Terrain

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

Navigation world models plan by foresight, predicting the future that each candidate action sequence produces and selecting the best, rather than mapping observations to actions directly. Unlike urban settings where a predicted scene is a sufficient proxy, off-road navigation hinges on the robot--terrain interaction, so the prediction must cover not only what the camera will see but what the robot will feel. However, existing scene-focused models do not predict how much the robot will slip, tilt or shake along a planned trajectory. Proprioception captures these dynamics directly and, when used as input, improves the prediction of the physical future. We present Feel-WM, the first off-road navigation world model that conditions on proprioception and predicts what the robot will feel alongside what the camera will see. The physical future takes the form of a future proprioceptive state and a failure risk, both learned from the robot's own experience without human labels. The planner rolls out the physical future alongside the scene and weighs the predicted failure risk against goal similarity in a separable score. Experiments on real off-road data and in simulation demonstrate that Feel-WM outperforms visual-only navigation world models in open-loop planning and closed-loop rough-terrain navigation across wheeled and legged platforms. Deployed on a Husky on mountain trails, Feel-WM plans onboard, predicts rough ground ahead and steers around it, completing courses that an end-to-end policy fails.

Teleoperation, a human-in-the-loop control scheme, allows a human operator to remotely command and guide a mobile robot to navigate in off-road environments, yet fluent and user-friendly tele-navigation requires an alignment of traversability evaluation between human and robot. In the teleoperation system, the human operator typically utilizes off-site incomplete and delayed feedback via a human-machine interface to make a judgment of traversability, while the robot makes such an evaluation based on in situ onboard sensory information, which could cause divergent traversability estimation and thus generate mismatched decisions and actions. Existing approaches for traversability modeling, estimation, and prediction are mainly derived from the view of robots, i.e., robot-centric, and are practically suitable for fully autonomous mobile robots, but neglect the influence of human operators. To address this problem, this paper extends the concept of traversability from robot-centric to human-centric by accounting for the operator's cognitive states, such as attention, workload, and risk tolerance or awareness, termed tele-traversability. We first revisit the definitions and roles of traversability in robotics and then extend them to teleoperation settings. Finally, we highlight future trends and open challenges of tele-traversability toward human-centric teleoperation systems.

Research in humanoid robotics has achieved rapid progress in locomotion, and recent results have pushed the boundary on autonomous navigation. We demonstrate that a standard single-stage RL navigation pipeline struggles to scale to multi-level and multi-story terrain, limited by the difficulty of complex humanoid terrain interactions such as stairs. To overcome this challenge, we decompose the navigation problem into two pieces. First, we train a policy operating on the reduced order dynamics but with full 3D LiDAR observations to navigate complex, multi-story terrain. We then utilize this navigation knowledge to kickstart a policy operating on the full-order humanoid dynamics, with a frozen locomotion policy in the loop. Additionally, we demonstrate that applying a Poisson safety filter to the navigation policy output recovers safety in the presence of out-of-distribution obstacles, without dropping navigation success rate. We demonstrate the resulting RoM-Nav policy on a Unitree G1, accomplishing mapless multi-floor navigation covering trials with over 10m of vertical displacement and over 100m of path length. Project page with videos https://wdc3iii.github.io/rom-nav/ .

A vehicle's heading affects both the surfaces beneath its tires and its pitch and roll. We present Vehicle-Conditioned Terrain Planning (VCTP), which retains these relationships by evaluating shared elevation and surface-ID layers at eight headings. Body geometry constrains admissibility, while loaded wheel contacts determine modeled surface cost and predicted pitch and roll. Established D* Lite and vehicle-state search use these evaluations to plan routes with forward and reverse motion. When observations change, VCTP recomputes every affected body or contact query. In fully observed two-track simulations, sampling at wheel contacts rather than at the vehicle center lowers modeled surface cost by 39.3% while shortening the route. In offline planning on RGator recordings, VCTP also reduces modeled costs over identified surfaces and observed support relative to distance-focused planning, although incomplete coverage leaves full-route rankings unresolved. Selective updates match full recomputation in all 474 comparisons using recorded map changes. These results identify when wheel-contact placement and vehicle heading affect route choice.

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

Active perception allows autonomous agents to select their viewpoints rather than passively process the viewpoints given to them, enabling them to target where to reduce uncertainty about their environment. Learned systems typically encourage this behavior with hand-designed proxy objectives, such as coverage or curiosity bonuses, that may conflict with the task. In this work, we propose a method to learn emergent active perception (LEAP) without augmentation of the task objective. We formulate the problem of goal-oriented navigation over hazardous terrains with goals that must be discovered visually. We then propose an architecture for navigation policies with active perception, and train them on a terrain curriculum where task pressure alone leads to the emergence of gaze control. Key to this emergence, LEAP works on a gaze-invariant representation that integrates depth images into egocentric belief maps. We validate its performance in held-out evaluation scenarios, where it achieves a 92.7% success rate, compared to 74.2% for scripted or 34.5% for passive perception, and comes within 4.6 points of a privileged oracle. We validate that LEAP navigation policies, unchanged, can be directly applied to steering quadrupedal locomotion policies in physics simulation.

Wheel-loader excavation is a sequential decision problem in which every scoop changes the terrain available to subsequent actions. A practical world model must predict action consequences accurately, rank candidates in real time, and operate inside the closed loop of a full-size machine. We present the World-Action Model (WAM), which proposes multiple scoops, rejects geometrically inadmissible candidates, jointly predicts signed terrain change and loaded volume, executes the candidate with the largest predicted load, and replans from the newly observed terrain. On 32 geometry-disjoint MinSlope test episodes, adding world-model ranking to matched diffusion proposals reduces the mean scoop count from 651.8 to 540.6 (17.1%), preserves 32/32 completion, and improves every paired episode. In a complete-system comparison, WAM completes 32/32 episodes versus 29/32 for an independently trained soft actor-critic policy. Comparisons of input representations, spatial support, and five architectures identify an accurate and efficient physics-structured predictor. We further evaluate the interface on event-disjoint full-size-loader data and deploy the complete perception-proposal-prediction-selection-execution loop for autonomous excavation. The ROS2/TensorRT implementation processes five candidates in 72.4 ms on a Jetson AGX Orin. The simulation results establish decision-level gains, while the physical experiments demonstrate real-world closed-loop feasibility.

