Legged Robots

Bipedal robots are challenging to control because they operate close to instability, where small variations in foot-terrain contact can rapidly destabilize locomotion. On rigid terrain, bipedal robots mitigate this fragility by using well-established contact mechanics and control strategies. On flowable surfaces such as granular slopes, foot contact can induce large surface deformations and solid-fluid-like transitions, coupling terrain effects with robot dynamics, leading to underperformance or failure. This is partly due to the lack of reliable methods to represent the dynamics of flowable terrain, making it difficult to account for terrain effects in locomotion design. Here, we investigate how controlling terrain response can improve bipedal locomotion on granular slopes by studying the terradynamics of cleated feet, thin plates emanating from the foot soles. Systematic studies of a small-scale (1.4 kg) robophysical biped reveal that cleats with sparse and dense spacing lead to excessive terrain yielding and resistance, respectively, degrading performance and leading to failure. An intermediate cleat spacing distributes interaction forces to maintain substrate stresses near (or below) the yield threshold, enabling walking on granular slopes up to 30 degrees. Guided by these principles, we design a foot that actively adjusts cleat depth and accommodates both rigid and granular terrain. We also demonstrate that the principles of effective foot-terrain interaction translate to a larger (15 kg) autonomous biped. Our study presents an alternative to conventional body-centric robot control approaches, which regulate terrain-induced effects through body motion, by instead regulating terrain interactions through limb-centric approach.

Reinforcement learning (RL) algorithms classically suffer from poor sample efficiency. In robotics, a recent line of work has emerged addressing this problem by encoding physics priors in the learning process. However, most of these approaches are validated on well-defined, low-dimensional benchmark systems rather than high-dimensional robots with complex nonlinear dynamics. In this paper, we introduce \textit{SKooP (Symmetric Koopman Predictions)}, an approach combining the advantages of morphological symmetries with those of a Koopman model learned via autoencoder to enhance policy learning. SKooP learns a Koopman model of the system dynamics alongside the policy. The resulting Koopman predictions are used as privileged observations for the critic, allowing the agent to learn based on smoother, more informative features. We also incorporate group symmetries into the actor, critic, encoder and decoder networks to produce a highly equivariant policy. The SKooP approach is validated via in-depth analysis of the learned Koopman models and symmetric policies to showcase how each of these influences the agent's performance. We also show that the learned policies are transferable to different simulation environments. Our results show that SKooP consistently reduces convergence time and increases the learned reward for multiple challenging bipedal locomotion tasks on a quadruped robot. Project page: https://evelyd.github.io/SymmetricKoopmanPredictions

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.

In this paper, we propose Adversarial Dynamics Priors (ADP) for perturbation-resilient humanoid locomotion control. Existing motion prior-based methods induce natural motion styles by imitating kinematic motion features, but they do not directly regularize dynamics features, such as CoM motion, centroidal momentum, contact forces, and contact states. To address this limitation, we replace kinematic motion-style feature with selected dynamics features extracted from locomotion trajectories as the target of adversarial regularization. To this end, we use trajectory optimization to construct a reference dataset and train a discriminator to evaluate whether policy-induced temporal windows are consistent with the resulting reference distribution. Without explicit motion tracking, ADP encourages policy rollouts to remain close to the reference support, even after perturbations. Experimental results show that, compared with AMP, the strongest baseline in our evaluation, ADP improves the $80\%$-success impulse threshold ($J_{80}$) by $16.7\%$, while reducing direction-averaged recovery time and velocity tracking error by $47.9\%$ and $35.4\%$, respectively.

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.

Reinforcement learning (RL) for quadruped locomotion commonly depends on fixed, hand-crafted, and Markovian reward functions that limit both interpretability of learned policies and lack explicit control over gait behaviors. We introduce a framework where distinct gaits are specified using parameterized constraints expressed in Signal Temporal Logic (STL). These include safety bounds, gait synchronization constraints, command tracking, and actuation bounds. From these specifications, we develop a reward shaping mechanism that provides learning agents a dense, continuous reward landscape that encodes desired behavior. We define parametric STL templates for three speed regimes (walking-trot, trot, bound), calibrate their parameters from reference rollouts, and compute rewards from using smooth approximations of STL robustness over the rollouts. The generated rewards can be used to provide shaped gradients compatible with Proximal Policy Optimization (PPO). We instantiate the approach on Google's Barkour quadruped robot in MuJoCo XLA (MJX). We use parallelization within the simulator to improve training speeds and use domain randomization to robustify learned policies. We show that compared to a baseline of hand-crafted rewards, the STL-shaped rewards yield tighter velocity tracking and more stable training. Videos can be found on our project website: https://stl-locomotion.github.io/.

