RL for Legged Locomotion

Learning-based approaches to locomotion have risen in popularity in recent years, showing the capability for complex legged locomotion and whole-body control. Reinforcement learning (RL), the primary learning-based approach for locomotion, often utilizes a high-performance simulation tool, providing a controlled and efficient training and development environment. However, policies that perform well in simulation frequently encounter unexpected challenges when deployed on a physical system, known as the sim-to-real gap. This work presents a robust RL locomotion framework capable of whole-body control. The proposed RL framework utilizes Nvidia's new set of simulation tools, Isaac Sim, and its companion RL framework, Isaac Lab, for training, achieving a zero-shot sim-to-real policy. The performance of our policy is validated on physical hardware using the Unitree Go1, with experimental results showing similar velocity tracking performance to the quadruped's integrated controller, with a greater ability to recover from large disturbances, and achieve linear velocities of 2.0 m/s and angular velocities of 1.8 rad/s.

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.

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.

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

Humanoid roller-skating is difficult because the robot must coordinate whole-body balance, rolling contacts, and velocity-dependent posture regulation. This paper presents an adversarial motion prior based reinforcement learning framework for two humanoid roller-skating gaits: Pump Glide skating and Push Glide skating. The two gait datasets are collected independently through motion capture and retargeted to the humanoid robot separately. The retargeted data are then smoothed and resampled into reference motion states for AMP training. The two gaits are learned by independent AMP training pipelines with separate reference datasets, separate policies, and independent reward architectures. Simulation experiments are designed to evaluate gait quality, velocity tracking, turning, and gait-specific reward ablations.

Model-free reinforcement learning has enabled impressive humanoid locomotion; however, control on steep slopes remains largely unexplored. Unlike flat or discrete terrains, sloped terrains impose a persistent gravitational bias that demands simultaneous stability and posture control. Consequently, under generic reward formulations, policies can converge to slow, conservative low-center-of-mass (CoM) crouched gaits. In this work, we propose a novel two-stage physics-guided framework, dubbed HumoSlope, dedicated to robust humanoid locomotion on diverse sloped terrains. Specifically, Stage I establishes a terrain-consistent balance prior by introducing a slope-adaptive Zero Moment Point (ZMP) regularizer evaluated directly on the local inclined support plane rather than a world-horizontal reference. To prevent the resulting policy from defaulting to a crouched posture, Stage II introduces the Biomechanical Slope Gait Adapter (BSGA). Utilizing extracted macroscopic terrain descriptors as privileged, training-only signals, BSGA dynamically gates soft reward priors to modulate CoM height and lower-limb coordination based on the estimated slope geometry -- encouraging hip-dominant uphill propulsion and knee-oriented downhill braking. Crucially, the deployed actor remains entirely proprioceptive, requiring no online exteroceptive sensing. Extensive Sim-to-Real experiments demonstrate that our framework effectively mitigates posture degeneration and enables blind, continuous traversal of outdoor grass slopes up to 62.7% ($32.1^\circ$), validating a physics-guided approach to challenging slope terrain adaptation.

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.

Scalable reinforcement learning has popularized high-throughput sampling architectures, which significantly compresses the training time for off-policy methods in robotic locomotion. However, the rapid increase of data volume and update frequency undermines the stability of value-based methods and diminishes the plasticity of policy networks. To address these challenges, this work presents FastDSAC, a fast and high-performance variant of the Distributional Actor-Critic algorithm designed for parallel sampling scenarios. Specifically, we introduce a truncated Gaussian distribution to approximate the learned policy, which effectively excludes out-of-distribution actions that strain target value estimation while keeping necessary stochasticity for exploration. The proposed action constraint functions as an implicit regularization, which counteracts the plasticity loss typically caused by aggressive gradient updates. This preservation of network adaptability enhances sample efficiency, particularly in scenarios with a high update-to-data ratio, and accelerates the early training process. In contrast to prior fast reinforcement learning approaches that rely on discrete value distributions, our method utilizes a continuous Gaussian representation equipped with adaptive variance regulation, which improves value estimation accuracy by sampling confident and informative transitions. Extensive experiments on MuJoCo Playground and HumanoidBench demonstrate that FastDSAC not only stabilizes the overall training process but also achieves superior asymptotic performance and faster convergence compared to state-of-the-art baselines.