Humanoid locomotion on granular terrain remains a significant challenge due to its complex foot-terrain interaction dynamics that are difficult to model. Existing approaches either ignore granular contact dynamics or incorporate simplified normal force models with heuristic tangential components. In this work, we present a physics-grounded granular contact model based on three-dimensional resistive force theory (3D RFT) and efficiently simulate granular terrain for reinforcement learning (RL) training. Unlike traditional rigid contact models and simplified granular contact models with ad-hoc heuristics, our contact solver produces physically accurate granular intrusion dynamics without resorting to heuristics. It captures realistic penetration and tangential drag during training, enabling the policy to learn behaviors that transfer reliably to real-world granular terrain where rigid contact models fail. To adapt to varying terrain conditions, we train a terrain-adaptive locomotion controller via teacher-student RL, using a variational autoencoder to encode terrain information into a compact latent representation. Simulation studies using material point method (MPM) with NVIDIA Newton demonstrate that our method generalizes to unseen granular terrains, achieves a significantly higher success rate than baselines, and demonstrates zero-shot terrain identification and adaptation. We further validate our approach through extensive hardware experiments across diverse real-world granular terrains including basalt, dry sand, and beach sand. To the best of our knowledge, this is the first demonstration of agile humanoid locomotion on real-world granular terrain. Project page: https://humanoid-gm-locomotion.github.io/HUMANOID-GM/

Open-loop multilegged locomotion over rough terrain has been interpreted as matter transport over a noisy channel: leg-ground interactions are discrete basic active contacts, terrain deletes or perturbs those contacts, and spatial redundancy concentrates the resulting thrust and arrival time. That construction is repetition-like because every module carries the same scalar locomotion task. It consequently provides neither a positive task rate nor a decoder that changes with the surviving contact set. Here we formulate locomotion instead as a quantized finite-frame expansion with erasures. A d-dimensional body-level command is mapped into N>d heterogeneous local contact commands. Rough terrain erases or corrupts frame coefficients, while a contact-gated compliant morphology physically realizes the weighted active-subframe decoder. For a linear-Gaussian model, mechanical equilibrium is exactly the posterior mean, tangent stiffness is posterior precision, and mechanical compliance is posterior covariance. Equal-norm Parseval frames are shown to be minimax optimal against one missing contact, two-contact robustness is governed by frame coherence, and a harmonic frame gives a directly realizable gait family. For independently surviving contacts of probability q, random Gaussian gait frames admit exact reconstruction at every analog dimension rate R<q, with a binomial reliability exponent, whereas recovery of arbitrary commands is impossible for R>q. Residual contact noise yields an asymptotic per-mode amplification 1/(q-R) and a vanishing mechanical stiffness margin at the threshold. An information-locomotion inequality and an exact incremental-redundancy rule direct the next gait component toward the softest task-relevant unresolved mode. The resulting analog frame-coding theorem establishes a finite relative redundancy and converse as part of a fundamental limit theory of legged locomotion.

Autonomous exploration on uneven terrain requires ground robots to balance exploration efficiency, coverage completeness, and terrain safety. Detailed tsrrain reasoning improves local reliability but can slow large-scale exploration, whereas coarse region guidance expands quickly in open areas but can miss narrow passages and irregular traversable boundaries. To address this challenge, this paper presents TASG-Explore, a traversability-aware sector-guided exploration framework for ground robots. The framework first performs hierarchical traversability analysis using variable-voxel ground fitting and adaptive 8-bit obstacle encoding. It then splitting cost map into sectors, incrementally updates sector clusters, extracts terrain-coupled frontier viewpoints, and maintains a dynamic topological roadmap with unknown topological hypotheses. Finally, a sector-guided planner selects region targets and inserts local viewpoints to generate efficient exploration routes. Benchmark experiments in diverse challenging environments, including caves, forests, and rugged hills, show that TASG-Explore achieves the best overall performance among six representative state-of-the-art planners. The proposed traversability analysis improves processing efficiency by 6.3 times while maintaining high accuracy, and the exploration planner improves exploration efficiency by 51% and increases coverage by up to 2.95 times in rugged hill scene. Large-scale real-world experiments further demonstrate the practical value of the proposed method.

Quadruped robots have demonstrated impressive agility in parkour locomotion across complex terrains. However, most systems still rely on human intervention for high-level planning, and autonomous parkour navigation remains underexplored. The key challenges include fine-grained velocity regulation, long-horizon anticipatory behaviors, and tight coupling between perception and embodied execution. To address these challenges, we propose a Multimodal Diffusion Policy (MulDP) that integrates visual perception with robot proprioception and goal information to generate temporally coherent and anticipatory navigation velocity commands, tightly coupling perception with embodied control to enable robust autonomous navigation. To support the training of MulDP, we construct the first Quadruped Parkour Navigation Dataset (QPND), a multimodal dataset that encompasses diverse navigation behaviors and complex terrains. Extensive simulation and real-world experiments demonstrate that MulDP enables robust long-horizon autonomous navigation and effective traversal across complex terrains.

Autonomous navigation in space requires reliable terrain assessment for safe operations, especially in underground environments with limited communication, computing resources, and power budget. This paper presents a lightweight method for real-time vibration-aware traversability mapping using a Light Detecting And Ranging (LiDAR) point cloud and Inertial Measurement Unit (IMU) measurements. An initial vibration proxy is estimated from terrain geometry by applying Random sample consensus (RANSAC) to local point-cloud patches produced by a Simultaneous Localisation And Mapping (SLAM) algorithm. In parallel, the IMU provides local observations of the vibration experienced by the rover during traversal. The point-cloud-based prediction is then corrected online using Recursive Least Squares, allowing the system to adapt the geometric estimate to the measured rover response. The approach is evaluated in a lunar analogue environment, an outdoor field, and an underground mine.