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.

As humanoid robots become increasingly dynamic, coupling them with reinforcement learning offers a promising approach to solving the complex, underactuated mechanics of passive inline skating. Equipping a humanoid robot with passive inline skating wheels presents an opportunity to combine the versatile agility of humanoids with the high-speed, energy-efficient locomotion strategies utilized by human skaters. In this paper, we train and deploy a reinforcement learning control policy that enables novel locomotion strategies for a humanoid robot modified to equip consumer inline skates instead of conventional feet. Unlike previous work limited to quadrupedal robots or actively driven wheels, our system allows for precise 6-DoF control of the skates to execute dynamic, edge-driven propulsion strategies. Our skating strategies emerge entirely from our reward structure, without reliance on human motion data, imitation learning, or kinematic priors. We overcome the inherent instability of passive wheels and simulation contact artifacts by utilizing different geometric wheel models (spherical and ellipsoidal) during training and validation, along with a custom success-based command curriculum and a specialized rolling reward. Consequently, our policy demonstrates up to a 50% reduction in Cost of Transport (CoT) compared to standard walking gaits. The resulting policy successfully transfers zero-shot to the physical Booster T1 hardware. Real-world deployments demonstrate dynamic balance, the ability to reject active physical perturbations, and agile locomotion strategies capable of turning at speed. A video of our results can be found at https://www.youtube.com/watch?v=-_APcOS7uFo.

Recent progress in humanoid behavior models has been driven in large part by abundant human motion data, but comparable motion data is scarce for non-humanoid legged robots such as quadrupeds, hexapods, and quadruped manipulators. A promising alternative is to repurpose human motion across embodiments; however, direct retargeting often produces motions that are visually plausible yet physically inconsistent or difficult to track under robot dynamics. We present X-Morph, a human-motion-to-robot-behavior pipeline that converts human motion into deployable locomotion and loco-manipulation policies for diverse non-humanoid legged morphologies. A cross-morphology retargeting stage converts human motions into kinematically plausible, intent-preserving robot references, which are then tracked by a privileged RL policy and distilled into a causal student policy. We evaluate X-Morph on three morphologically distinct platforms: a quadruped, a hexapod, and a quadruped equipped with a manipulator. The resulting policies track diverse retargeted motions, generalize to unseen human motions, and support downstream use cases including video-based teleoperation, behavior-prior control, and text-conditioned motion generation. These results suggest that large-scale human motion can serve as a substrate for learning broad, reusable behavior priors beyond humanoid robots. Project page: https://maker-rat.github.io/morph/

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.

Reinforcement learning (RL) for locomotion frequently converges to locally optimal but undeployable behaviors, such as vibrating limbs or scooting on the torso, that maximize return without producing a usable gait. We present MPC-Injection, a low-overhead method that steers RL toward a designer-preferred gait by inserting transitions into the replay buffer from a model predictive controller solving the same Markov decision process. Unlike reward shaping, MPC-Injection does not require redesigning the task reward, and unlike adversarial imitation learning, it adds no discriminator, no kinematic retargeting, and no auxiliary objective. Instead, the controller's preferred behavior is transferred to the policy purely through the replay state distribution. On a 2D walker in simulation and with sim-to-real evaluation on a Go2 quadruped, we show that MPC-Injection drives the policy into the controller's behavior basin using a one to two-term task reward, producing gaits qualitatively comparable to those of reward shaping with twenty-one tuned terms and of adversarial motion priors without their discriminator and retargeting overhead. We further analyze how the injected transitions bias actor-critic updates toward controller-visited states, allowing the policy to learn behaviors that pure RL may fail to reach under simple reward functions.

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/.

Vision-Language-Action (VLA) models have recently demonstrated strong generalization in robotic manipulation, yet their applicability to whole-body, contact-rich humanoid locomotion remains severely underexplored due to data scarcity, the absence of dynamically consistent demonstrations, and the difficulty of encoding optimality and safety in learning-based pipelines. This work introduces a unified framework WOLF-VLA that integrates whole-body optimal-control (OC) motion synthesis with large-scale multi-modal dataset to train VLAs capable of generating humanoid locomotion policies directly from natural-language instructions. We construct a comprehensive dataset of dynamically feasible humanoid trajectories across six locomotion-related task families, each parameterized by environmental variations, object colors, placements, and visual distractors. We train a VLA model using the collected joint trajectories, ego-centric visual observations and natural language instruction, yielding a policy that exhibits strong reasoning and robustness to initial-condition variability, and competitive performance across several tasks and environment settings. A systematic ablation study demonstrates the impact of each modality on the model performance. The full dataset, model checkpoints, and benchmarking simulation suite will be openly released, establishing a reproducible dynamically consistent benchmark for whole-body humanoid locomotion rich VLA control and enabling future research in scalable transfer of instruction-driven locomotion policies.

