, and ideal state-feedback control, a fixed standard suite yielded 44 correct complete messages from 53 receiver exposures across 17 nominal broadcasts; 13 broadcasts passed all group-level decoding and execution checks. Three additional no-message or input-fault controls met their expected outcomes. A separately reported supplemental suite, using the same frozen code at the default geometry, achieved 14 successful receiver exposures across three broadcasts. Near-range and wide-angle configurations exposed tracking and recognition failures, while unsuccessful receivers remained stationary. These finite simulation results support the feasibility of a waggle-dance-inspired broadcast-to-action mechanism under the tested conditions and identify the present perceptual and protocol limits.

In order to make Reinforcement Learning algorithms applicable in real world scenarios, safety must be ensured even under adverse operating conditions. In this work, we consider the challenge of adversarial feature missingness: a scenario in which an adversary occludes features from the agent's observation in order to reduce performance as much as possible. We formally define adversarial missingness for Reinforcement Learning and compare it to the related concepts of $\ell_\infty$-norm bounded adversarial perturbations and learning with missing data. We develop an adversarial training algorithm and show its effectiveness in increasing robustness against adversarial missingness on three MuJoCo benchmark environments. Compared to a baseline trained with random uniform missingness, our method achieves better robustness on all three tasks.

Reinforcement learning has produced capable controllers across a broad range of legged-robot tasks, but a subset of these tasks fail to converge under standard training: those for which most exploration trajectories terminate before producing useful gradient signal. To address such tasks we introduce the \emph{Actuator Dynamics Curriculum}, a procedure that initializes joint stiffness at a high value and anneals it toward the system-identified value as completed episode lengths grow. Using a cart-pole system as a representative example, we show that higher closed-loop joint natural frequency under critical damping enlarges the viability kernel of the underlying Markov Decision Process, increasing the fraction of initial states from which the task is feasible. We validate the kernel monotonicity on the cart-pole and apply the curriculum to a quadrupedal-to-handstand transition on the Boston Dynamics Spot, a narrow-viability task where training under fixed identified stiffness plateaus at a policy that never completes the transition. The trained policy executes the transition in simulation across 10 seeds and transfers to hardware. More broadly, our results suggest that simulated actuator dynamics is a useful axis along which to design curricula for tasks in which exploration is bottlenecked by termination conditions rather than by reward signal.

This paper proposes an open-set ego-noise separation framework for legged-robot audition via annotation-free adaptation and pretrained-model transfer. The framework removes robot-specific ego-noise while preserving environmental sounds whose classes are not specified in advance. Acoustic sensing provides cues about a robot's surroundings beyond the visual field, but walking-induced ego-noise from footstep impacts, joint-backlash rattling, and motor noise severely contaminates the recordings. The framework first uses RecurGraph to select ego-noise-dominant clips from the unlabeled recordings by aggregating clip embeddings into an embedding centroid and propagating scores over an audio-embedding graph. The selected clips are mixed with diverse environmental sounds from a large-scale sound-event dataset to provide paired mixture--target supervision for open-set separation. Transfer-DiT then adapts a general-purpose zero-shot neural separator to achieve high-fidelity open-set ego-noise separation for the target robot. Experiments with bipedal and quadrupedal robots show reliable clip selection and improvements in separation quality and downstream task performance over baseline separators. These results demonstrate the feasibility of annotation-free adaptation without separately recorded ego-noise-only data or manual clip-level annotations.

QLAUN Bot (Quad-Legged Adaptive Unmanned Navigator Robot) is a torque-controlled quadruped robot that is research-oriented, cost-effective, and aimed at achieving simultaneous robustness and agility while being completely 3D-printed. It is a quadruped robot that is aimed at empowering robotics research at universities and research institutes in Lebanon and the MENA region. Using a novel electronics-free leg design strategy, we present a modular robot with interchangeable and easily replaceable legs. The 15 kg robot possesses 12 DoF (Degrees-of-Freedom) with three per leg, each paired with a completely 3D-printed Quasi-Direct Drive (QDD) actuator that consists of a brushless DC motor and a low-ratio gearbox transmission that is connected to a belt transmission system for significantly increasing the torque outputs at the joints. We present legs that have decoupled hip and knee actuators to improve the overall modularity of the robot. QLAUN is almost completely 3D-printed using polylactic acid (PLA) and assembled using off-the-shelf parts to create a robust, agile, and affordable robot for legged robot locomotion research. The legs possess joints with wide ranges of motion, including a continuous hip flexion-extension joint. A compliant foot, printed using TPU-95A is also implemented for alleviating hard impacts and handling terrain uncertainties. This extended abstract aims to introduce QLAUN, a novel platform for robotics research, emphasizing the design concepts and principles that underpin its development to the academic and research communities in the field of robotics.

Partially observable locomotion requires a policy to act when task-relevant properties of the robot--environment state are not fully specified by instantaneous observations. Existing approaches often address this challenge by explicitly estimating missing physical variables or processing extended observation histories through structured architectures. We take a different view: partial observability is fundamentally an information-retention problem. The decisive question is not how task-relevant information enters the network, but whether the policy's internal state retains it. Guided by this perspective, we propose SleepWalking for Robot Locomotion (SWAQ), a one-stage end-to-end framework that uses next-step privileged physical reconstruction to shape what a recurrent history representation retains during policy learning, while the deployed actor uses only a direct history-to-action pathway. Under aligned training settings, SWAQ achieves a 15.0% higher peak mean terrain level than DWAQ, the strongest non-exteroceptive baseline, while using 44.4% fewer inference MACs per control step. Layerwise probes further show that information associated with the reconstructed physical variables remains linearly decodable through the policy head up to the layer preceding the action output. Complementary theoretical analysis relates privileged-variable recoverability to the achievable-return gap between history-based and privileged-information policy classes. These results suggest that semantic objectives can structure learning without requiring a corresponding architectural decomposition of the deployed controller.

This paper presents a real-time control-constrained Differential Dynamic Programming (DDP) framework for underactuated legged robots. To address the limitation of classical DDP in handling control constraints, we propose an Accelerated Projected Gradient (APG)-based control-constrained DDP (ABC-DDP), which efficiently computes constrained solutions and identifies active sets without repeated Karush-Kuhn-Tucker (KKT) inversions. A virtual constraint is introduced to integrate control constraints within a feasibility-driven multiple-shooting framework, enabling stable optimization even from dynamically infeasible initializations. The proposed method supports real-time model predictive control (MPC) with short horizons under strong underactuation. Simulation results demonstrate static two-leg standing under external disturbances, along with diverse dynamic motions including slow catwalk, upright walking, and high-speed running within a unified MPC framework. To the best of our knowledge, this is the first demonstration of static two-leg standing of a quadruped robot achieved using real-time finite-horizon MPC.

