Robot Locomotion

Rolling motion planning is challenging because rolling contact imposes nonholonomic constraints and the configuration evolves on a curved manifold. The problem becomes substantially harder in multi-contact settings, where multiple bodies roll without slip and the contact states are coupled. This paper presents a new framework for multi-contact path planning in spherical rolling robotics under no-slip constraints. We first derive a compact kinematic model for multi-sphere rolling using Montana's contact-coordinate formulation, where each contact is represented by a stacked five-state vector. Building on this model, we construct a Voronoi-based roadmap directly on the spherical contact manifold, incorporating spherical-cap obstacles and mutual-exclusion regions via on-manifold collision checking, and refine discrete graph paths using manifold-consistent log-exp smoothing. The resulting smoothed surface paths are then lifted to admissible multi-contact rolling motions through the derived Montana kinematics and validated via forward simulation. We further evaluate feasibility and path quality versus trajectory smoothness, Voronoi seed density, and computation time. The proposed framework provides a foundation for extending the method to non-spherical geometries, time-varying obstacle environments, and experimental validation on physical rolling robotic platforms.

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.

A companion study introduced joint durability into the dimensional design of the Theo Jansen walking linkage and found its classical "holy numbers" Pareto-dominated, but it modelled the revolute joints as ideal, clearance-free pins, so its wear figures were relative rankings, not a prediction of in-service degradation. Here we relax that idealization. We build a forward-dynamic model of the Jansen leg in which a revolute joint becomes a clearance joint with a continuous normal contact law (Lankarani-Flores, hysteresis-damped) and Ambrosio friction, integrated as a constraint-stabilized differential-algebraic system, and couple it to the Archard law in a wear->clearance->impact feedback loop. Three findings emerge. First, neglecting clearance underestimates the peak joint load: the clearance model gives a peak contact force of ~104 N at the load-bearing pin against ~48 N for the ideal joint (~2x amplification), rising to ~426 N when two joints carry clearance at once. Second, the coupling is strongly impact-sensitive--single trajectories are non-monotonic and can reverse the design ranking, a chaos consistent with the literature--so designs must be compared statistically; over an ensemble of 16 randomized phases the optimized joint is robustly more durable, with per-cycle wear ~9-7x lower (peak force ~4x lower) at one clearance joint and still ~1.7x lower on both with two (p<0.01 throughout). Third, the wear is strongly non-uniform--it concentrates on a ~10 deg load arc--so assuming uniform clearance growth underestimates local clearance growth by ~36x. The clearance-free durability advantage thus survives the chaotic, multi-joint, non-uniformly-worn coupling in the ensemble mean. We deliver the first clearance-coupled forward-dynamic model of the Jansen leg and specify a falsifiable protocol to test each prediction.

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.

This paper presents "PenduMorph", a wireless reconfigurable rolling spherical robot designed as a modular platform for enclosed locomotion and inter-module interaction in challenging environments. The proposed robot extends our previous pendulum-actuated rolling disk concept to a fully enclosed spherical architecture integrating a 2-DoF internal pendulum, onboard control, battery-powered operation, and magnetic docking. The design aims to combine independent rolling mobility with protected hardware and reliable reconfigurability. We first present the robot design and an analytical study of the magnetic coupling mechanism to evaluate retention and interaction between coupled modules. We then experimentally investigate key motion behaviors at both the single-module and dual-module levels, including independent rolling, magnetic coupling, and coordinated coupled motion. The results show that the proposed platform enables stable wireless operation and a set of distinctive reconfigurable rolling behaviors, providing a useful foundation for future modular spherical robots operating in contact-rich and demanding environments.