Humans traverse complex terrain over long distances without losing balance, whereas perceptive humanoid policies become fragile as perception and control errors accumulate. We present SOLO, a unified framework addressing two compounding causes of this long-horizon fragility: dense terrain reconstruction smooths action-critical details, and pointwise imitation lacks temporal credit assignment. Its Query Reconstructor (QR) uses Fourier-encoded cell queries to retrieve spatially specific evidence from depth-proprioception tokens, preserving sharp terrain boundaries. Trajectory-Aware MSE (TA-MSE) Distillation adds next-state teacher-student disagreement to the PPO reward, enabling Generalized Advantage Estimation to propagate future disagreement penalties to preceding actions. In simulation, QR reduces height-map L1 error by factors of 3.3-4.0, while TA-MSE surpasses PPO and MSE+PPO in curriculum progression. On stress-test terrains, SOLO achieves 97.5% mean traversal success and 96% stepping-stone success, versus 75.0-75.6% and 0-3% for dense-reconstructor variants. Deployed zero-shot with only a chest-mounted depth camera and proprioception, SOLO completes a continuous 1.5-km outdoor route and an indoor mixed-terrain course. Project page: https://sunpihai-up.github.io/solo/

General-purpose motion trackers enable humanoid robots to follow diverse whole-body motions while maintaining balance, but are trained only on flat ground, failing to exploit bipedal mobility over complex terrain. Cross-terrain controllers, meanwhile, are task-specific or accept only low-dimensional locomotion commands. We introduce InterTrack, the first behavior world model (BWM) for robust whole-body tracking with environment interaction. Its Transformer jointly predicts the next action, state, and behavior distribution, learning environment-conditioned dynamics. To scale interaction training data, an automatic annotation pipeline reconstructs 3D support geometry from retargeted motions. At deployment, the policy handles commands implausible in the current environment in a "best-effort" manner. Quantitatively, InterTrack achieves an 81.3% success rate on terrain interaction (4.3 times the best evaluated baseline) and a 99.3% fall-recovery rate, while also improving free-space tracking and outperforming three leading tracking baselines across all of these regimes. To our knowledge, we provide the first demonstration of real-time cross-terrain whole-body teleoperation on a humanoid robot, alongside object interaction, stable responses to missing supports, and robust recovery from falls.

This paper presents a parameter-dependent linear matrix inequality (LMI) framework for trajectory tracking of nonholonomic mobile robots subject to severe multiplicative wheel slip on variable-terrain surfaces. The sampled convex formulation, augmented with grid-to-continuum residual certification, simultaneously establishes semi-global differential input-to-state stability, a prescribed exponential decay rate, regional pole placement, and a gain-bounded feedback proxy for actuator-limited operation. A central contribution is an explicit upper bound on the additive disturbance induced by bounded multiplicative slip in the Kanayama error coordinates, bridging the physical slip mechanism and the convex synthesis paradigm. The auxiliary gain matrix and inverse storage metric are parameterized affinely in the reference velocities, while the storage metric inherits nonlinear dependence through pointwise matrix inversion. Stability is established via a cascade analysis combining variational contraction, forward invariance, slip-induced disturbance bounds, and dissipation-based trajectory reconstruction. Numerical validation compares three controllers across six reference trajectories, six disturbance classes, and a 60-second variable-terrain test featuring six severe slip patches with bidirectional slip ratios reaching +/-50%, replicated on two geometries. Supplementary studies address Gaussian sensor noise, compound stress-testing, and embedded-platform computational feasibility. Across 100 Monte-Carlo runs the proposed controller achieves complete trajectory containment within the certified envelope. On the variable-terrain scenario, peak tracking error is reduced by 12% against the fixed-gain LMI baseline and 49% against the manual baseline, with the constant-gain baseline infeasible at the prescribed decay rate.

This paper presents a collaborative UAV-UGV navigation framework for high-altitude, snow-covered terrain, where reduced visibility and unstable ground render conventional methods ineffective. We introduce a custom efficient U-Net architecture that falls under the computational constraints for real-time road segmentation, utilizing a novel synthetic snow data augmentation technique to achieve 96.5% segmentation accuracy. For UAV localization, we implement an Extended Kalman Filter (EKF) fusing onboard GPS and IMU data, achieving a maximum observed positional error of +-0.5 meters. The UGV position is determined via a visual tracking pipeline using YOLOv5 and depth data from the UAV's RGB-D camera. A dynamic path planning algorithm utilizes this segmentation to adjust for snow drifts, enabling successful navigation in obscured test environment with minimal deviation.

Generating large-scale, freely explorable 3D worlds from open-ended text remains challenging because a system must jointly maintain global spatial coherence, rich local content, and explicit assets suitable for downstream editing and reuse. We present WorldClaw, a fully agentic, coarse-to-fine framework for open-world 3D scene generation. Planning agents translate a text prompt into a structured specification of regions, terrain, assets, materials, and spatial relations. WorldClaw then builds a globally coherent terrain foundation from semantic layouts, reusable assets, generative or procedural materials, and a region-aware height field. For detail-demanding regions, it generates terrain-conditioned compositions, reconstructs editable textured meshes, and recovers their placement on the terrain; render-based agents further refine terrain, objects, appearance, and contacts. Across diverse open-world prompts, WorldClaw produces large-scale scenes with coherent spatial organization, visually compelling local content, and editable instance-level assets while preserving a consistent global terrain structure.

The dynamical Lie algebraic (DLA) theory of variational quantum algorithms (VQAs) predicts commonplace exponentially vanishing loss and gradient variances for sufficiently deep parametrized circuits. In this work, we show that these predictions fail dramatically in the shallow-circuit (and particularly constant-depth) regime for the Quantum Approximate Optimization Algorithm (QAOA) applied to the maximum independent set (MIS) problem. In a large-scale numerical study across $\sim$23,000 problem instances, we find that barren plateaus are rare, while landscapes whose variances polynomially increase with system size---which we term "cragged terrains"---are common across graph families. This aggregate polynomial growth persists both for generic, low-symmetry random graphs and for highly symmetric vertex-transitive graphs, indicating that DLA-based variance predictions do not describe landscape scaling in this regime. As a stopgap alternative to the theory, we train empirical hardness models to predict instance-wise hardness metrics for QAOA-MIS. While these models generalize poorly, they nonetheless recover the correct landscape scaling class (barren plateau vs. cragged terrain) with high fidelity. Taken together, our results identify shallow QAOA for MIS as a prototypical setting in which asymptotic, unitary-design-centric predictions may be fundamentally insufficient to describe shallow variational quantum algorithms more broadly, emphasizing the need for more empirically-informed models of VQA loss landscapes.