Hardware failures require legged robots to rapidly reorganize coordination and gait timing to maintain stability and mobility. This is particularly challenging for larger quadrupeds, where increased mass and tighter actuation limits reduce the feasibility of aggressive, high-frequency compensation strategies often observed on smaller platforms. In this work, we propose a deep reinforcement learning approach for fault-tolerant locomotion under actuator power loss. The method employs an asymmetric actor-critic architecture in which the critic has access to privileged information during training, while the actor learns to reconstruct a corresponding latent representation from proprioceptive observations. We introduce a latent-alignment loss that encourages consistency between actor and critic representations. Additionally, we augment the action space with a learnable gait frequency parameter, enabling adaptive gait timing in response to terrain variations and actuator degradation without predefined faulty-leg strategies. The approach is validated in high-fidelity simulation on uneven terrain and real-world experiments on flat ground using a 68 kg quadruped robot.

Legged robots require robust agility to perceive and interact with complex and dynamic environments within a constrained time. However, most existing quadruped locomotion works rely on velocity-tracking policy, which struggle to reach precise targets within strict temporal constraints. Moreover, integrating real-time perception with agile locomotion for highly dynamic targets remains challenging due to sensor latency and processing delays. To concretely study and benchmark such agility in dynamic settings, we introduce a challenging ball-catching task for legged robots. This paper proposes an integrated framework that combines a vision module for landing point and time prediction with a direct position and time conditioned RL locomotion policy, instead of intermediate velocity commands. Beyond the method design, this work presents a system-level contribution that completes real-time robotic interception system that integrates multi-camera perception, online trajectory prediction, low-latency target communication, and sim-to-real locomotion control into a closed-loop deployment pipeline. By explicitly predicting the future spatial-temporal target, our approach mitigates perception latency during dynamic interception. We conducted extensive ball-catching experiments for the legged robot. Through comparative experiments against a velocity-tracking baseline, our direct target-conditioned approach achieves a higher success rate in catching balls with predicted landing spots within 2 meters and flight times between 0.8 and 1.2 seconds. This shows that the robot has successfully completed the dynamic ball-catching task under our tested setup. Furthermore, our policy exhibits a smaller performance gap after deployment, suggesting improved sim-to-real behavior in these trials.

In this paper, we present TRACE (Tokenized Robust Attention for Contact-Aware Estimation), an end-to-end learned proprioceptive odometry estimator for legged robots under unreliable contact conditions. The proposed estimator directly predicts relative displacement, relative rotation, and body-frame velocity from a recent history of onboard inertial and joint measurements. To improve robustness under unreliable contact conditions, we introduce a foot-aware cross-attention module that adaptively weights IMU and leg-wise kinematic tokens without relying on manually defined contact or slip thresholds. The estimator is trained with direct supervision and two physics-inspired auxiliary losses that promote kinematic consistency and reliable use of leg information. To reduce policy-specific overfitting and consequently improve sim-to-real transfer, simulation training incorporates policy randomization, followed by partial real-world fine-tuning of the temporal encoder and prediction head. Experiments across diverse indoor and outdoor terrains demonstrate consistent reductions in position drift compared with classical filtering-based, hybrid, and purely learning-based baselines. Ablation studies further validate the contributions of the proposed training objectives, policy randomization, and real-world fine-tuning, particularly under unreliable contacts and sim-to-real mismatch.

Quadruped robots are a promising platform for search and rescue missions because they can navigate cluttered indoor environments that may be restrictive for wheeled systems. However, in unknown rescue scenarios, autonomous exploration must balance map expansion with the likelihood of finding victims, which is not explicitly addressed by clas- sical frontier selection strategies. This paper presents a situation aware frontier prioritization method for single robot quadruped search and rescue. The proposed approach preserves the frontier exploration framework, but extends frontier ranking with information gain, observation deficit, rescue relevance, terrain penalty, and travel cost. The method is eval- uated in Gazebo simulation with a quadruped robot in two indoor rescue scenarios with different levels of difficulty. The first scenario is used as a sanity check, while the second introduces stronger clutter and frontier ambiguity. Experimental results show that all methods perform reliably in a simple scenario, whereas in a complex scenario is different. In that setting, the proposed method achieves the highest completion rate and the highest victim recovery among the evaluated approaches. These results indicate that situation aware frontier prioritization is beneficial when frontier choice becomes nontrivial and rescue utility must be balanced against generic exploration objectives.

State estimation is a key component in model-based control of walking robots and, more broadly, applicable wherever hidden variables must be inferred. The Kalman filter is widely used to estimate floating-base position and velocity by fusing multiple sensing modalities. However, tuning noise parameters is challenging and typically requires expert knowledge. Moreover, fixed noise parameters are unsuitable for varying gaits and environments. We propose an online adaptation strategy for the process noise covariance matrix Q and the measurement noise covariance matrix R. Specifically, we introduce a filter residual and innovation-based covariance adaptation method for legged robot state estimation and evaluate it against a baseline approach relying on IMU and foot force measurements. The proposed adaptation is implemented within an Invariant Extended Kalman Filter (InEKF) fusing IMU and leg kinematics. Experiments on indoor and outdoor datasets with a Unitree Go2 quadruped show that adapting R is sufficient and improves accuracy by 25% for the trotting gait compared to the fixed-tuned InEKF. Finally, the proposed residual-based adaptation achieves comparable performance to the foot force approach, without requiring foot force measurements or additional parameter tuning.

Kinematic models provide reliable motion constraints for odometry estimation in featureless environments, where exteroceptive sensing degrades and IMU integration drifts. Learning-based kinematic models can achieve more accurate odometry estimation than model-based methods by capturing nonlinear effects; however, most existing learning-based models are trained on a single embodiment and generalize poorly to new embodiments. This generalization is difficult because the meanings and structures of proprioceptive measurements vary across embodiments, including the number of joints and ground-contact elements (e.g., wheels, feet). To address this challenge, we propose KING, a Graph Neural Network (GNN)-based kinematic model that explicitly incorporates robot embodiments by representing them as a common graph. We show that wheel and leg kinematic models can be expressed by a unified representation, enabling a single model for both wheeled and legged robots. Trained on datasets spanning diverse embodiments, KING provides a unified representation of wheeled and legged kinematics and achieves high-accuracy odometry estimation in real environments. KING estimates accurate odometry using only an embodiment description (e.g., a URDF file) and on-board proprioception (encoders and an IMU) and can be adapted to new robot embodiments through few-shot learning with only one minute of data, avoiding retraining from scratch on a new dataset for each robot. The project page is available at: https://smrg-aist.github.io/king_project_page/

Humanoid and quadrupedal robots have the potential to revolutionize the way we work, interact, and coexist with intelligent machines. To understand their effects on society and how they can enable scientific discovery, we assess the current capabilities of these systems along hardware, locomotion, autonomy, data, and applications. We identify recent advances and key open challenges that must be overcome to enable widespread adoption and new use cases for legged robots. Last, we provide an outlook on the future of legged robots, exploring their ethical considerations, economic potential, policy implications, and broader societal effects.