Compliant mechanisms are important in robotics because they can improve adaptability, safety, and energy efficiency while reducing hardware complexity. This paper presents SPiralRoll, a novel torsion-spring-based underactuated compliant mechanism for rolling robots and compliant robotic actuation. The mechanism uses arc-distributed elastic members and two motor inputs to realize three physically observable output motions: rotational motion, radial expansion/contraction, and axial spin induced by nonlinear compliant deformation. Two configurations, namely full-arc and single-arc designs, are developed and experimentally evaluated. Beyond benchtop validation, the mechanism is integrated into a spherical rolling robot, where proof-of-concept experiments demonstrate forward rolling and turning. The results show that the full-arc design provides better structural support and smoother deformation, whereas the single-arc design yields larger deformation and stronger inertial excitation, making it more suitable for pendulum-driven rolling locomotion. Overall, SPiralRoll provides a low-cost, compact, and fully 3D-printable solution for underactuated compliant rolling robots and adaptive robotic joints.

This paper presents a full nonlinear constrained dynamic model of MonoRollBot, a novel 3-DoF spherical rolling robot driven by a single motor, a lead-screw transmission, and a spring-coupled internal moving mass, together with motion analysis of its behavior. To the best of our knowledge, this is one of the first full nonlinear nonholonomic models reported for a mono-actuated, super-underactuated spherical rolling robot of this kind. Because rolling without slipping is nonholonomic, the dynamics are derived using the Lagrange--d'Alembert formulation, with the lead-screw relation imposed as a holonomic constraint and the rolling condition imposed in Pfaffian form. The formulation retains the complete generalized coordinates of shell translation, shell attitude, screw travel, nut rotation, and radial mass motion. Simulations and representative motion studies show qualitative agreement with prototype behavior and reveal how gravity, compliance, and inertia jointly shape the locomotion and motion capabilities of this strongly underactuated robot. The resulting model also provides a mechanically consistent basis for future state estimation and hybrid controller design for this nonholonomic mono-actuated rolling robot.

The Jansen linkage is a single-degree-of-freedom planar leg mechanism whose eleven "holy numbers" were evolved by Theo Jansen to optimize the foot-path gait alone, with no regard for the wear of its revolute joints. This paper introduces a durability objective into the design of the Jansen leg. A parametric forward-kinematic model (two-circle-intersection solver), an inverse-dynamic model (constraint-Jacobian / Lagrange-multiplier formulation of a seven-body, ten-joint system, independently cross-verified by a reduced-DOF energy method), and an Archard wear model are coupled to evaluate, for any set of link lengths, both gait quality and the per-cycle sliding wear at every pin. Because the wear is computed on ideal, clearance-free revolute joints, the resulting wear figures are a relative comparative ranking rather than an absolute life prediction. A bi-objective problem -- composite gait error versus total joint wear, subject to step-length, ground-clearance, duty-factor and assembly constraints -- is solved with NSGA-II. Under the adopted gait metric the classical Jansen design is Pareto-dominated: for a representative design, link-length adjustments within +/-29% simultaneously flatten the stance (-28%), smooth the stance velocity (-58%) and reduce total joint wear by ~56%. A sensitivity study shows the wear advantage is robust across a crank-speed x payload envelope (48%-56%) and identifies the link lengths that most strongly govern wear. A variance-based global (Sobol) analysis confirms that two link lengths dominate the wear variance, and a Monte-Carlo manufacturing-tolerance study shows the wear advantage degrades gracefully under realistic fabrication error. The framework provides a practical route to longer-lived walking linkages and a baseline for future wear-clearance-impact coupled studies.