Reward design remains a major bottleneck in reinforcement learning for robot locomotion, where successful policies often depend on carefully tuned, task-specific reward functions. Preference-based reinforcement learning offers an alternative, but existing LLM-based methods typically ask for a single overall judgment between behaviors, making it difficult to capture the multiple competing objectives that underlie high-quality locomotion. We present Multi-Objective AI-Informed Preference Learning (MAPL), a framework that learns locomotion rewards from high-level natural language objectives rather than manually engineered reward equations. MAPL prompts a large language model to compare trajectories independently along semantically meaningful criteria, using generic language descriptions that are terrain-invariant and require little domain expertise. These objective-wise preferences are used to train a multi-head preference scoring model, whose outputs are aggregated to form a scalar reward for policy optimization. Across four quadruped locomotion environments, MAPL trains policies using only LLM-generated preferences and achieves performance comparable to or better than expert-designed rewards, while eliminating task-specific reward engineering.

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.

Lunar micro-rovers under 50 kg are a rapidly growing vehicle class, yet open, benchmarked tools for running optimization across design trades remain scarce. Rover sizing is a highly coupled problem with a feedback loop specific to surface vehicles: a heavier rover sinks deeper into loose regolith, deeper sinkage costs more power, more power requires a larger array, and the array adds mass. We present RoverDevKit, a tradespace exploration toolkit with an open evaluator that couples a closed-form wheel-soil model with bottom-up mass, solar-power, thermal-survival, and traverse models. It is fast enough to serve as the fitness function of a multi-objective genetic algorithm (NSGA-II): one search of 3000 mission evaluations takes under a minute on a single laptop core. We use it to map the trades among distance traveled, vehicle mass, and slope capability on mare, polar, highland, and crater-rim missions. Across those missions the limiting factor changes: energy storage at high latitude, slope traction on loose highland regolith, and traverse range on mare and crater-rim terrain. The wheel-soil model matches measured single-wheel drawbar pull on two independent datasets to within the 20-30% error typically reported for this class of model, and the mass model predicts published 5-50 kg rover masses to 10.5% median absolute error. A check against five published in-class designs places them near the designs the optimizer selects. Re-running the search after applying that wheel-soil comparison error leaves these conclusions unchanged.

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.

Perceptive legged locomotion over discontinuous terrain (e.g., stairs, gaps, and obstacles) requires adaptive behavior, as a single conservative gait cannot produce the anticipatory maneuvers needed for abrupt topology changes. Cast as multi-task reinforcement learning, this problem introduces a tension between sharing and separation. Tasks use a common locomotion base but have conflicting rewards, so a policy must share behavior while avoiding value interference. Prior work addresses only one side, with monolithic policies sacrificing specialization and hierarchical sub-policies sacrificing generalization across transitions and unseen terrain. We propose CTS-MoE, which combines a dense mixture-of-experts actor with perception-based gating to compose shared behaviors and a multi-critic with task-specific value heads to prevent interference. The model is trained end-to-end in a single-stage concurrent teacher-student setup that handles partial observability and avoids sequential distillation, with task labels used only during training. At deployment, routing depends solely on perception, allowing terrain adaptation without a high-level selector or terrain classifier. Experiments on a Unitree Go1 in simulation and on hardware across seen and unseen terrains show task-aware specialization, with lower tracking error and higher success rates than monolithic baselines. Project Website: https://cts-moe.github.io/ .

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.

Load transportation with quadruped robots is strongly affected by the dynamics of the physical interface between the robot and the load. Passive spring-based arms reduce weight and complexity compared to active manipulators, but their spring-damper dynamics can introduce oscillatory forces that degrade locomotion stability. This paper derives an extended Zero Moment Point (ZMP) formulation that includes passive payload-interface dynamics, relating stiffness, damping, and payload mass to the stability margin. The analysis shows that underdamped configurations can resonate with locomotion harmonics. Based on this insight, we augment a Single Rigid Body Dynamics model with passive subsystem dynamics and integrate it into a Model Predictive Control framework. In simulation, the proposed controller reduces stability violations by up to $10\times$, from $7.0\%$ to $0.7\%$, and increase locomotion efficiency by lowering horizontal ground reaction force effort by up to $15\%$ compared to a nominal baseline. Hardware experiments with a $2\,\mathrm{kg}$ payload show stable locomotion under pull-release disturbances where the nominal controller fails. The same model also enables end-effector tracking through passive arm dynamics without direct arm actuation.