While reinforcement learning for legged robots has achieved high motor performance, it has been constrained by the limited exploration capability of actions confined to the joint space. To address this issue, this study proposes a new method, Wrench-Augmented Reinforcement Learning (WARL), which introduces a wrenche (force and torque) into the action space. The proposed method combines wrench-guided exploration with a success rate-based curriculum mechanism to expand exploration capabilities in the early stages of learning, with the ultimate goal of acquiring behaviors based solely on joint control. Experiments using a quadruped robot demonstrated that WARL can learn robustly across diverse terrains and motor tasks without requiring terrain-specific reward adjustments or complex curriculum designs. Furthermore, an ablation study verified the effectiveness of the Switching Curriculum, which gradually eliminates the wrench. On the other hand, we also show that introducing a wrench can encourage behaviors that do not sufficiently exploit the robot's physical embodiment. These findings suggest that while wrench-based exploration enhancement is effective for improving learning efficiency, designing it in a way that is consistent with the robot's physical structure is a critical future challenge.

Reinforcement learning (RL) for legged robots is advancing locomotion, demonstrating its ability to adapt to new and challenging terrain. Traditionally, these RL locomotion frameworks are position-based, making the policy less adaptable to terrain types and requiring state estimation techniques in the observation space, i.e., linear velocity. Moreover, these RL frameworks often use small, lightweight quadrupeds that are limited in their viability for high-complexity tasks due to hardware constraints. This work explores an RL torque control framework for heavyweight high-torque quadrupeds. The RL framework in this paper can traverse rough terrain and effectively track a desired linear velocity without requiring knowledge of the agent's current velocity. Using Nvidia's Isaac Sim and Isaac Lab, simulation results of the RL torque control policy are shown on the Unitree B1 quadruped, achieving speeds of 3.5 m/s and 1.5 rad/s. In addition, the quadruped can walk up and down stairs without the aid of an exteroceptive sensor.

Reinforcement-learning navigation policies for legged robots select actions reactively from current observations and short-term memory, with limited capacity to anticipate how moving obstacles will evolve in the near future. In dynamic environments, this reactivity causes the robot to respond too late because collision risk depends on short-horizon scene structure rather than on current obstacle positions alone. Lightweight predictive supervision applied to the policy's recurrent state during training can encode anticipatory obstacle dynamics without modifying the inference-time controller. We augment a reactive LSTM-SRU navigation backbone with an auxiliary JEPA-style predictor and SIGReg regularization: during training, the predictor supervises the deterministic hidden state to anticipate its own next state; at inference, it is fully discarded, incurring zero additional computational cost. On simulated and real-world navigation benchmarks with dynamic obstacles, our method substantially improves navigation success while reducing collision rates through the predictive training signal alone, without additional inference-time parameters. Real-robot deployment on a Unitree Go2 demonstrates zero-shot sim-to-real transfer: the controller navigates cluttered indoor and dynamic outdoor environments without fine-tuning, with evasive behavior consistent with the collision reduction observed in simulation.

This paper presents a safety-critical distributed nonlinear model predictive control (DNMPC) framework for cooperative payload transportation by teams of quadrupedal robots. The proposed approach models the robotic team and the shared payload as a dynamically coupled networked system with rigid holonomic coupling constraints arising from cooperative transportation. To enable distributed real-time optimization, the centralized finite-horizon optimal control problem is decomposed into parallel local NMPC subproblems coordinated through the alternating direction method of multipliers (ADMM). The resulting distributed framework enforces consensus over both payload-state and interaction-wrench trajectories while explicitly incorporating acceleration-level holonomic coupling constraints within the distributed predictive control formulation. Safety-critical obstacle avoidance constraints for both the robotic agents and payload are enforced using higher-order control barrier functions (HOCBFs). The framework is validated through numerical simulations with teams of two, three, and four quadrupedal robots transporting shared payloads in cluttered environments. Real-time experiments on two- and three-robot teams demonstrate safe and robust transportation under payload uncertainty and external disturbances. Compared with centralized NMPC, the proposed framework achieves up to 23% reduction in average NLP solve time while maintaining comparable closed-loop performance. Ablation studies further demonstrate robustness to communication delays and show that explicit payload-state consensus and holonomic constraints substantially improve payload tracking and distributed coordination over existing wrench-only consensus formulations.

Navigating dynamic and crowded environments presents significant challenges for quadruped robots due to severe sensor occlusion and unpredictable human motion. Existing approaches face a trade-off: model-based methods, such as Velocity Obstacles (VO), theoretically guarantee safety but rely on accurate obstacle motion estimates that often fail in dense crowds, while end-to-end learning methods offer robustness but lack motion prediction capability of obstacles, leading to collisions or conservative behaviors. To solve this, we propose VOP-Nav, a novel navigation system that combines the geometric safety of VO with the agile adaptability of end-to-end learning. Using only local onboard observations, our system avoids explicit obstacle detection and tracking pipelines. The VOP-Net processes multi-frame LiDAR data to implicitly encode dynamic constraints and predict a safe velocity region derived from Velocity Obstacle theory. Importantly, the VO predictions serve a dual role: they are used as input to the navigation policy during inference and as a reward signal during training to encourage safe motion. Evaluations in Isaac Gym demonstrate that VOP-Nav achieves higher success rates than all baselines while balancing locomotion speed and collision avoidance. Real-world deployment on a Unitree Go2 quadruped robot further validates the system's robustness and efficiency in complex indoor and outdoor dynamic environments.

Reinforcement Learning (RL) has demonstrated remarkable capabilities for solving complex robotic control problems, but its lack of safety guarantees severely limits deployment on hardware. In particular, as legged robots and manipulators often operate near safety-critical boundaries, out-of-distribution states can lead to failure upon deployment. To address this, we introduce Acc-CBF-QP, an acceleration-based Quadratic Program (QP) safety filter using Control Barrier Functions (CBFs) that constrains any RL policy onto a safe set at runtime without modifying training. The method applies to unconstrained and Safe-RL policies, and enforces joint position, velocity, torque, and collision constraints within a unified optimization framework. A key contribution is the formulation of RL+QP tasks that regulate deviation from the RL command when constraints would otherwise be violated. We introduce a TorqueTask, minimizing torque deviation, and a Forward Dynamics Task, minimizing induced acceleration deviation, thus providing principled control over safety-performance trade-offs. Experiments on a 7-DoF Kinova Gen3 manipulator and a 19-DoF Unitree H1 humanoid, both in simulation and on hardware, highlight substantial reductions in constraint violations. On the real H1 hardware, a Safe-RL policy alone yielded 10.04 violations/s, which were reduced by 92% to 0.80 violations/s when augmented with Acc-CBF-QP. On the Kinova Gen3, Acc-CBF-QP fully eliminated violations. Nominal task performance of the RL objective is preserved in violation-free regimes. Under aggressive velocity commands on H1, Acc-CBF-QP improves execution by preventing constraint-induced shutdowns, yielding longer survival times. The full pipeline is open-source.