Mapping paddy rice from very-high-resolution imagery in mountainous and hilly regions is difficult because terrain alters optical appearance and increases confusion with visually similar vegetation. We present TRNet for 0.5-m GaoJing-1 red--green--blue (RGB) imagery, a 5-m TanDEM-X digital elevation model (DEM), and derived slope. Separate visual and terrain encoders preserve modality-specific features. At an early encoder stage, Topographic Energy-Spectral Rectification applies terrain-conditioned low-frequency modulation and asymmetric high-frequency regulation to suppress steep-slope clutter and conditionally enhance compatible low-slope rice cues. The Topography-guided Paddy Structure Decoder combines semantic, rice--background boundary, and interior cues, using coarse terrain as context. Experiments used an Area A internal test set and held-out Area B, which had steeper terrain and lower rice prevalence. TRNet achieved rice intersection-over-union (IoU) values of 85.10% and 80.68%, exceeding the original Dual-Encoder U-Net by 9.15 and 18.83 percentage points, respectively. Ablation and slope-stratified results linked these gains to frequency rectification, structure learning, and fewer steep-terrain false positives. The results support coarse topography as a contextual prior for very-high-resolution paddy rice mapping.

Off-road mobility requires autonomous mobile robots to generalize across heterogeneous vehicle fleets and continuously changing terrain conditions. Existing cross-vehicle adaptation approaches generally assume flat terrain, while terrain-aware kinodynamic models often require platform-specific data collection and retraining. To this end, we propose VertiAKD, a unified framework for transferring and adapting off-road kinodynamic knowledge across diverse vehicles on geometrically and semantically complex terrain simultaneously. VertiAKD learns a shared mobility representation that jointly encodes vehicle configurations, trajectory transitions, and local elevation and semantic terrain features. Given limited data from a novel vehicle operating on unseen terrain, VertiAKD identifies the most relevant mobility descriptors and transfers their knowledge to initialize a terrain-aware kinodynamic model via function encoders, which is then periodically refined online from streaming observations without gradient-based retraining. We evaluate VertiAKD in the Verti-Bench simulator, built on the Chrono multi-physics engine, and on five physical configurations of the Verti-4-Wheeler platform. With only one minute of new trajectory data and associated terrain features, VertiAKD reduces long-horizon prediction error by up to 34.52% over direct mobility descriptor transfer across diverse unseen vehicle configurations and 94.43% over competing baselines. We further demonstrate robust closed-loop trajectory tracking in both simulation and physical experiments, highlighting the effectiveness of terrain-aware cross-vehicle knowledge transfer for accurate modeling and reliable off-road navigation.

Estimating traversability in unstructured environments requires conditioning on robot embodiment, as the same terrain can be traversable for one platform and unsafe for another. Existing methods often transfer predictions across morphologies through late-stage trajectory filtering rather than encoding platform constraints in the learned representation. We propose Capability-Aware Traversability (CAT), a framework that embeds physical limits directly into the spatial feature space. CAT grounds dense supervision masks in physical trajectories through an interactive annotation pipeline and modulates semantic terrain maps with robot-specific traversability vectors through Spatially-Adaptive Denormalization (SPADE) blocks. Across human-annotated and trajectory-aligned datasets, CAT leads all ranking-based metrics, improving AUROC by 11.0% on physically executed trajectories and AUPRC by 15.8% on human traces over the strongest baseline. Ablations show that spatial conditioning and per-robot prototypes produce capability sensitivity beyond generic path prediction. Deployments on a legged quadruped and a wheeled skid-steer demonstrate embodiment-aware obstacle avoidance on embedded hardware at 4.8 Hz.

Robotic navigation in unstructured environments requires robust situational awareness to safely traverse hazards such as steep slopes and rocky terrain. To address this challenge, perception systems increasingly rely on multimodal sensor fusion. Specifically, integrating thermal imagery with standard optical and depth sensors enhances terrain differentiation, directly improving the reliability of mapping algorithms. This paper presents PRISM, a multimodal perception system for terrain mapping in unstructured settings. PRISM leverages a custom sensor suite to capture aligned RGB, depth, and thermal (RGB-D-T) imagery. At its core is OmniUnet, a novel vision transformer-based network specifically designed for multimodal semantic terrain segmentation. We validated the proposed system using two newly annotated datasets (BASEPROD and LAENTIEC) and demonstrate its real-world applicability through physical field experiments. Deployed on a resource-constrained embedded computer, PRISM efficiently generates traversability maps that directly enable autonomous navigation via a rover's Guidance, Navigation, and Control (GNC) subsystem.

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.

High-speed off-road autonomy requires precise closed-loop control for a target vehicle while remaining robust across changing terrains. Recent forward kinodynamic (FKD) prediction foundation models suggest a promising path, starting from a generalist model and specializing it to the target platform. However, effective specialization remains challenging, as it often requires substantial real-world data, and models adapted to one setting can still overfit to specific terrains or driving regimes. We present OptCar (Optimized Car), a recipe for bridging the gap from generalist to specialist FKD models that preserves cross-terrain generalization while optimizing performance for a specific vehicle. $\texttt{OptCar}$ introduces a history-conditioned dynamics adaptation module that encodes recent state-action observations into a dynamics context token, and then fine-tunes the generalist model using limited real-world data together with targeted synthetic rollouts from environment-specific system identification. In closed-loop model predictive control (MPC) experiments across three terrains and an out-of-distribution cart-pulling task, the largest gains appear at 6m/s, the highest speed evaluated and the regime in which slip dominates tracking error. On vegetation and dirt, the most slip-diverse terrain, OptCar reduces 6m/s trajectory tracking error by roughly 55% relative to a fine-tuned AnyCar baseline, and remains the most accurate even when an unseen cart payload changes the dynamics. With only 5 minutes of real data per terrain, OptCar is competitive on road with a specialist trained on 30 minutes of road data, and substantially outperforms it once the terrain changes.