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.

Humanoids deployed in human-centered environments must handle force-interactive tasks, where external contacts introduce unexpected disturbances that disrupt locomotion accuracy and stability. Existing learning-based approaches rely on broad domain randomization, task-specific force objectives, or learning-based force estimators from motion history, each of which compromises accuracy, task transferability, or out-of-distribution (OOD) robustness. We present Analytical Disturbance-Aware Policy Training (ADAPT), a framework that equips humanoid policies with a physically grounded disturbance observer. The core of ADAPT is an analytical whole-body disturbance observer that estimates residual force/torque online with the accessible robot dynamics, without requiring force/torque sensors. Fed directly into the policy, the estimated disturbances give the humanoid an explicit, physics-derived sense of external force/torque that can generalize across diverse unseen scenes. Experiments on a Unitree G1 humanoid show that ADAPT achieves accurate disturbance prediction and stronger robustness than a proprioception-only baseline under torso perturbations, standing pushes, and asymmetric hand payloads, with improved velocity tracking even on OOD disturbances. Moreover, ADAPT enables penalizing inferred disturbances at lower-body joints to encourage lighter locomotion.

Soft robots leverage compliant materials to generate motion through controlled elastic deformation, making them ideal for delicate tasks such as underwater exploration and biomimetic marine systems. Although hydraulic/pneumatic actuation remains pivotal for such systems, the lack of systematic design frameworks has hindered the development of robots capable of complex 3D motion, such as fish-like swimming. This work introduces a topology optimization method to automate the design of a hydraulic soft fish tail, explicitly addressing the design-dependent coupling between fluidic actuation and structural deformation. We use a Darcy law-based model augmented with a drainage term to simulate spatially varying hydraulic pressure loads, translating these into consistent nodal forces via finite element analysis. The employed robust multi-criteria optimization formulation balances deformation efficiency, fluid-structure interaction, geometric manufacturability, and required stiffness for optimizing a bioinspired soft fish tail for 3D swimming kinematics. The optimized tail topology is incorporated into a pneumatic network actuator and computationally validated under various hydraulic loads, achieving tunable undulatory amplitudes and multiaxis bending for depth adjustment. The optimized 2D tail outperforms its rectangular counterpart. By cascading optimized tail segments, we demonstrate programmable swimming patterns in soft robotic fish tails at different hydraulic loads. This work advances the systematic codesign of hydraulic actuators and soft structures, offering a pathway to automate underwater robots with optimized design and vertebrate-like agility in confined aquatic environments. Our implementations and simulations are publicly available at 'https://github.com/PrabhatIn/TO-SoFiT'.

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/.

Recent reinforcement learning approaches have shown great promise in improving humanoid motion tracking performance and achieving fall recovery under disturbances. However, most existing works treat motion tracking and fall recovery as different tasks and require multi-stage training with specialized recovery rewards and/or separate recovery policies. Moreover, existing reinforcement learning-based methods often terminate training episodes immediately after severe tracking failures, limiting recovery-oriented exploration in unstable or fallen states. To address the above issues, we propose Stubborn, a streamlined and unified reinforcement learning framework to achieve robust humanoid motion tracking and fall recovery. Specifically, Stubborn uses an asymmetric Actor-Critic architecture and consists of three major components. First, a yaw-aligned tracking representation is adopted to reduce sensitivity to global drift and heading disturbances while preserving gravity-related balance information. Second, we introduce a Bernoulli-based probabilistic termination mechanism that enables the policy to encourage exploration of fall-recovery behaviors under varying failure modes. Third, we propose a probabilistic termination and tracking-error-driven strategy that dynamically reshapes the sampling distribution based on tracking performance, increasing the training efficiency for difficult motion segments and unstable states. Extensive comparisons with SOTA methods and ablation studies show that Stubborn achieved competitive performance, and the proposed probabilistic termination mechanism and adaptive sampling strategy contributed to the performance and robustness gains. For real-world demonstrations, please refer to https://aislab-sustech.github.io/Stubborn/.