Prompt extraction of victims from water is crucial in water surface rescue missions. However, previous research on rescue robots has seldom addressed this issue. This paper presents QuadBoat, a bio-inspired unmanned surface vehicle (USV) designed to track and retrieve victims from water. QuadBoat features a quadrupedal robot configuration, enabling it with highly adaptable and agile maneuverability through its actively adjustable posture. Employing an inverse kinematics-based controller and cascaded model predictive control (MPC)-PID controller for overall movement, QuadBoat can accurately track and retrieve objects on the water surface. Maneuverability demonstrations validate QuadBoat's high agility, while a series of tracking experiments, including leg action tracking and trajectory tracking, confirm its high motion accuracy and system mobility. Finally, visual-based tracking and object pickup experiments further verify QuadBoat's target tracking capabilities and its effectiveness in executing rescues, both indoors and outdoors.

Enabling quadrupedal robots to traverse complex terrains-from rugged outdoor environments to urban landscapes-requires seamless integration of multiple motor skills, smooth transitions between gaits, and high-speed perceptive locomotion using only onboard sensors. We present APT-RL (Action Pretrained Transformer-based Reinforcement Learning), a unified framework that enables multi-skill locomotion to achieve high-speed traversal in complex environments through autonomous skill transitions utilizing only onboard perception and computation. Our approach generates large-scale, feature-rich 2D motion datasets through trajectory optimization with simplified dynamics. These datasets enable training of diverse, reusable locomotion skills that transfer effectively to a real quadruped robot operating on complex uneven terrains. The resulting high-quality skills serve as strong priors for efficient learning of complex downstream tasks and extend naturally to 3D environments, enabling smooth, high-speed multi-skill locomotion in deployed policy. Real-world experiments demonstrate the framework's capabilities: the robot performs agile maneuvers through complex indoor obstacles and outdoor wild environments, including dynamic drop-down maneuvers that reach instantaneous peak speeds of up to 6 meters per second. A single onboard policy enables robust traversal of diverse obstacles, including stairs, hurdles, stepping stones, gaps, and fallen branches, demonstrating the versatility and effectiveness of our approach.

Loco-manipulation has recently shown promising capabilities; however, achieving high-precision control, managing the high-dimensional action space induced by many degrees of freedom (DoFs), and fully exploiting the inherent redundancy of whole-body systems remain challenging. In this paper, we propose a novel whole-body control framework that effectively addresses these challenges by decomposing the complex loco-manipulation problem into partial reference motion generation and low-level imitation control. We introduce a new Kinematic Normalizing Flow (KNF) model, trained on a large-scale kinematic dataset, that generates diverse yet feasible partial reference motions. A high-level controller is then trained to navigate the KNF's latent space to exploit redundant solutions, while a low-level controller ensures physically feasible and accurate motion execution. We validate our approach on the quadrupedal robot equipped with a six-DoF robotic arm. In simulation, experimental results show that our approach significantly outperforms state-of-the-art methods in terms of tracking accuracy and feasible workspace coverage. For hardware deployment, we evaluate the system over 24 episodes across 8 different mobile loco-manipulation tasks. The system achieves end-effector pose-tracking errors of 4.5 cm and 0.14 rad, while maintaining accurate locomotion tracking with linear and angular velocity errors of 0.1 m/s and 0.01 rad/s, respectively, outperforming competitive baselines. Our method represents a practical and powerful solution for accurate and generalized whole-body loco-manipulation in high-DoF robotic systems, with promising potential for diverse downstream robotic tasks.

State estimation is essential for quadruped robots, enabling robust locomotion, navigation, and control. While many estimators have been proposed in the literature, existing implementations are often tied to specific robots or software stacks, making fair comparisons difficult. This lack of a general-purpose benchmarking framework hinders reproducibility and slows down algorithmic innovation. In this paper, we introduce Chalito, an extensible MATLAB/Python library for benchmarking filter-based state estimation algorithms in quadruped robots. Chalito imports robot models directly from URDF, supports multiple filtering approaches, and is designed to be easily extended with new methods. The framework runs on both simulated and real datasets, enabling systematic evaluation across robots and filters. To the best of our knowledge, this is the first open-source library exclusively dedicated to benchmarking filtering algorithms for quadruped robots.

The motion controller is one of the most fundamental modules in embodied intelligence systems. Driven by large-scale human motion-capture data and the motion-tracking paradigm, humanoid control has achieved remarkable progress in recent years. However, migrating this recipe to the quadrupedal setting is far less straightforward: animal motion data is scarcer and harder to capture at scale than human data, and cross-embodiment retargeting remains fragile. We present ABot-C0, a generalist motion-control system for quadruped robots that establishes three complementary behavior foundations: a scalable multi-source motion-data pipeline, robust policy learning across motion tracking, locomotion, and scene interaction, and a unified deployment stack for reliable real-world operation. Fundamentally, we construct a data pyramid through conditional video-generation synthesis, annotated motion capture, teleoperation, and human design, producing 16,074 physically feasible motion clips as the data foundation for diverse motion-learning demands. With large-scale motion data, a Flow-Matching generalist policy demonstrates, for the first time, a scaling law for quadruped motion tracking: performance improves consistently as training scales up, with zero-shot capability to track unseen motions. We then go a step further toward robust all-terrain locomotion by adopting a three-stage privileged-to-perceptive framework with temporal LiDAR memory and terrain-predictive supervision. Collectively, these components form a motion generalist that coordinates multi-policy execution, smooth behavior transitions, energy-efficient control, and safety mechanisms for real-world deployment. Extensive experiments on urban-terrain autonomous navigation and companion-style multimodal interaction demonstrate that quadruped robots can move beyond functional demos toward product-level behavioral intelligence.

This paper presents a novel layered planning and control framework based on multi-rate nonlinear model predictive control (MR-NMPC) that enables quadrupedal robots to perform hybrid bipedal locomotion with wall-assisted support in constrained environments. Real-time trajectory optimization for this locomotion presents significant challenges, as the controller must simultaneously plan for both the contact points and the continuous trajectories of the robot's center of mass (CoM) and orientation within the robot's nonlinear dynamics while accounting for unilateral contact constraints, underactuation, and the switching nature of the robot's dynamics. At the high level of the control framework, an MR-NMPC is proposed, which dynamically plans both the discrete-time trajectories of the contact points and the continuous-time trajectories of the CoM and orientation, using a single rigid body (SRB) dynamics model. By incorporating contact-point planning within the multi-rate optimal control framework, this approach enhances dynamic stability compared to heuristic foot placement strategies. At the low level of the control framework, a nonlinear whole-body controller (WBC) based on virtual constraints and a quadratic program enforces full-order dynamics and tracks the MR-NMPC references. The proposed approach is validated through extensive numerical simulations demonstrating the robust wall-assisted bipedal locomotion of a Unitree A1 quadrupedal robot on rough terrains and under external disturbances in a constrained environment. Comparative analysis shows that the proposed MR-NMPC achieves a 2.9 times higher success rate compared to conventional MPC with heuristic-based foot placement strategies in negotiating irregular terrain at high speeds.