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/

Humanoid robot motion learning requires not only task-oriented control policies but also physically feasible and natural behaviors that can be transferred to real robots. However, robot-feasible motion data are often scarce: raw human demonstrations may be incompatible with the robot morphology, open-source clips vary in quality, and simulation-collected robot trajectories still require feasibility checking. To address these challenges, we propose a data-centric training and deployment pipeline that integrates motion data curation, real-to-sim model adaptation, AMP-based reinforcement learning, and sim-to-real deployment. We validate the framework on the Booster T1 robot and further provide preliminary cross-platform validation on Booster K1.

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 behavior by inserting transitions generated in the same environment by a model predictive controller (MPC). 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. We analyze how the injected transitions bias the learning, allowing the policy to converge to behaviors that pure RL may fail to reach under simple reward functions. On a 2D walker in simulation and with sim-to-real evaluation on a Go2 quadruped, we show that MPC-Injection produces gaits qualitatively comparable to those of reward shaping and adversarial motion priors. We also show that MPC-Injection can complete a barrel roll that pure RL fails to achieve under the same simple reward and can select between trotting and bounding gaits only through changing the injected MPC data.

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/.

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-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.

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/ .

Robotic jumping is pivotal in applications such as search and rescue and logistics, where crossing obstacles and enhancing mobility efficiency are critical. The Spring-Loaded Inverted Pendulum (SLIP) model leverages simplified spring-mass dynamics that naturally encode biologically plausible hopping motions, yet its performance degrades on irregular terrain due to idealized assumptions regarding contact and joint dynamics. Meanwhile, Reinforcement Learning (RL) can adapt to diverse and complex environments but often requires extensive data from unguided exploration. The complementary strengths of SLIP's physically grounded baseline and RL's adaptive capabilities motivate a hybrid framework that overcomes these individual limitations. We therefore propose Spring-loaded Reinforcement Learning (SRL), which integrates SLIP-based feedforward control signals with RL-driven real-time feedback, enabling continuous optimization of robotic jumping. Experimental results demonstrate that SRL can achieve more stable jumps with much less training time than the baseline method, maintaining an average position tracking error below 0.1 m and velocity tracking errors within +/-3% of the target values. Through bipedal and quadrupedal simulations of ground and stair jumping, as well as sim-to-sim and sim-to-real validations, SRL exhibits robust adaptability to various task requirements and environmental complexities, underscoring its potential for real-world deployment.

Learning-based quadrupedal locomotion typically relies on complex reward formulations that entangle task specification, operational limits, gait preference, and terrain adaptation within a single optimization objective. We instead treat these functions through distinct mechanisms: rewards for task specification, constraints for operational limits, energy minimization for gait preference, and exteroceptive perception for adapting energy use to terrain difficulty. We show that these components jointly enable efficient, terrain-adaptive locomotion, and that removing each component exposes a distinct failure mode. Our formulation removes explicit gait priors (including air-time, contact-count, and foot-clearance targets) in favor of emergent behavior. Compared to a conventional complex-reward baseline, our formulation achieves comparable terrain traversal while reducing cost of transport by 56% and operational-limit violations by 96%. The resulting policies transfer zero-shot to a physical Unitree Go2 using LiDAR-based elevation mapping. Project website with videos: https://tinyurl.com/locomposition.

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/

End-to-end reinforcement learning (RL) has shown strong potential for legged robot navigation, yet existing approaches commonly rely on continuously updated robot-to-goal states from external state estimation modules, leaving part of the navigation problem outside the learned policy. In this work, we seek to push the limits of end-to-end sim-to-real RL navigation by investigating whether a legged robot can internally maintain the spatial context required for long-horizon navigation. To this end, we study goal-initialized navigation, where the goal is provided only once at the beginning of an episode, with no subsequent external relative-goal updates. We present GUIDE, an end-to-end RL framework that jointly learns navigation and internal directional awareness from onboard observations. GUIDE leverages multi-frequency proprioceptive history to capture egomotion and auxiliary spatial-anchor prediction to maintain task-relevant spatial states, while temporal depth observations provide local environmental geometry. The navigation policy is trained entirely in simulation and transferred zero-shot to the real world. Across cluttered environments and structured mazes, GUIDE reliably avoids obstacles, escapes dead ends, and reaches distant goals using only onboard sensing. These results demonstrate that robust sim-to-real legged navigation can be achieved without continuously providing external robot-to-goal estimation, opening a promising direction for future research on more self-contained end-to-end navigation.