Multi-objective reinforcement learning for humanoid robots must coordinate locomotion and manipulation within a single policy. A natural design choice is whether to use a single (unified) critic that estimates the combined value of all objectives, or separate (dual) critics with disjoint reward signals. We present a controlled comparison on the Unitree G1 humanoid (23 active DoF) in NVIDIA Isaac Lab, training loco-manipulation policies through a sequential curriculum spanning 13 levels from stationary reaching to walking with variable-orientation targets. In standardized evaluation, dual-critic policies reach targets 3.5$\times$ faster (6.5 vs. 22.6 simulation steps), achieve 2$\times$ higher throughput (14.3 vs. 7.0 validated reaches per 1,000 steps), and attain higher validated reach rates (65.2% vs. 53.8%) compared to the unified-critic policy. Notably, additional anti-gaming reward mechanisms provide no further improvement beyond the architectural change alone (60.9% vs. 65.2%). These results have direct implications for the emerging paradigm of RL fine-tuning of imitation-learned policies: when refining a pre-trained manipulation policy with RL, a unified critic risks suppressing the learned behavior through competing locomotion gradients. These findings demonstrate that critic architecture is a primary - and often overlooked - design choice in multi-objective humanoid RL, with greater impact than reward engineering on reaching efficiency.

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.

Perceptive bipedal locomotion over sparse terrain remains a difficult challenge: model-based methods are precise but brittle to uncertainty, while model-free methods are robust but struggle to discover the precise, constrained motions required for safety-critical locomotion where small errors can cause catastrophic failures. We propose a model-assisted reinforcement learning (RL) framework that combines both perspectives in three steps: (1) generate a safe reference trajectory using simplified models; (2) train a privileged teacher policy guided by a control Lyapunov function (CLF) reward built around the safe reference trajectory; and (3) distill the teacher into a vision-based student policy. We show that this model-assistance procedure produces physically grounded locomotion, improving sample efficiency, reducing the need for a complex learning curriculum, and achieving smoother locomotion behavior alongside stepping stone performance comparable to model-free baselines. We validate our approach in simulation and demonstrate successful deployment on a Unitree G1 humanoid robot navigating sparse footholds with lateral constraints.

Deploying legged robots in extra-terrestrial environments includes many challenges due to complex terrain interactions, energy, and thermal constraints. For effective mechanical design of a lunar exploration quadrupedal robot, careful consideration of motor torques, energy expenditure, and cost of transport is required. The lunar surface is composed of granular regolith, which impacts the locomotion of legged robots and their performance. Locomotion algorithms trained with rigid contact assumptions are also ineffective when applied to environments with soft contacts, such as granular surfaces, which can result in instability and poor tracking. In this report, the physical modelling of the granular lunar surface-robot foot contacts is applied to a simulation environment with locomotion trained using Reinforcement Learning. A comparison is conducted between the policy trained on rigid contact and soft contact environments, analysing the gait and locomotion performance metrics. The analysis demonstrates that soft contacts simulating regolith surfaces pose additional challenges for Reinforcement Learning based training, result in a qualitatively different gait, and increase the overall energy expenditure.

Falling is an inherent risk for humanoid robots operating in unstructured environments. Existing reinforcement learning methods that leverage expert motion priors are predominantly trained on flat-ground fall-recovery tasks and typically rely on hard switching between separate recovery and locomotion controllers. As a result, such policies struggle to achieve smooth and robust recovery behaviors when deployed on complex terrains such as slopes and gravel. This paper presents \textbf{CG-MuTra}, a unified continuously-gated multi-scale discriminator framework for multi-terrain adaptive fall recovery. CG-MuTra introduces a proprioceptively-derived continuous gate $α= f(z_{\mathrm{root}}, s)$ that softly blends three discriminators operating at different temporal horizons: frame-level stability ($Φ_{\mathrm{frame}}$, $H=1$), temporal smoothness ($Φ_{\mathrm{seq}}$, $H=5$), and gait periodicity ($Φ_{\mathrm{gait}}$, $H=10$). This design enables seamless recovery-to-locomotion transitions without explicit mode switching. Furthermore, we propose a Terrain-Pose Risk Coupling Sampler (TPRCS) that explicitly couples dangerous edge initial poses with terrain dynamics during training, forming a closed-loop synergy with the terrain-privileged shaping term $Ξ_κ$. We validate CG-MuTra on a Unitree G1 humanoid across grass, slopes ($10^\circ$--$15^\circ$), and gravel in both simulation and hardware. Experimental results demonstrate that CG-MuTra achieves smooth, highly robust fall recovery and locomotion transitions across multiple terrains while maintaining a single deployable policy.