Learning-based control has revolutionized dynamic locomotion, yet navigating unstructured terrain remains limited by a robot's incomplete awareness of imminent ground contact. While global perception systems such as LiDARs and depth cameras provide environmental context, they are frequently plagued by latencies, occlusions, and the high computational cost of dense geometric reconstruction. On the other hand, proprioceptive feedback is purely reactive, initiating corrections only after impact has occurred. This work explores embedding a minimal suite of low-cost, high-frequency infrared proximity sensors directly into the feet of a quadrupedal robot. These sensors provide "pre-contact" feedback that is robust to self-occlusions and significantly less computationally demanding than conventional vision-based pipelines. By integrating these localized signals into a reinforcement learning framework, we enable the robot to anticipate terrain discontinuities such as gaps and stepping stones that are problematic for traditional perception stacks due to occlusions or state estimation drift. We demonstrate that such sparse, near-field sensing can be reliably modeled in simulation and transferred to the real world with high fidelity. Experimental results show that local proximity sensing substantially improves traversal robustness over discrete terrain and offers a low-power, low-latency alternative or complement to complex global perception suites in unpredictable environments. For more information about results and methods, please see the project website: https://sites.google.com/view/foot-tof/home.

Quadruped robots have achieved remarkable locomotion, yet their behavioral repertoire remains confined to a few gaits--far from the expressive, companion-like presence long envisioned for them. Attempts to import the humanoid recipe of large-scale motion data have inherited one tacit assumption: that robot motion must first pass through an animal body, making data collection dependent on cooperative animals, reconstruction fragile across species, and retargeting ill-posed across incompatible morphologies. We propose Uni-Mo, a fully automated pipeline that removes the animal from the loop by reframing data scarcity as a generation problem: an LLM proposes motion prompts, a video diffusion model synthesizes the corresponding robot behaviors, and the generated videos are lifted into 3D reference trajectories used to train tracking policies deployed on a real Unitree Go2. To make naively-drifting generations reliably extractable, we introduce an Identity Consistency Loss that enforces appearance coherence across frames. We release Quad-Imaginarium at https://github.com/Amap-Robotics/Quad-Imaginarium, the resulting open-source dataset of 7,488 language-annotated quadruped motions (18.5 hours) spanning acrobatic and performative behaviors. We validate 392 randomly sampled motions on a real Unitree Go2 with a 96.7% deployment success rate, complemented by a 97.6% success rate across the full dataset in simulation.

Legged robots deployed in planetary exploration and other remote environments must maintain reliable locomotion despite actuator failures and challenging terrain conditions. Although reinforcement learning has achieved strong results in legged locomotion, monolithic policies can struggle to efficiently represent the diverse control strategies required to compensate for different fault conditions. In this work, we propose a fault-aware modular control architecture that explicitly leverages fault-diagnosis information to activate specialized control experts associated with distinct actuator failure modes. Experimental results show that explicit fault-conditioned modular policies consistently outperform monolithic policies of comparable size, achieving higher locomotion performance across failure scenarios. Moreover, the proposed modular architecture retains competitive performance even under significantly reduced network capacity, highlighting its suitability for compute-constrained robotic platforms, such as those typically employed in space applications. The code associated with this work is available at: https://github.com/iit-DLSLab/fault-locomotion-isaaclab.

Climbing hollow stairs remains a challenging problem for quadruped robots due to the high risk of leg trapping, severe depth sparsity, and high-frequency depth-sensing noise. In this paper, we propose StairMaster, a novel three-stage reinforcement learning framework for stable locomotion on such extreme discontinuous terrains. Our architecture integrates a Cross-Attention mechanism to extract structural features from noisy depth data, alongside a Spatial-aware Recurrent Unit (SRU) that maintains robust spatio-temporal memory to mitigate perception blind spots. To bridge the sim-to-real gap in depth perception, we propose a high-fidelity sim-to-real depth sensor modeling pipeline that faithfully replicates real-world sensor artifacts. Additionally, we employ a 3D waypoint-guided active perception reward for proactive sensing, alongside hollow gap kinematic and stair edge penalties to ensure precise foothold placement. We successfully deployed StairMaster on a Unitree Go2 robot, demonstrating its ability to conquer hollow stairs with an unprecedented incline of up to 55$^\circ$ through zero-shot transfer. To the best of our knowledge, this is the first RL-based policy to achieve such steep hollow stair climbing in real-world environments. Project Website: https://sivan666666.github.io/StairMaster/.

Wheeled-legged robots possess both agile mobility for traversing complex terrains and high efficiency, making them suitable for long-distance transportation applications. Conventional actuated wheeled robots require specialized hardware and electrical design due to the incorporation of wheel components. We propose a novel and low-cost passive wheeled legged robot equipped with standard casters on each leg to obtain omnidirectional mobility. The control method employs an asymmetric actor-critic structure, enabling the utilization of the privileged information of the passive caster's angles and velocities. We develop a caster base posture adjustment strategy based on velocity commands, utilizing actuated joints to modify the caster base joint axis posture and thereby adjust the propulsion direction of the casters. Moreover, we implemented multiple propulsion modes to achieve varying degrees of caster twisting oscillation, converting these into propulsive force. We conducted a slalom test and mode switch experience, which shows the passive wheeled quadruped could achieve omnidirectional movement versatility, and reduce the cost of transport (COT) by up to 89.1% with respect to legged motion.

Universal quadrupedal locomotion remains limited by the difficulty of integrating perception across diverse robot morphologies. State-of-the-art controllers rely on single-robot training or blind policies that omit real-time perception, leading to poor cross-embodiment generalization. Designing locomotion policies that remain robust across related quadruped morphologies while incorporating perception is challenging. Moreover, fully perceptive policies are often sensitive to noise, whereas blind controllers lack terrain awareness. In this work, we study how perception should be integrated into morphology-aware reinforcement learning architectures for deployable quadrupedal control. Building on MorAL, we train morphology-specialized universal controllers on multiple reference quadrupeds using adaptive terrain curricula. We compare a blind baseline, a critic-perceptive variant (MorAL+), and a fully perceptive actor-critic (PPAL). Policies are evaluated in simulation on flat and rough terrains, and deployed on ANYmal hardware. Results show that critic-only perception improves robustness and tracking consistency over blind baselines while remaining more stable than fully perceptive policies under perception noise. These findings highlight that perception placement and curriculum design are key factors for scalable, morphology-aware locomotion.

Legged robots rely on accurate ground interaction awareness to traverse variable terrains, such as slippery surfaces. Existing slip detection methods often rely on kinematics and proprioception, which lack the sensitivity to detect early-stage slips that occur prior to catastrophic instability. Thus, this paper presents SlipSense, a novel framework for online force-based slip detection using a custom lightweight sensorized foot for quadrupeds to detect slip. The framework integrates a multimodal sensor design with a LSTM-based model to infer ground reaction forces and detect slip-indicative anomalies during locomotion. The proposed framework is deployed on a Unitree Go1 quadruped to demonstrate blind online slip detection over a slippery terrain. Our method detects early-stage slips down to an average displacement of 24.1 +/-6.4mm with an overall accuracy of 85.9%. This represents a 3.3-fold finer detection resolution and a 24% relative accuracy improvement over a standard kinematic baseline that uses foot velocity inferred through state estimation. The work in this paper serves as a foundation for force-aware gait adaptation in legged robotic locomotion, allowing future controllers to estimate terrain friction and adjust constraints, thus improving the overall stability of the system.