Reliable autonomous navigation in unstructured off-road environments remains a critical unsolved challenge due to extreme terrain diversity, drastic illumination variations and acute sensor degradation. Recent developments have approached the problem as a traversability costmap estimation or visual navigation task. However, many exhibit heavy reliance on RGB modality, leading to poor performance in varied illumination such as glares, shadows or low ambient light. Achieving robust generalization in such conditions requires integrating modalities that provide supplementary scene information. Such multi-modal methods suffer from a rigid dependency on the presence of near-perfect sensor inputs, leaving them unable to robustly handle sensor degradation or individual modality failure. To address these limitations, we introduce MAMMOTH (MAsking Multi-Modal inputs for Off-road Traversability Heuristic-informed navigation), a unified end-to-end navigation policy for robust off-road visual-goal-conditioned navigation and undirected exploration. Specifically, MAMMOTH efficiently fuses multi-modal observations (RGB, Thermal, 3D Pointcloud and Ego Velocity) and is trained with a modality dropout scheme, enabling it to generalize to missing modalities at inference time. Furthermore, we employ a diffusion policy to learn the joint conditional probability distribution of physically-grounded trajectories and a intrinsic traversability heuristic. MAMMOTH utilizes this heuristic to prefer safer, smoother trajectories. We validate MAMMOTH through extensive real-world robot experiments in distinct off-road environments, including night-time operation. Our results demonstrate superior performance, with significant improvements in collision avoidance, terrain-aware planning and generalization to missing modalities. The code and dataset used for this work will be made publicly available.

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.

Reliable terrain understanding is a prerequisite for autonomous robot navigation. Yet, the widespread RGB-based perception can fail under low illumination, shadows, and material ambiguities. In this work we propose DRIFT, a lightweight multispectral framework that combines raw spectral bands and illumination-tolerant band-ratio representations through a dual-stream residual architecture and a differential fusion branch. Band ratios attenuate multiplicative acquisition effects (illumination/sensor gains), while the differential fusion explicitly highlights discrepancies between absolute-band and ratio-derived cues, which improves the robustness to noisy or partially unreliable spectral measurements. In the paper (i) we evaluate DRIFT on a new oil-on-soil multispectral dataset acquired using a MicaSense RedEdge-P camera mounted on an Unmanned Aerial Vehicle, and (ii) we provide an additional controlled study on water-on-grass under varying illumination and thermal perturbations (hot/cold water) to analyze NIR-sensitive effects. DRIFT consistently improves over strong baselines, while remaining compatible with edge deployment.

Accurate 3D terrain maps are essential for emergency response when assessing wildfire hazards. However, wildfire-prone regions often span vast areas where conventional reconstruction methods underperform. Airborne LiDAR systems provide high-resolution terrain data, but they are expensive and infrequently updated. Image-based methods offer a lower-cost alternative, but struggle due to sparse visual features and limited image overlap. We propose a multi-modal reconstruction framework leveraging outdated Digital Elevation Models (DEMs) as geometric priors for image-based 3D reconstruction. Our key innovation is physics-based pixel-pixel alignment between images and DEM data, dramatically reducing computational complexity by eliminating expensive feature matching procedures. To validate our approach, we developed a large-terrain simulator based on a real wildfire-prone area, generating realistic images enabling a comprehensive evaluation. Given posed images and legacy DEMs, our method produces high-fidelity depth maps while maintaining real-time performance. We find significant improvements in reconstruction accuracy and computational efficiency over existing techniques, offering a scalable solution for wildfire response.

Choosing a learning rate scheduling strategy is critical to neural network training, but manual selection is costly and rarely exhaustive. While classical AutoML approaches often treat the scheduler as a secondary hyperparameter, we systematically investigate its impact on classification accuracy across a diverse pool of architectures. We evaluated 30 representative architectures from convolutional and transformer families within the LEMUR neural network dataset. Through automated source-code injection, we applied 25 scheduler configurations across nine PyTorch families, evaluating a total of 3,938 model variants on CIFAR-10. Our best configuration achieved a top-1 accuracy of 86.45%, with 237 variants exceeding 80%. The results show that the choice of scheduler depends heavily on the architecture: CosineAnnealingWarmRestarts and CyclicLR consistently outperform basic decay strategies. The resulting accuracy landscape, contributed to the LEMUR nn-dataset, provides a practical reference for principled scheduler selection.

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.

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.

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.

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/ .

Accurate position estimation is crucial for the successful implementation of future lunar landings using autonomous vehicles, especially in dangerous environments with sparse terrain features. In this paper, we propose a terrain relative navigation (TRN) algorithm combining our deep-learning crater detector, which was designed specifically for the NASA Crater Detection Challenge problem, and an Extended Kalman Filter (EKF). Our detector analyzes crater features from the monocular images acquired from orbit, and their matches with craters from a global database are identified via a Hungarian assignment approach followed by the consensus-based outliers removal method. The estimated measurements are then used to refine an EKF, where spacecraft pose estimation in the Lunar-Centered Lunar-Fixed (LCLF) frame of reference, augmented with altitude aiding information, constrains radial drift. The simulation results indicate that even if the spacecraft is off from its actual location up to 5 km, TRN could recover from this situation, achieving navigation error reduction to a few hundred meters. It should be noted that in order to maintain crater feature correspondences, it is important to match the image resolution and the scales within the scene to the detector training set distribution.

Humanoid robots have achieved strong locomotion capabilities, but reliable navigation on versatile terrains remains challenging because obstacle avoidance must be coordinated with dynamically feasible motion. In this work, we present GuideWalk, a unified end-to-end framework that integrates traversability-aware navigation guidance with terrain-adaptive locomotion teacher for humanoid navigation. Specifically, we introduce a navigation module that provides explicit velocity guidance, decoupling obstacle avoidance from terrain conditions to enable robust planning across diverse environments. We propose a composite teacher distillation scheme, where goal-directed commands and dynamically consistent actions are aggregated and distilled into a single policy. To further improve robustness, the distilled policy is refined with reinforcement learning and an auxiliary behavior cloning objective, which promotes exploration while preserving desirable teacher behaviors. Experiments demonstrate that GuideWalk achieves stable and effective navigation while maintaining stable humanoid locomotion.

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.