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/.

Foothold selection on structured terrain requires explicit reasoning about contact planarity, surface steepness, and kinematic reachability, properties not captured by a single height-based terrain signal. We propose a multi-channel terrain cost combining flatness, steepness, and velocity-aware height feasibility, plus a forward climb reward, that simultaneously drives a GPU-parallel divergent component of motion (DCM) foothold planner and shapes a dense per-step affordance reward for an asymmetric actor-critic policy trained with proximal policy optimization (PPO) from depth images. A Bézier swing trajectory with adaptive apex bias extends foothold tracking to joint position-and-orientation, using the arc tangent to guide sole orientation through riser crossings and tread landings. To support payload tasks, we introduce a lower-body compliance training procedure in which a virtual wrench is injected at a sampled load attachment point, generating physically consistent force and moment; wrench-aware compliance targets replace rigid pose penalties, and the policy learns to yield to load-induced perturbations without force sensing. The full system trains end-to-end with standard PPO, no distillation, and no teacher-student staging, and is deployed on a humanoid directly from simulation with configuration changes only. In simulation, the policy reaches $1.0~\mathrm{m/s}$ on stairs with risers up to $0.20~\mathrm{m}$ and improves payload robustness up to ${\sim}15~\mathrm{kg}$ centered load and for moment-dominated wrist loads without fine-tuning. We also provide a qualitative hardware demonstration on structured terrain. Project website: https://fai-rl-tech.github.io/tact-locomotion.github.io/

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.

Reinforcement learning (RL) policies enable dynamic legged locomotion but lack mechanisms to avoid violations of safety constraints that are absent during training. Large-scale offline safe learning is impractical for covering all edge cases. Existing safety frameworks either rely on reduced-order models that cannot reason about whole-body behaviors or require conservative recovery controllers that degrade task performance. We propose a predictive safety filter that post-hoc filters the nominal contact locations fed to the RL policy. When a collision is predicted, a sampling-based optimizer asynchronously searches for safer contact sequences using a full-physics model, while a learned value function bootstraps long-horizon returns. Our three algorithmic components (geometric projection of sampled contacts, momentum-augmented updates, and replica-exchange) make the optimization tractable in a discontinuous contact landscape. We validate the filter on a quadruped robot in dense, cluttered environments, both in simulation and in the real world, showing substantial reductions in safety violations with minimal deviation from the nominal input.

Achieving both anthropomorphic naturalness and robust terrain traversal remains a fundamental challenge in humanoid locomotion. Existing Reinforcement Learning (RL) approaches typically rely on fixed motion priors, limiting their adaptability to varying environments. We propose Terrain-conditioned Generative Motion Priors (T-GMP), a module that captures a terrain-conditioned latent motion manifold from a few expert state-terrain demonstrations using a Conditional Variational Autoencoder (CVAE). The learned priors enable smooth style transitions, facilitating a unified policy that adapts to terrain variations. We integrate T-GMP into an adversarial learning pipeline with our proposed Foothold Penalty, where a discriminator dynamically modulates naturalness constraints conditioned on local terrain features, guiding the generation of versatile and human-like motions. Experimental results demonstrate that our method outperforms existing baselines in traversal success rate and motion smoothness, while preserving biomimetically natural and physically coordinated motions.

This paper presents ERNEST, a four-wheeled planetary rover concept equipped with a two-degree-of-freedom Active Gimbal Suspension that combines yaw and roll actuation to enable wheel reconfiguration, steering, and active load redistribution. A single neural network controller, trained to track a desired path across challenging terrain, fully unlocks the capabilities of this actuated suspension system for autonomous obstacle negotiation. A reinforcement learning framework is developed using the high-fidelity DARTS simulation engine, which combines rigid-contact dynamics and Bekker-Wong terramechanics, enabling the emergence of locomotion strategies adapted to loose-soil conditions. To obtain a single unified controller across heterogeneous terrains, a policy consolidation strategy merges the experience of terrain-specialized agents into one neural network, eliminating the need for explicit terrain classification and controller switching. The resulting controller operates on a combination of proprioceptive and exteroceptive feedback, including sparse stereo-derived terrain elevation, chassis attitude, joint states, and force-torque measurements. Zero-shot transfer to the physical rover is achieved through domain randomization, sensor noise injection, and model-to-real system identification. Experimental results demonstrate autonomous traversal of rock fields, a Bickler trap (bump obstacle), a wheel-high step, sand ripples, and sandy slopes. On a 20° sandy slope, the learned controller reduces the cost of transport by 37% on dry sand despite the additional actuation, and achieves superior performance on wet sand where the passive suspension becomes completely immobilized. A video accompanying this paper is available at https://youtu.be/d684P5a3xMc