This paper proposes an energy-recycling rimless wheel with spring-clutch legs. The proposed mechanism uses a lockable clutch to store part of the impact-induced elastic energy after foot contact and reinject it in the next gait cycle. First, we develop a hybrid dynamic model of the energy-recycling rimless wheel. Second, numerical simulations are used to examine the dynamics, local stability of periodic gaits, and the Cost of Transport (CoT) of the proposed mechanism. The simulation results show that the proposed mechanism reduces the CoT by up to 16.13% compared with a benchmark viscoelastic-legged rimless wheel with telescopic spring-damper legs. Compared with the rigid rimless wheel, the viscoelastic-legged and energy-recycling models reduce the CoT by more than 50%. The energy-recycling model also maintains locally stable periodic gaits over the tested slope and stiffness ranges. Finally, prototype experiments on an inclined plane are conducted to examine the feasibility of the proposed mechanism. The experimental results show that the proposed rimless wheel achieves passive walking on a shallow 1° slope, corresponding to a CoT of approximately 0.02. These results suggest that the proposed spring-clutch mechanism can improve the simulated walking efficiency of the energy-recycling rimless wheel, while the prototype experiments support the feasibility of passive walking with the mechanism.

Magnetically programmable soft elastomers enable complex shape morphing and locomotion dynamics in small scale soft robots under external magnetic fields. Benefiting from their programmed deformation and wireless actuation capabilities, magnetic soft robots have emerged as promising platforms for targeted drug delivery, especially in human gastrointestinal tract. However, achieving controlled directional liquid cargo release toward desired tissue interface while preserving the encoded shape morphing and locomotion capabilities remain a significant challenge. Here, we report a new design strategy that employs an optimized magnetization profile to enable controlled directional release of aqueous cargo without compromising shape morphing and locomotion capabilities. Magnetic soft robots with a specific spatially distributed magnetization profile allow directional alignment of the release interface with the orientation of the external magnetic field. This orientation control ensures active alignment of the release interface toward the intestinal wall prior to drug release. An interconnected microporous elastomer is embedded within the robot for aqueous cargo storage, while a thin microcrystalline wax layer seals the release opening hole to isolate the stored liquid cargo from external environment during transport. Triggered release is achieved by mechanically rupturing the wax sealing layer under a higher magnitude external magnetic field. Controlled directional flipping, locomotion, and triggered release are decoupled through external magnetic field's direction and strength. The controlled directional release strategy reported here integrates directional targeted liquid cargo release, shape morphing, and locomotion, which establishes the groundwork for target drug delivery in gastrointestinal tract applications.

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.

Acoustic microrobots have emerged as a promising frontier for targeted drug delivery and minimally invasive medicine due to their high-power density and biocompatibility. Despite wide-ranging designs, conventional acoustic microrobots mostly rely on air microbubbles trapped within confined microcavities within the robot body, which suffer from limited operational longevity due to rapid gas dissolution and resultant shifts in resonance frequency. In this paper, we propose a robust, membrane-based acoustic microrobot that overcomes these limitations by employing a thin flexible Polydimethylsiloxane (PDMS) membrane bonded over confined microcavities for microstreaming. The introduced design physically prevents gas diffusion, ensuring stable performance over extended periods at high actuation voltages. We systematically characterized the membrane-based acoustic actuator longevity, demonstrating consistent streaming and propulsion for over 24 hours of continuous operation. In addition, by embedding magnetic microparticles into the structural body, these actuators were successfully employed as microswimmers with directional control using low-intensity (2 mT) external magnetic fields. Finally, we demonstrate the scalability of the proposed design architecture down to ~100 um. This membrane-based approach establishes a reliable framework for the development of high-endurance acoustic microactuators and microrobots capable of performing long-term tasks.

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.

Recent advancements in Resistive Force Theory (RFT) enable approximation of ground reaction forces for locomotion in sand without the computational expense of modeling interactions with individual grains. However, these tools have been absent in 3D physics engines commonly used for robot simulation. We explore if resistive force approximations are sufficient, when integrated with standard dynamics calculations, to provide a stable substrate for a freely walking robot. To determine this, we implement 3D Granular Resistive Force Theory (3D RFT) in a physics simulation engine, MuJoCo. We verify simulations in multiple scenarios to demonstrate that key trends due to end effector shape, speed, and loading are preserved. Our implementation predicts both walking distance and foot sinkage of a 12-Degree of Freedom hexapod robot within 7% of experiments in sand. While RFT has inherent approximations, the open source tool described here has potential to help develop new and improved robot designs to traverse granular media substrates.