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/

Simulation is central to robot learning, yet the sim-to-real gap remains a major bottleneck. Existing approaches often tackle visual or dynamic gaps separately, overlooking how these individual mismatches accumulate and propagate throughout the robot's state evolution. In this paper, we introduce QuadVerse, an integrated framework that uses reconstructed scenes as a calibration substrate for aligning visual perception, physical interaction, and actuator dynamics. From captured RGB videos, we reconstruct geometry-constrained 3D Gaussian Splatting (3DGS) scenes that support batched photorealistic ego-view rendering and collision-ready semantic mesh extraction. The meshes further enable contact calibration by initializing spatially varying friction priors and refining them through trajectory-based posterior search. To address remaining actuator discrepancies, QuadVerse trains a residual dynamics compensator by replaying real-world trajectories on the contact-calibrated terrain, reducing the entanglement between terrain-induced contact errors and actuator non-idealities. Experiments show that QuadVerse improves reconstruction quality and locomotion tracking over relevant baselines. Leveraging this foundation, we demonstrate robust zero-shot visual-navigation policy deployment without task-specific real-world rollouts.

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

Agile humanoid locomotion across diverse challenging terrain demands both wide perceptual coverage and precise local geometry understanding. Motivated by the way humans selectively look at relevant terrain during locomotion, we introduce TAGA, a Terrain-aware Active Gaze learning framework for Attention-based humanoid control. By fusing vision, proprioception, and motion commands, our framework guides the model to learn anticipatory cues and actively attend to specific areas of the height scan, selectively using these informative regions for the downstream network. This adaptively increases the information density of observations under tight onboard computational constraints, thus enabling fine-grained perceptive locomotion over larger-scale terrains. We find that such gaze behaviors can naturally emerge through reinforcement learning alone, without requiring additional supervision or explicit guidance, significantly improve training efficiency. As a result, the trained policy demonstrates robust and generalizable locomotion in simulation and on hardware, including reliable terrain-aware foothold selection, elevated-platform traversal, competitive sparse-foothold traversal, and the largest reported real-world gap traversal distance of 1.2m among perceptive humanoid locomotion systems, while maintaining stability under severe perceptual disturbances and environmental interference.

Laws and institutions shape individual outcomes through complex interactions with citizens' diverse circumstances, yet how different voting methods navigate this coupled landscape remains poorly understood. We model collective governance as optimization on NK fitness landscapes, where shared bits (laws) are updated by voting while individual bits (personal traits) remain fixed. A cross-dependency parameter $α$ controls how legislation's effects depend on individual circumstances. We compare eight standard voting methods and a generalized scoring family across landscape ruggedness $K \in \{1,\ldots,20\}$ and $α\in [0,1]$ with 1000 runs per configuration. Under direct democracy, the optimal voting method undergoes sharp phase transitions as a function of landscape complexity: cardinal score voting dominates on smooth landscapes, ordinal scoring with $p=0.35$ at low-to-moderate ruggedness, Borda count across a wide middle range, and STAR voting at the highest complexity. A two-parameter empirical formula reduces the $(K, α)$ plane to a single complexity axis for visualization. Borda count achieves the highest mean fitness and lowest variance across most of the parameter space. We further introduce a representative democracy model parameterized by identity weight $β$ and candidate self-interest $p_{\mathrm{self}}$. Representation reshapes the complexity-dependent structure even under favorable conditions: cardinal score voting dominates across most regimes, with plurality emerging as the top method at high $β$ and low-to-moderate $p_{\mathrm{self}}$.

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.

Implicit neural representations (INRs) model a signal as a continuous coordinate-to-value function. For terrain elevation data, this supports analytic derivatives, arbitrary-resolution decoding, and a smooth surface model of the underlying heightfield. However, fitting and storing a separate INR for every tile does not scale to large terrain datasets. Amortized neural representations reduce this cost with a shared network: a new tile is mapped to a compact per-tile payload, and a shared decoder reconstructs the heightfield from it. Most such methods are hypernetworks that predict the payload in a single forward pass, while others recover it through a short per-tile optimization. These methods were developed primarily for natural images, and their suitability for terrain heightfields remains unclear. We introduce a controlled benchmark on a 1 m/pixel terrain dataset and evaluate three representative methods under a unified protocol. Observing a clear cross-domain gap, we propose HUVR+SIREN, a hypernetwork that adapts the strongest benchmarked method (HUVR) by replacing its coordinate decoder with a smooth, analytically differentiable one. It attains the best height and derivative fidelity on the benchmark with no additional per-tile storage and lower decode cost, and tolerates aggressive post-training quantization with negligible quality loss, giving a compact terrain neural format. Ablations and diagnostics further identify which design choices transfer to terrain and show that the per-tile bottleneck is already near its useful limit, leaving the remaining gap in the shared hypernetwork's architectural design.

Aerial navigation on Mars requires vision-based pipelines that are robust to the diverse illumination conditions and terrain morphology of the Martian surface. A key bottleneck for training and evaluating such methods is the scarcity of large-scale, annotated aerial datasets. We present MARTIAN, an open-source Blender-based rendering framework that leverages real HiRISE orbital map products to synthesize realistic aerial views of the Martian terrain under controllable lighting conditions and at varying altitudes. MARTIAN generates observations with accurate pose annotations, directly addressing the scarcity of training data for vision-based navigation on Mars. The framework has been validated through its deployment in concurrent work on map-based localization systems for Ingenuity and future Mars rotorcraft, where synthetically trained deep image matchers were successfully evaluated on real Mars imagery. MARTIAN is publicly available at: https://github.com/nasa-jpl/martian.

Terrain understanding is fundamental for mobile robots operating in unstructured outdoor environments. Existing vision-based traversability estimation methods rely on robot-specific annotations or semantic class mappings, limiting transferability across platforms and requiring costly re-annotation when robot capabilities change, while standard semantic segmentation methods only focus on specific predefined classes, which do not capture the variety of terrains. In this work, we propose a transformer-based architecture that jointly performs class-specific semantic segmentation and class-agnostic terrain segmentation within a unified network, called Trinity. Terrain regions are segmented based solely on visual appearance, without predefined semantic labels or robot-dependent traversability scores. This formulation enables the learning of robot-agnostic visual terrain priors that can be combined with robot-specific experience for downstream tasks such as traversability estimation, visual odometry, and mission planning. To enable large-scale training with diverse terrain appearances, we extend the OAISYS simulator and introduce RUGDSynth, a synthetic dataset inspired by RUGD with class-agnostic terrain samples. Furthermore, we present the EXTerra Dataset, providing real-world images annotated with both class-specific and class-agnostic terrain labels. Experiments demonstrate the feasibility of the proposed task and the effectiveness of our joint segmentation approach in complex outdoor environments. Code and datasets will be released with this publication (after review).