In humanoid motion control, model predictive control (MPC) offers physically grounded prediction and constraint handling, while reinforcement learning (RL) enables robust whole-body skills through large-scale simulation. However, using MPC inside RL often requires time-consuming problem construction or excessive training overhead, making such frameworks difficult to justify in practice. This work studies efficient training-time MPC guidance for humanoid locomotion and manipulation, termed MPC-RL. We introduce a centroidal-dynamics MPC reward formulation that leverages guidance from MPC trajectories in training time. To make this practical in massively parallel RL, we develop $π^n$MPC, a parallel-in-horizon and construction-free batched GPU MPC solver that operates directly on time-varying dynamics to avoid high memory usage and pre-compilation. Through a variety of comparative studies and hardware validations, we have found that MPC-RL achieves superior performance in locomotion and manipulation skills. The code base is available at https://github.com/junhengl/mpc-rl.

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.

Humans primarily rely on walking and running to traverse complex terrains. Similarly, humanoid robots should be able to smoothly transition between walking and running while maintaining natural and stable locomotion. However, unifying gait transition and multi-terrain adaptation within a single policy remains challenging due to gradient interference between tasks and the distribution shift caused by terrain variations. Although Mixture-of-Experts (MoE) architectures can mitigate multi-skill interference, direct joint training often fails to achieve clear expert specialization. To address these challenges, we propose CoRe-MoE, a two-stage reinforcement learning framework that decouples gait generation from terrain adaptation. In the first stage, a stable locomotion policy is learned to produce natural walking and running behaviors with smooth transitions. In the second stage, a terrain-aware MoE branch is introduced, and the gating network is trained with a contrastive objective to learn structured terrain representations and promote expert specialization. The final action is obtained through weighted fusion of the base gait policy and the terrain-aware branch, enabling the policy to preserve stable locomotion while adapting to complex terrains. Extensive simulation results demonstrate that the proposed method outperforms baseline approaches in terms of success rate, locomotion stability, and multi-terrain adaptability. Furthermore, zero-shot deployment on a Unitree G1 humanoid robot validates the effectiveness of our framework, achieving robust walking and running across stairs, slopes, steps, obstacles, and unstructured outdoor terrains while maintaining accurate foothold control and dynamic stability.

We study the problem of scaling dynamic loco-manipulation from a single free-rolling sphere to multiple spheres transported simultaneously on the back of a wheel-legged quadruped, without fences, grippers, or mechanical stops. Multiple identical free-rolling spheres form an unordered set with no persistent identity: their ordering may change independently at each history frame, creating a \emph{per-frame permutation symmetry} that standard history-concatenation set encoders do not explicitly enforce -- these encoders impose only a shared, diagonal permutation symmetry over the full history. We show that this symmetry mismatch leads to a concrete failure mode in curriculum-based reinforcement learning. Within the same PPO training budget, flat MLPs and branch-wise encoders plateau at or below the two-sphere stage, while a history-concatenation Deep Sets baseline (\HCDS) fails to progress past the two-sphere stage in our runs unless ball-to-slot assignments are randomised during training, suggesting that it exploits slot indices as a curriculum shortcut rather than learning identity-free multi-sphere dynamics. We propose \textbf{Per-Frame Deep Sets (\PFDS)}, which performs permutation-invariant pooling within each history frame before temporal readout; we prove that \PFDS is $\Gframe$-invariant and universally approximates continuous $\Gframe$-invariant policies. A $2{\times}2$ ablation over encoder architecture and slot randomisation separates the architectural and data-augmentation pathways, and \PFDS reaches the five-sphere stage with 100% no-drop transport in simulation across all five random seeds. We further distill the \PFDS teacher into \TactSet via DAgger, replacing privileged sphere-state observations with a $16{\times}16$ Boolean union contact map, yielding a compact and naturally $\Gframe$-invariant tactile representation.