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.

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.

We present the Swima, a bioinspired 900-mg swimmer propelled by two 10-mg high-work-density (HWD) actuators driven by shape-memory alloy (SMA) wires. We integrated onboard power and computation by using a custom-built printed circuit board (PCB) and an 11-mAh 3.7-V 507-mg single-cell lithium-ion (Li-Ion) battery, which in conjunction enable autonomous swimming in excess of 18 min. The Swima can swim at speeds of up to 22.4 mm/s (0.56 Bl/s), achieves turning rates of up to 14°/s, and can follow 0-degree heading reference trajectories with root mean square (RMS) values of tracking errors of about 6.5° across multiple tests. This robot is the first subgram microswimmer with onboard power, actuation, and computation developed to date.

The recent popularity of robotics, combined with the steadily decreasing cost of robotic hardware, has lowered the entry barrier to robotics research and enabled rapid advancements in the field. One of the primary examples is the Unitree Go2 quadruped robot, which is often used by researchers in the areas of locomotion, navigation, control, and others. Many researchers use the Go2 robot in combination with techniques like imitation learning, reinforcement learning, and behavioral cloning to allow machine learning systems to take full control of the robot. At the same time, many of those techniques require demonstration data consisting of the robot's kinematics information and actions applied to the motors. Obtaining such data is difficult, requires building complex pipelines, and can take significant time. To aid in those kinds of efforts, we present Kine2Go - a dataset with 800 diverse gait kinematics trajectory motion data for the Unitree Go2 robot, derived from 40 distinct policies. Our pipeline accepts data from various quadruped morphologies and translates them to a Go2-compatible format. Then we use Reinforcement Learning to train policies following a given motion, and finally we gather data from those policies, which grants robust, perturbed kinematic data with corresponding motor-level actions.

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/

This paper proposes, an improved version of the 3 in sewer pipe inspection robot equipped with an emergency evacuation mechanism. The low traction force and poor stepover capability, which were challenges of the first version, have been improved by simply connecting the propulsion units. The coupled propulsion units feature a differential mechanism capable of posture changes via a single wire, enabling adaptation to pipe diameter variations. To traverse obstacles like pipe joints, a control method was devised that detects obstacle contact through current load on the drive wheel motors and slackens the wire. This method was verified through simulated pipe experiments. Load comparisons were made using current waveforms applied to the drive wheels. Our proposed control method significantly improved the step-over capability of the new articulated robots.

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/.

Soft robots are valuable robophysical platforms for studying body-caudal undulatory locomotion, but their compliant bodies are difficult to control precisely under changing hydrodynamic loading. Conventional proportional-integral-derivative (PID) feedback stabilizes periodic undulation in static water, but can accumulate flow-dependent tracking delay and increasing inter-trial variability when environmental flow becomes non-trivial. Here, we evaluate whether augmenting PID control with a Linear Repetitive Learning Estimation Scheme (PID-LRLES) recovers tracking accuracy and repeatability under dynamic flow. The LRLES generalizes classical integral action from constant to periodic, non-constant references, while using a stable transfer-function realization whose poles have negative real parts to avoid the long-term instability issues of classical repetitive control. Closed-loop experiments were carried out in a recirculating flow tank at five bulk flow speeds spanning 0 to 32.6 cm s^-1, using an embedded soft capacitive bending sensor at a 1 kHz control-loop rate. With controller gains tuned once in static water and then held fixed across all conditions, PID-LRLES tracked the periodic bending-envelope reference more closely than the PID baseline and significantly reduced the inter-trial spread of the per-trial RMSE (paired Wilcoxon signed-rank test, p = 1.8 x 10^-4, n = 25). Embedded soft proprioception and cycle-to-cycle learning act as complementary contributors to robustness: the sensor exposes the periodic hydrodynamic bias in body deformation, while the learning term absorbs it over recent oscillation cycles. By reducing flow-dependent control-induced variability, the approach provides an enabling layer for future robophysical studies seeking to isolate the effects of morphology, sensing, and environmental flow on aquatic locomotion.