Limbless terrestrial animals exhibit exceptional locomotor versatility and control, currently unmatched by engineered counterparts. Here, we introduce a computational framework that enables soft synthetic snakes to navigate unstructured, heterogeneous 3D terrains. Our approach is grounded in bio-inspired actuation and sensing models that reduce the control complexity inherent to high-degree-of-freedom, continuum bodies. These models are integrated into a reinforcement learning architecture to derive environment-traversing policies. Training first occurs in simplified, homogeneous terrains to learn locomotion primitives. These are then composed into adaptive strategies for complex landscapes. We demonstrate robustness by deploying a snake in high-fidelity 3D environments reconstructed from real-world imaging, achieving reliable navigation. Overall, this work provides a physically-realistic simulation platform and practical insights for the control of continuum systems in natural terrains.

Planetary rovers operating in extraterrestrial environments often encounter significant mobility challenges due to varying terrain features such as gradients and granularity. While recent works in multimodal wheel design have explored adjustments in stiffness, compliance, and diameter as a means to improve terrain adaptability, full wheel grouser-adjustable designs remain largely unexplored. Grousers are a compelling feature to actuate, as granular terrains tend to require increased grouser height for improved wheel performance. As a result, we introduce [Anonymized Robot Name], a multimodal wheel capable of continuously adjusting its grouser height for terrain adaptation. The platform was evaluated across four representative surfaces, including vinyl flooring, coarse rock, pea gravel, and sand under two packing states, spanning a range of granular conditions. Results from 750 experimental trials demonstrate that adaptive deployment reduces slip by 30.0--58.0% and improves travel time and energy consumption by up to 77.4% in granular regimes relative to fixed configurations. Using the terrain trial data, a simplified scaling analysis was developed and validated, suggesting a relationship between terrain granularity and optimal grouser height for the tested configuration. No single grouser height minimized slip across all terrains, underscoring the limitations of fixed-wheel systems commonly used for planetary exploration. This observation reinforces the potential of grouser-adaptive morphology, such as [Anonymized Robot Name], as an effective solution for enhancing rover mobility across diverse and mobility-challenging extraterrestrial environments.

Digital elevation models (DEMs) underpin terrain analysis in Geographic Information Systems (GIS), but in their common raster form, they rely on interpolation for off-grid sampling and finite-difference operators for derivative-based analysis. Implicit neural representations (INRs) offer a continuous alternative, but prior terrain INRs lack explicit frequency control, neglect the gradient structure of terrain, and remain too large and costly to train for practical deployment. We present ImplicitTerrainV2, which advances terrain INRs toward a compact, efficient neural terrain data format by combining a spectral control mechanism with wavelet-guided spatial adaptivity, derivative-aware supervision, and post-training model compression. At its core, a wavelet complexity field (WCF) derives spatially-adaptive frequency masks from analytically computed wavelet coefficients, localizing high-frequency capacity to complex terrain regions. The same field guides complexity-aware adaptive sampling that concentrates training in high-complexity regions, while gradient matching applies extra supervision to enforce the smooth manifold structure of terrain DEMs for improved derivative fidelity. Post-training mixed-precision quantization and entropy coding reduce storage to 1.23 bpp with a 0.28 dB PSNR drop. On 50 Swiss terrain tiles, ImplicitTerrainV2 reaches 66.25 dB end-to-end PSNR, improving over the prior work by 5.70 dB while using 3.2x fewer parameters and training in 55 s per tile on a single GPU. Our compressed neural format is competitive with several established DEM codecs in rate-distortion performance, while additionally supporting off-grid point queries, closed-form derivative evaluation, and resolution-independent reconstruction, which may benefit many downstream GIS applications.

Kinodynamic planning for car-like vehicles on uneven terrain requires simultaneously optimizing competing objectives such as path efficiency and pose stability. This work presents an adaptive epsilon-constraint method integrated into a Model Predictive Control (MPC) framework, where the epsilon bounds are dynamically adjusted based on terrain descriptors to explore the Pareto front in real time. To capture vehicle-terrain dynamics, we develop a semi-parametric model combining analytical vehicle dynamics with a Sparse Gaussian Process (SGP) trained on the same terrain descriptors. The proposed epsilon-MPC is evaluated against MPPI and GAKD baselines, achieving a 94% navigation success rate while reducing maximum orientation deviation by 24% and improving multi-objective trade-off quality by 23%.

Integrating machine learning (ML) with physical models (PM) has emerged as a promising way of retrieving geophysical parameters from remote sensing data. In this context, a ML model for estimating forest height from TanDEM-X interferometric coherence measurements has recently been proposed, that constrains the learning process through a PM. While the features used for training and inversion where selected to ensure the physical consistency of the solutions, they could not resolve all height / structure and baseline / terrain slope ambiguities in the data. To improve this, the extension of the feature space with optical Landsat data is proposed able to provide complementary information on forest type or structure. The extended model is applied and validated on several TanDEM-X acquisitions over the Gabonese Lopé national park site and assessed against airborne LiDAR measurements. Results show a 13.5% reduction in RMSE and a 16.6% reduction in MAE compared to the original hybrid model, confirming the added value of multispectral inputs.

We present a method for training reference-guided, perceptive reinforcement learning locomotion policies for humanoid robots in which reference trajectories are modulated in training to be consistent with terrain geometry. Aiming to deploy our method with standard navigation autonomy infrastructure, we synthesize SE(2)-controllable reference trajectories inside the RL training loop, projecting desired footsteps onto valid footholds and adjusting swing-foot and center-of-mass trajectories to match the terrain. The resulting policy exposes a clean SE(2) velocity interface compatible with standard navigation planners. In simulation, environmentally-conditioned references significantly improve reference tracking performance compared to environment agnostic references. On hardware, we integrate the policy with an MPC + control barrier function planner and demonstrate long-horizon (>70m) closed-loop autonomous navigation on the Unitree G1 through outdoor environments containing rough terrain and consecutive flights of stairs, with all sensing and computation onboard.