Recent advances in control have enabled bipedal-wheeled robots to traverse slopes and single-step obstacles, yet long staircase traversal remains challenging as current teacher-student frameworks suffer from weakened dynamics-aware representations and incomplete terrain geometry encoding. To bridge this gap, we propose DynaWM, a dynamics-aware representation learning framework. To enhance terrain encoding capability and enable transparent assessment, we introduce a world model as a regularizer to enforce forward-dynamics awareness, preserving comprehensive terrain geometry while facilitating hierarchical encoding visualization. To stabilize knowledge transfer, we employ a momentum target encoder to provide consistent distillation targets, preventing dimensional collapse from non-stationary teacher updates. Evaluation of the learned representations through Principal Component Analysis (PCA) visualization and quantitative metrics reveals that our encoder hierarchically captures terrain geometry with higher terrain encoding capability, leading to enhanced terrain adaptability and motion smoothness. Experimental results in simulation and real hardware demonstrate that our method achieves superior terrain adaptability and motion smoothness, enabling bipedal-wheeled robots to overcome diverse continuous stairs, as shown in Fig. 1.

Co-design of legged robots with elastic elements is challenging due to the non-differentiability of contact dynamics and mechanism engagement. This paper presents SurGE, a framework that computes surrogate gradients of the design objective through a differentiable pipeline consisting of a kinodynamic single-rigid-body (Kino-SRB) model and a design-aware control policy, and injects them into CMA-ES via mean shift with cosine-annealed step decay. On a 4-DOF design space of a hopping robot with unidirectional parallel spring, SurGE achieves 6 times lower cross-seed standard deviation and 18% tighter population concentration compared to vanilla CMA-ES, while matching or improving the best objective. Hardware experiments on a 2D design subspace show that, starting from a hand-tuned initial design, SurGE reduces the design objective by 37.65% on hardware, with the improvement trend identified in simulation transferring consistently to the physical system. SurGE provides the potential to accelerate non-differentiable co-design problems in legged robots via surrogate model gradients.

Legged-wheeled robots have long been studied for their potential to combine the efficient flat-ground mobility of wheels with the rough-terrain capability of legs. However, examples of their application to long-range autonomous navigation in real environments remain limited. This paper reports our effort to build a deep reinforcement learning (DRL) based locomotion controller and an autonomous navigation system for the commercially available legged-wheeled robot Go2-W, and to apply them to long-range autonomous navigation in a real environment. For locomotion control, we extended a proprioception-only policy, which we had previously developed for quadruped robots, to the 16-DoF legged-wheeled robot. We also found that wheeled locomotion concentrates the load on the hip joints and causes heat concentration that hinders sustained travel, and obtained a policy that suppresses it by distributing the load. We evaluated the system at the Tsukuba Challenge 2025, demonstrating that it can autonomously traverse an approximately 2.8 km route including sidewalks, a park, and stairs without stopping due to overheating.

Human legs exhibit high efficiency, agility, and impact absorption, with toes playing a crucial role in these capabilities. While many attempts have been made to implement human-like toes in robots, they have not fully replicated human characteristics nor rigorously validated their benefits. We propose a 14-DOF biped robot emulating human toes' lightweight, high-torque, robust nature. To quantitatively analyze the effectiveness of the active toes in terms of agility, efficiency, and impact absorption, we developed a high-fidelity simulation training environment that reflects actual actuators with coupled transmissions and accurate power consumption. To ensure a fair comparison between configurations with and without active toes, we designed a minimal RL reward function and applied an identical training procedure to both. The simulation results indicate that, at 1.33 m/s walking, the toe-equipped robot reduced CoT by 17.5% and heel-strike GRF by 5.0% compared with the toe-ablation configuration. On the agility test, average and maximum path deviation decreased by 25.0% and 34.0%, respectively.

Legged robots are increasingly deployed in forests for ecological surveying and monitoring, yet their autonomy is often interrupted consequent to the challenges posed in traversing forest environments. Forest entrapments, for example, when a robot's legs are ensnared in vines or other vegetation, result in loss of stability and toppling. Such events not only disrupt the mission and require manual intervention, but also risk damage to the robot hardware. To address the absence of a dedicated dataset to investigate these failure modes in forest environments, we present ForEnt, a multi-modal dataset collected with the low-cost Unitree Go2 quadruped across eight forest sites in the Southampton Common Woodlands, UK. For our dataset, over approximately 1.7 km of traversals in 11 sequences were conducted, yielding 69 recorded entrapment events. ForEnt includes time-synchronized RGB-D images, LiDAR scans, proprioceptive data, and third-person video, enabling analysis of terrain factors contributing to entrapment and providing labeled sensor streams for reproducible benchmarking. By supporting the evaluation of entrapment detection strategies, ForEnt lowers the barrier to developing robust quadruped robot deployments in challenging forest environments.

Quadruped robots are increasingly expected to navigate through narrow passages, cluttered indoor scenes, and large-scale 3D unstructured environments. Existing local planners commonly approximate the robot using isotropic geometric inflation or rely on planar and elevation-map representations, leading to conservative motion in tight spaces and limited reasoning about overhanging structures. This letter presents SCAN-Planner, a spatial collision-aware local planning framework for long-range quadruped navigation. A yaw-aware twin-cylinder footprint is used to model the elongated robot body, enabling whole-body collision evaluation through sparse queries in an inflated 3D occupancy map. We further introduce a projected A* search that generates collision-free guidance on an interpolated ground-following surface, with z-gradient suppression to avoid obstacles horizontally while maintaining vertical stability. For large-scale deployment, a robot-centric sliding map with boundary fallback provides high-resolution local collision checking and recovery from local dead ends. Simulation and real-world experiments demonstrate that SCAN-Planner generates safe, smooth, and efficient trajectories in dense clutter, 3D unstructured scenes, stair traversal, and long-range navigation tasks.

In this letter, we present a hierarchical control framework that enables wheeled bipedal robots to perform planar object sliding tasks with their wheeled legs. The proposed approach formulates a nonlinear model predictive controller (NMPC) based on a reduced-order three rigid bodies (TRB) dynamical model that explicitly accounts for the hip roll degree of freedom and multiple wheel-environment contact modes, which is essential for lateral stepping and pedipulation tasks. Within this framework, the NMPC simultaneously regulates robot locomotion and interaction forces, allowing the robot to stably execute both rolling and object manipulation behaviors. A trajectory-optimization-based robot-object motion planner is developed to generate reference motions that incorporate stick-slip transitions in ground-object contact. Two representative pedipulation motions, namely scooting and lateral sliding, are validated through real-world hardware experiments, in which the robot successfully retrieves a 1 kg object from under a desk and slides a 4 kg object over a distance of 0.228 m via scooting.