In this paper, we introduce the Soft Lamprey-Inspired Dual Environment Robot (SLIDER) and a proper modeling and optimization procedure employed to design the robot. We represent the primary fluid environment actions - inertial effects, vortex forces, and viscous dissipation - using Lighthill's theory for large-amplitude elongated bodies. For structural design parameters such as internal pressure, tail size, and body stiffness, a fast, geometrically and materially nonlinear model is developed and validated. The fluid-structure interaction equations are solved implicitly with an efficient second-order box method. A pneumatic manifold robotic system is employed to actuate SLIDER in a quiescent water tank environment, allowing cross-comparison of computational and experimental results. We find that low-frequency swimming is dominated by resistant environmental forces, whereas higher-frequency swimming is primarily affected by inertial fluid forces. Using our efficient model alongside a genetic algorithm, we co-optimize a swimming control pattern and caudal fin design (subject to SLIDER's climbing morphology) to achieve a tethered swimming speed of 21.7 +/- 0.4 cm/s (0.59 Bl/s). Furthermore, we investigate the optimization procedure for a multimodal robot performing both swimming and climbing tasks.

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.

Monopedal hopping robots are conceptually simple but highly dynamic and inherently unstable. Achieving robust 3D hopping is still difficult because ground reaction forces are available only during the short stance phase, while the robot is underactuated in flight. A key unresolved issue is how to improve flight-phase control authority. Propeller assistance provides a promising solution, but it requires careful coordination of leg-generated contact forces and propeller thrusts across stance and flight. This paper presents Pro-OMEGA2, a propeller-assisted 3D monopedal hopping robot with an active 3-RSR parallel leg and a trunk-mounted tri-rotor for auxiliary attitude regulation. To address the force coordination challenge, we propose a Hierarchical Force Allocation (HFA) framework based on a single rigid body (SRB) model. The leg generates the main stance contact wrench, while the tri-rotor provides auxiliary attitude regulation, compensating the residual attitude moment in stance and maintaining attitude during flight. Real-robot experiments in indoor and outdoor scenarios demonstrate sustained 3D hopping, including terrain transitions and impulsive push recovery, validating robustness under unmodeled contact and external disturbances.

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/

Powered prostheses conventionally rely on impedance controllers that require extensive manual tuning and explicit mode classification. In this work, we present real-time deployment of an end-to-end prosthesis controller that estimates continuous actuator signals from onboard sensors, eliminating the need for intent classifiers and subject-specific tuning. Temporal Convolutional Networks were trained on a multi-terrain dataset from 18 individuals with transfemoral amputation and deployed in real time across five locomotion modes. Four participants (three able-bodied, one with transfemoral amputation) ambulated across level ground, ramp ascent and descent, and stair ascent and descent. During level walking, the deployed controller reproduced the training-data scaling of peak ankle torque with walking speed (deployed 0.85 Nm/kg per m/s, p = 0.001; training 0.96 Nm/kg per m/s, 95% CI [0.42, 1.50], p = 0.002), after excluding one outlier traced to atypical prosthesis loading. During ramp ascent, the controller scaled knee pre-flexion with grade (deployed 2.92 deg/deg, p = 0.027; training 3.30 deg/deg, 95% CI [1.83, 4.77], p < 0.001). During ramp descent, the controller increased resistive knee torque relative to level walking (deployed +0.16 Nm/kg, p < 0.001; training +0.16 Nm/kg, p = 0.008). Seamless stair transitions were generated for both intact- and prosthetic-side-leading sequences in ascent and descent, despite the training data containing only one limb-leading sequence. These results provide initial evidence towards end-to-end control that can provide unified, mode-adaptive prosthetic assistance without subject-specific tuning.

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.