Although reinforcement learning has significantly advanced humanoid locomotion, perceptive policies still struggle on sparse-foothold terrain and constrained environments. Success in these scenarios requires both broad terrain awareness and precise foothold selection, two perceptual roles that conventional encoders often entangle. To address this challenge, we propose Global-Local Attention Decomposition (GLAD) for terrain encoding in humanoid locomotion. Realized by a coarse-to-fine encoder over a robot-centric elevation map, GLAD explicitly separates these objectives: a global attention branch utilizes attention pooling to summarize the surrounding terrain context, while a state-conditioned local attention branch sparsifies and encodes precise foothold-relevant geometry. This explicit attention decomposition prevents the dilution of fine-grained spatial cues while reducing training overhead. Experiments demonstrate that GLAD enables reliable locomotion over challenging gaps, stepping stones, and stairs. Furthermore, the learned policy exhibits emergent terrain-responsive behaviors, autonomously following narrow paths and avoiding obstacles under simple velocity commands without explicit navigation planners. In real-world deployment on a Unitree G1 humanoid robot using onboard LiDAR, the proposed method achieves robust zero-shot sim-to-real transfer across diverse sparse-foothold and obstacle-rich domains.

To enable reliable climbing locomotion of quadruped robots on ferromagnetic surfaces, this paper presents a high-load-density electro-permanent magnetic foot with controllable adhesion, featuring force-feedback circular Halbach-net electro-permanent magnet (CHN-EPM) adhesion units and a magnetization control system. Due to its three-dimensional magnetic circuit structure and flux-concentration effect, the CHN-EPM enables a distributed parallel magnetic flux path with enhanced flux utilization, resulting in reduced sensitivity to air-gap variations and allowing effective adhesion to be maintained even under partial contact conditions. The proposed CHN-EPM generates a maximum adhesion force exceeding 1000 N with a load-to-weight ratio over 200:1. A magnetization driver and a two-stage pulse current control strategy are developed to regulate the excitation current amplitude and duration, enabling accurate and reliable magnetization. By incorporating a flexible pressure sensor for contact force feedback, the system can effectively monitor attachment and detachment states, ensuring robust adhesion switching under uncertain contact conditions. The proposed system is integrated into a commercial quadruped robot (Unitree GO2), demonstrating high-load adhesion on ceiling and vertical-wall surfaces and stable locomotion on painted, perforated, and curved ferromagnetic surfaces.

Extending humanoid traversal to the open world is key to practical deployment in human environments, but remains challenging. The robot must use vision to ensure safe and reliable foot placement on heterogeneous terrain under highly dynamic motion, while producing coordinated, natural whole-body behaviors. We propose SSR, an efficient end-to-end framework for egocentric vision-based humanoid traversal that jointly learns these capabilities. SSR introduces imagined foothold guidance, which learns to model forthcoming swing-foot contacts and evaluates their support to guide pre-touchdown swings toward stable regions, reducing edge slips. It further employs equivariant latent-space symmetry augmentation to efficiently induce bilateral coordination under high-dimensional visual observations, and uses terrain-specific multi-discriminator motion priors to encourage human-like behavior across scenes. Extensive experiments show that SSR achieves safe, stable, and high-quality locomotion on diverse real-world terrains, including stairs with varied structures and extreme challenges such as wide gaps and high platforms, while enabling reliable long-horizon traversal in open outdoor environments.

Symmetry is a central organizing principle in natural systems, yet its use as a unifying design strategy in robotics has largely remained limited to geometric form. We show that symmetry can instead be leveraged at the level of dynamic actuation capability. We introduce dynamic symmetry, the uniformity of a robot's attainable center-of-mass accelerations, and formalize it through a measure coined as dynamic isotropy. Across more than 1000 simulated morphologies, we found that higher dynamic symmetry consistently improved trajectory tracking, task success, robustness, resiliency, and energy efficiency, with the benefits becoming most pronounced as dynamic isotropy approached its theoretical limit. To study this regime systematically, we developed Argus, a family of spherical robots designed to explore the effects of increasing dynamic symmetry. Members of the Argus family vary in their actuation geometry and dynamic symmetry level while sharing a common architectural principle: radially oriented linear actuators that directly shape the robot's center-of-mass dynamics. Among them, we built a physical 20-leg Argus variant that achieved near-extreme dynamic isotropy and demonstrated orientation-invariant locomotion, agile traversal of cluttered and deformable terrain, rapid self-stabilization, and resilience to partial actuator failures. Its distributed sensing further enabled omnidirectional perception and object interaction during continuous motion. These results show that designing robots for symmetry not only in morphology but also in their attainable dynamics provides a powerful and general pathway toward agility, robustness, and multifunctionality in uncertain terrestrial and extraterrestrial environments.