Autonomous navigation of quadrupedal robots in diverse environments fundamentally relies on resilient Simultaneous Localization and Mapping (SLAM). While visual-inertial SLAM has matured across wheeled, handheld, and aerial platforms, a critical evaluation gap remains regarding how hardware-level sensor configurations affect performance under the aggressive dynamics of legged locomotion. Quadrupeds introduce distinct embodiment-induced sensory challenges, including foot-impact shocks, high-frequency mechanical vibrations, and rapid angular rotations, which degrade standard perception pipelines. To address this gap, we present a systematic evaluation of state-of-the-art visual, visual-inertial, and LiDAR-visual-inertial SLAM methods using the GrandTour dataset recorded on an ANYmal D quadruped. We isolate and quantify the impacts of camera modalities, shutter techniques, and inertial sensor tiers, analyzing their trade-offs across localization accuracy, algorithmic robustness, and computational resource utilization. Our empirical findings demonstrate that hardware selection has substantial influence on system resilience: stereo configurations consistently outperform monocular and RGB-D modalities, global shutter cameras significantly mitigate motion-induced tracking failures compared to rolling shutter cameras, and, crucially, standard inertial integration can degrade the performance of primarily vision-based frameworks under harsh legged locomotion. These insights additionally offer concrete design guidelines for tailoring custom sensor payloads to achieve dependable perception on agile legged systems.

Sampling-based Model Predictive Control (SMPC) is a promising strategy for contact-rich robotic manipulation, combining gradient-free optimization with massively parallel GPU simulation. Yet, most prior work relies on simplified dynamics or remains confined to simulation. We present an MPC framework that leverages JAX for large-scale parallelization and efficient computation, coupled with the high-fidelity MuJoCo MJX simulator, and deploy it on a Franka Research 3 executing the Push-T manipulation task through a complete real-to-sim-to-real pipeline. The MTP variant with structured global sampling outperforms unimodal baselines such as CEM, MPPI, and PS across tasks that require mode switching, both in simulation and on hardware. Furthermore, we evaluate online domain randomization within the MPC sample budget, showing that contact-initiation parameters yield interpretable adaptation signals, whereas global physics parameters provide feedback that is too weak for reliable exploitation at typical replanning frequencies. These findings highlight key challenges for sampling-based MPC in contact-rich manipulation-contact sensitivity, tight compute budgets, and the difficulty of obtaining informative domain-randomization signals in real time.

Robots operating in homes, warehouses, and other object-rich environments need memory systems that can find specific object instances on demand. Object-level memory alone is often insufficient: scenes contain many plausibly matching objects, and users refer to the target through relations to landmarks and surrounding objects (e.g. ``the tall lamp below the dartboard and to the left of the poster''), demanding a relational spatial memory that supports retrieval through semantic, appearance, and spatial predicates over objects. To achieve this, we present FARM (Find Anything using Relational Spatial Memory), which builds, in real time at 5-10 Hz, a compact, open-vocabulary, object-level memory with geometry, visual-language descriptors, and viewpoint evidence. At query time, FARM uses VLMs to parse the query and score visual evidence, while grounding spatial constraints explicitly through object symbols and relational predicates. This structured use of VLMs enables more accurate and robust retrieval than end-to-end reasoning over frame histories or scene-graph context. In experiments on 44k language queries spanning 67 indoor and outdoor scenes, ranging from 15 to 15,000 m^2, FARM improves Recall@5 and Recall@10 over prior methods by 164% and 224%, and a final VLM reranking stage improves Accuracy@1 by 35%, while running in real time. We further demonstrate closed-loop deployment on a quadrupedal robot using onboard sensors and compute.

Dexterous manipulation is fundamentally a problem of interaction dynamics: the hand must track precise finger trajectories, regulate the contact force exchanged with grasped objects, respect actuation and safety limits, and remain predictable when contact persists -- objectives in tension for any fixed-gain controller. A sustained contact torque $τ_{\text{ext}}$ through a joint stiffness $K_d$ produces the structural bias $e_\infty=τ_{\text{ext}}/K_d$, so stiffening for accuracy sacrifices contact safety while softening yields by design. We make these interaction dynamics explicit and actuator-agnostic through a constant-$A_d$ double-integrator backbone, instantiating the offset-free architecture established for physical human-robot interaction (pHRI) and preserving its modeling assumptions on the reduced residual dynamics. An algebraic feedforward reduces the tendon transmission -- hydraulic, cable, pneumatic, twisted-string, or series-elastic -- to a constant-coefficient double integrator, so the QP cost inverse is precomputed offline and a 10-step receding-horizon QP runs at 500,Hz under contact-force (ISO/TS 15066), actuation, and jerk constraints. An encoder-only augmented-Kalman disturbance state drives steady-state error to zero under constant contact loads in the nominal detectable case. In simulation, a hydraulically actuated finger -- the worked example, adding pressure and cavitation constraints -- attains 0.6,mrad RMS, 0.1,mrad steady-state, and 7.3,mrad peak deflection under 1.5,Nm contact: 153$\times$, 1500$\times$, and 21$\times$ better than classical impedance. The realized first-move stiffness (18$\to$323,Nm/rad with update rate) is independently verified, and the architecture scales to a 16-DOF LEAP Hand MuJoCo model, recovering from 2.5,N grasp disturbances within 0.7,s.

Fall recovery is critical for autonomous legged locomotion. Existing methods have demonstrated that some legged robots, such as humanoids and quadrupeds, are capable of fall recovery from diverse postures by utilizing arms or coordinating multi-legs to generate support forces. Without arms or other legs to provide supportive assistance, a bipedal-wheeled robot must rely solely on the actuation of its legs, making recovery particularly difficult. To address this, we introduce FTSR (Force-guided Teacher-student framework with Stage-wise Rewards). The force-guided method constructs an external auxiliary force during simulation training that correlates directly with the robot's real-time height, explicitly formulating this force as an optimizable constraint. Through constrained reinforcement learning, the policy is guided toward reducing force dependency gradually and increasing the body height, developing internal recovery strategies despite having no arms for support. Height-progressive stage-Wise rewards progressively structure posture stabilization during recovery and transition to sustained locomotion, integrated with teacher-student architecture distilling privileged knowledge of force effects and recovery dynamics. After simulation training, the policy is deployed on a physical armless bipedal-wheeled robot and extensively evaluated. Experiments confirm robust and reliable fall recovery under diverse challenging conditions, demonstrating strong environmental adaptability and motion robustness, while maintaining full post-recovery motion capability. The framework also generalizes effectively to a high-DOF humanoid, confirming its practical generalizability. The project page is available at https://2350575870.github.io/force-guided.github.io/

In this paper, we propose a method that applies Inertial-Leg (IL) tokenization to an attention-based network for proprioceptive state estimation in legged robots. Unlike existing learning-based state estimators that concatenate all sensor measurements into a single flat vector, the proposed architecture represents inertial measurements and leg-wise measurements as individual tokens and uses an attention mechanism to learn the relative importance of each measurement.This design allows the network to reweight each measurement according to the current contact condition, reflecting the fact that the reliability of forward kinematic measurements depends on whether the corresponding foot is in contact. Unlike conventional contact-aided estimators, however, the proposed method learns this behavior without relying on an explicit contact estimator or on explicit measurement updates based on a stationary contact assumption. To validate the proposed method, we conducted experiments on a Unitree Go1 robot, including debris terrain not modeled in simulation and gait patterns not seen during training. Experimental results show that the proposed method achieves better estimation performance than existing learning-based state estimators under unseen gait patterns and also improves performance over contact-aided model-based methods.