Terrain segmentation is a fundamental capability for autonomous mobile robots operating in unstructured outdoor environments. However, state-of-the-art models are incompatible with the memory and compute constraints typical of microcontrollers, limiting scalable deployment in small robotics platforms. To address this gap, we develop a complete framework for robust binary terrain segmentation on a low-cost microcontroller. At the core of our approach we design Nano-U, a highly compact binary segmentation network with a few thousand parameters. To compensate for the network's minimal capacity, we train Nano-U via Quantization-Aware Distillation (QAD), combining knowledge distillation and quantization-aware training. This allows the final quantized model to achieve excellent results on the Botanic Garden dataset and to perform very well on TinyAgri, a custom agricultural field dataset with more challenging scenes. We deploy the quantized Nano-U on a commodity microcontroller by extending MicroFlow, a compiler-based inference engine for TinyML implemented in Rust. By eliminating interpreter overhead and dynamic memory allocation, the quantized model executes on an ESP32-S3 with a minimal memory footprint and low latency. This compiler-based execution demonstrates a viable and energy-efficient solution for perception on low-cost robotic platforms.

Many downstream decisions in complex terrain require fast wind estimates at a small number of user-specified locations and heights for a given forecast valid time, rather than another dense forecast field on a fixed grid. We present WindINR, a latent-state implicit neural representation framework for continuous high-resolution local wind query and sparse-observation correction. WindINR maps static terrain descriptors, a low-resolution background field, and continuous query coordinates to a high-resolution wind state through a latent-conditioned decoder. To enable rapid inference-time correction, WindINR separates reusable representation learning from sample-specific latent-state correction. During training, a privileged encoder infers a reference latent state from high-resolution supervision, a deployable latent predictor estimates an initial latent state from inference-time inputs alone, and their discrepancies are summarized into a dataset-adaptive Gaussian prior over latent corrections. At inference time, within the WindINR module, network weights remain fixed and only the latent state is updated by minimizing a regularized correction objective using sparse observations and their uncertainty. In controlled OSSEs over the Senja region, including a UAV-aided approach scenario and random-observation robustness tests, WindINR improves local high-resolution wind estimates by updating only a compact latent state rather than the full network. The corrected representation remains continuously queryable at arbitrary coordinates and, in our CPU benchmark, yields about a $2.6\times$ online-correction speedup over full-network fine-tuning, suggesting a practical interface between kilometer-scale background products, sparse local observations, and wind queries in complex terrain.

Heterogeneous air-ground robot teams combine complementary sensing modalities, mobility characteristics, and spatial viewpoints that can significantly enhance perception in complex outdoor environments. However, progress in multi-robot collaborative perception has been constrained by the lack of real-world datasets featuring overlapping multi-modal observations from platforms operating in unstructured terrain. We present GA3T (Ground-Aerial Team for Terrain Traversal), a real-world multi-robot collaborative perception dataset collected using a Clearpath Husky UGV and an Autel EVOII UAV across diverse unstructured environments, including forest trails, rocky paths, muddy terrain, snow piles, and grass-covered fields. The ground platform provides 3D LiDAR, stereo camera, IMU, and GPS data, while the aerial platform contributes RGB imagery, thermal/infrared observations, and GPS from a complementary overhead viewpoint, allowing for rich cross-modal and cross-view perception. The dataset is collected in 4 unique environments, with over 13,000 synchronized frames across approximately 29 minutes of operation, and includes both SAM3-based zero-shot segmentation and over 8,000 manually labeled images. A unique aspect of the dataset is its early-spring collection period, during which sparse tree canopies allow the aerial robot to partially observe the ground robot and terrain through the trees, allowing for occlusion-aware collaborative perception. Unlike prior multi-robot datasets that focus on SLAM or simulated cooperative driving, GA3T is specifically designed to support research on cross-view perception, air-ground viewpoint fusion, traversability estimation, and collaborative scene understanding in real off-road environments.

Radar sounders are electromagnetic instruments that can probe deep into the subsurface of Earth and other planetary bodies by processing the echo of transmitted radar waves. Conventional approaches for analyzing such data rely on approximate assumptions and often produce point estimates that ignore parameter correlations as well as galactic and measurement noise. We propose a simulation-based inference approach to terrain parameter inversion from radar sounder data, where synthetic observations from a GPU-based simulator are used to train a neural network-based density estimator for neural posterior estimation (NPE). By explicitly conditioning on reference surface assumptions, the proposed framework allows systematic evaluation of posterior robustness to reference surface variability. We demonstrate that our NPE model is well calibrated on simulated data and transferable to real Mars radar profiles, where we analyze terrain parameters using literature-informed reference values.

The popular 2009 voxel based videogame, Minecraft, contains several distinct disciplines. One of which is "parkour," gameplay that focuses on traversing a world's environment with maximum efficiency. The Minecraft online community has turned the game's physics engine into dynamic puzzles, requiring players to masterfully manipulate motion mechanics through frame precise timing of keystrokes. Actions such as sprinting, sneaking, and mouse direction are all combined to clear specific difficult jumps. Through this project, we design a genetic algorithm to generate weights for a neural network to autonomously evaluate inputs for block distances, terrain, and obstacles to determine the most optimal pathing.

Accurate terrain perception is essential for terrain-following flight of agricultural unmanned aerial vehicles (UAVs), yet remains challenging in real-world farmland due to occlusions, complex terrain geometry, and environmental disturbances. Millimeter-wave (mmWave) radar is a promising sensing modality for this task due to its robustness to adverse conditions; however, existing UAV-mounted radar systems rely on fixed field of view (FoV) and terrain extraction methods designed for dense LiDAR data, leading to incomplete and unreliable terrain estimation. To address these limitations, we present a low-cost rotating mmWave radar-enabled terrain perception framework for agricultural UAVs operating in complex farmland environments. Specifically, a mechanically rotating sensing design is introduced to enlarge spatial coverage and improve terrain observability beyond the limitations of fixed-view radar under dynamic low-altitude flight. Building upon this sensing capability, we further design a pose-consistent terrain reconstruction pipeline tailored for sparse, noisy, and partially observable radar data, enabling reliable ground extraction and continuous terrain surface estimation in challenging agricultural scenarios. The complete system is deployed on a real agricultural UAV platform and comprehensively evaluated through extensive field experiments. Experimental results demonstrate improved terrain coverage and estimation accuracy, achieving an F1 score of 94.42 for ground segmentation, while the closest rival only achieves 90.48. Thus, leading to more robust terrain following flight.