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.

Enabling humanoid robots to operate in complex, dynamic environments remains a critical challenge, fundamentally limited by the ability to navigate robustly, safely, and accurately. While reinforcement learning with velocity-commanded policies has achieved remarkable robustness in humanoid locomotion, this approach lacks explicit control of the foothold placement, leading to unsafe behavior, such as stepping onto human feet, or imprecise navigation, hindering the following manipulation task. Conversely, explicit foothold-tracking policies offer a promising alternative by directly being commanded with target foot poses. However, existing approaches are often limited by unrealistic state assumptions, compromising real-world deployment, or they are part of staged pipelines, making them tied to specific downstream tasks. In this work, we introduce a novel, lightweight framework for training general-purpose 3D foothold-tracking policies. By dynamically providing footstep support through a goal sampler, this method enables the learned policy to be agnostic to specific terrains. Our new target representation effectively mitigates challenges arising in the real world, such as noisy and inaccurate pose estimation and foot contact estimation. Designed for direct real-world transfer, our policy acts as a standalone low-level controller that can be seamlessly paired with various high-level foothold generators. We demonstrate the effectiveness of our framework through extensive experiments in simulation and in the real world. By coupling our policy with different upstream planners, we achieve natural and accurate locomotion in challenging settings, paving the way for loco-manipulation tasks in complex environments.

Designing high-performance legged robots requires jointly optimizing morphology and control. Model-free Reinforcement Learning (RL) offers an alternative to model-predictive control for developing robust controllers without explicitly specifying robot dynamics. Thus, we have seen theuse of RL to train controllers and evaluate designs for robot morphology optimization. While RL has shown success inlocomotion, using it in the co-design inner loop is expensive due to repeated policy training. Universal policies conditioned on morphology offer a promising alternative, but suffer from behavioral diversity collapse, converging to a single strategy that performs sub-optimally across designs. On the other hand, end-to-end Mixture-of-Experts (MoE) architectures fail due to a collapse in its representation. We propose Gaussian Evolutionary Specialists (GES), a framework that decouples design-space partitioning from policy learning to capture diverse behaviors explicitly. GES assigns specialist policies to evolving Gaussian regions and iteratively refines them via training, probing, and territory expansion. The resulting specialists are integrated into a design sampling loop, replacing costly re-training with direct evaluation. When tested on the Buoyancy-Assisted Light Legged Unit (BALLU), GES discovers designs with 5 - 25% higher performance than naive universal policies. On hardware, a GES optimized design overcomes a 24 cm tall obstacle - 3x improvement over the baseline BALLU design. Moreover, GES curtails design optimization time by 37%.

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.

Reinforcement learning has become the prevailing approach to humanoid locomotion control: policies transfer reliably from simulation to hardware and recover gracefully from disturbances. Motion quality, however, still lags behind: task-only rewards often converge to stiff, asymmetric gaits, while motion imitation methods improve appearance but become more sensitive to external disturbances because reference signals can oppose the transient poses needed to regain balance. We propose Predictive Style Matching, in which an offline predictor maps the robot's lower-body state history and velocity commands to interpretable upper-body joint and gait targets that shape the rewards during training. Because the targets are state-conditioned rather than time-indexed and the predictor is used only at training time, the deployed controller inherits the proprioceptive interface and inference cost of a task-only RL baseline. On the Unitree G1, in both simulation and hardware, PSM reduces upper-body style error by roughly an order of magnitude over task-only RL while preserving its fall-recovery rate, whereas the motion-imitation baseline attains the lowest style error but fails to recover from disturbances about five times as often.