Quadruped robots are capable of traversing a wide range of complex terrains with high flexibility. As highly mobile ground-based intelligent platforms, they can be equipped with modules for navigation control, environmental perception, and intelligent interaction, thereby serving as real-world mobile deployment platforms for various algorithms. In this paper, we introduce Y-BotFrame, an extensible embodied platform that turns a robot into an intelligent ground assistant. Y-BotFrame integrates multimodal perception capabilities, including speech, vision, and LiDAR, and employs a large language model as the cognitive core for environmental understanding, contextual reasoning, and task planning. The system maps user natural-language instructions into executable embodied task units that can be carried out by the robot. Y-BotFrame supports natural interaction through voice commands and visual feedback, removing the need for a remote controller and enabling efficient human-robot collaboration. With a highly extensible framework, Y-BotFrame supports plug-and-play integration of new functional modules as well as modular upgrades and iterative development, offering a reference implementation for the real-world deployment of general-purpose, instruction-driven embodied agents.The supplementary video is available at https://xdei-group.github.io/Y-BotFrame/.

Learning-based visual navigation for legged robots typically relies on continuous goal updates from hierarchical state estimation to provide a persistent directional reference. This reliance incurs additional sensory and computational overhead and deviates from fully end-to-end mobile autonomy. Furthermore, under partial observability, policies are prone to learn myopic behaviors, easily becoming trapped in dead ends and complex structural layouts. To address these limitations, we investigate a goal-initialized navigation setting, where the target is provided only once at the beginning of an episode, requiring the robot to operate based on intrinsic spatial memory without subsequent goal updates from external modules. In this work, we propose GUIDE, a fully end-to-end reinforcement learning framework designed to cultivate internal directional awareness. Specifically, GUIDE incorporates a spatial anchor predictor that leverages multi-frequency proprioceptive history to extract egomotion representations, thereby maintaining a persistent long-horizon spatial context for navigation. Concurrently, it utilizes raw depth streams to perceive local environmental geometry. We evaluate the proposed framework across both simulation and real-world scenarios on a quadruped robot. Experiments show that GUIDE learns reliable egomotion and directional awareness, enabling a fully end-to-end deployed policy to safely navigate through dense clutter and structured mazes without subsequent goal guidance or prior maps.

This paper presents Tessellated Biomes, a cyber-physical framework for the adaptive robotic construction and reconfiguration of modular multi-material assemblies. It challenges the linear lifecycle of standard construction by fusing (1) local microfactory fabrication, (2) discrete multi-material optimization, and (3) distributed robotic assembly into a unified circular process of spatial adaptation. The research details methods for the digital fabrication of self-aligning modular primitives in multiple materials (PLA, timber, and concrete) produced in local microfactories; the aggregation and optimization of these primitives into compression-based discrete structures; and the deployment of custom quadrupedal robots that collaboratively relocate material into realized physical aggregations. The framework is validated through the fabrication, optimization, and robotic assembly of discrete structures. Together, these results position Tessellated Biomes as a model for resilient, reconfigurable architecture.

Multi-quadruped coordination has attracted increasing attention due to its enhanced payload capacity, broader contact coverage, and improved adaptability to challenging tasks. Existing methods for multi-quadruped manipulation typically focus on predefined or closed task families, often relying on multi-agent reinforcement learning (MARL) to train task-specific coordination policies. However, such methods struggle in open-ended continual learning settings, where tasks arrive sequentially and robots are expected to acquire new coordination skills while reusing previously learned ones without catastrophic forgetting. To address this challenge, we propose Conquer, a semantic skill-library framework that formulates continual multi-quadruped coordination as a retrieve-adapt-update process. First, to accommodate varying team sizes across tasks, we design a team-structured Self-Allies-Goal (SAG) backbone that supports variable-cardinality robot teams by explicitly modeling each robot's own state, teammate context, and task goal. For each incoming task, Conquer constructs a task-level semantic descriptor from pre-execution information and retrieves a relevant skill from the library for adaptation. After successful execution, Conquer updates the skill library by extracting trajectory-level semantic descriptors and organizing them according to semantic distance, thereby enabling continual skill accumulation and cross-task knowledge transfer. Simulation experiments show that Conquer achieves a final average success rate of 95.6%, demonstrating strong forward transfer and negligible catastrophic forgetting. Real-world rollouts on Unitree Go2 teams further validate the deployment feasibility of Conquer for practical multi-quadruped coordination. Simulation and real-robot demonstration videos are available at: https://conquer-project.pages.dev/.

Robotic simulators are a cornerstone of modern research in aerial robotics, serving both as a vehicle for the development of new control algorithms and as the data source for training reinforcement learning (RL) policies. Yet, existing quadcopter learning environments often face a trade-off between physical fidelity, multi-agent support, and the throughput required by modern deep RL pipelines. In this paper, we present MuJoCo-Drones-Gym, an open-source Gymnasium-compatible multi-drone environment built on top of the MuJoCo physics engine. MuJoCo-Drones-Gym supports an arbitrary number of Bitcraze Crazyflie 2.x nano-quadcopters and exposes a modular API for selecting (i)~the physics model (rigid-body MuJoCo, explicit Python dynamics, or any subset of ground effect, blade drag, and inter-drone downwash), (ii)~the action interface (per-motor RPMs, collective normalized thrust, velocity setpoints, or PID waypoint commands), and (iii)~the observation space (kinematic state vectors, RGB / depth / segmentation cameras, or neighbourhood adjacency information). A PettingZoo ParallelEnv wrapper enables drop-in multi-agent reinforcement learning, while a suite of seven task environments, hover, velocity tracking, multi-drone hover, waypoint navigation, formation flight, gate racing, and a generic multi-agent template, demonstrates the breadth of the interface. We describe the environment design, the underlying physics and quadcopter dynamics, and illustrate its use through control and learning examples that mirror those of the closely related gym-pybullet-drones project, while taking advantage of MuJoCo's improved contact handling, rendering, and parallelizability.

The estimation of odometry in legged robots depends on the assumption that the velocity of the foot with respect to the world remains zero during the stance phase. Feedback for the main body velocity is derived from the kinematic serial chain of the feet making accurate leg phase detection is a critical subproblem. A considerable number of studies employ ground reaction force sensors mounted at the tip of the foot to classify, yet these sensors may not be universally available for all legged robots. Additionally, these sensors are often unresponsive to unaccounted disturbances, such as slippage, while the foot remains in contact with the ground. In this study, we propose a self-supervised representation learning framework for contact detection that utilizes the standard sensor set of joint encoders without reliance on force sensor augmentations. We employ learned representations to model the stance and swing phases probabilistically. The experimental results obtained confirm the efficacy of the proposed self-supervised contact detector. Our framework exhibited superior performance in comparison to supervised methods which necessitate sensor set augmentation and labeling, as well as baseline probabilistic approaches. Additionally, we make our code available to the public.