For robots to navigate safely and efficiently on soft, granular terrains, it is crucial to gather information about the terrain's mechanical properties, which directly affect locomotion performance. Recent research has developed robotic legs that can accurately sense ground reaction forces during locomotion. However, existing tests of granular property estimation often rely on specific foot trajectories, such as vertical penetration or horizontal shear, limiting their applicability during natural locomotion. To address this limitation, we introduce a physics-informed machine learning framework, Inverse Resistive Force Theory (I-RFT), which integrates the Granular Resistive Force Theory model with Gaussian Processes to infer terrain properties from proprioceptively measured contact forces under arbitrary gait trajectories. By embedding the granular force model within the learning process, I-RFT preserves physical consistency while enabling generalization across diverse motion primitives. Experimental results demonstrate that I-RFT accurately estimates terrain properties across multiple gait trajectories and toe shapes. Moreover, we show that the quantified uncertainty over the terrain resistance stress map could enable robots to optimize foot design and gait trajectories for efficient information gathering. This approach establishes a new foundation for data-efficient characterization of complex granular environments and opens new avenues for locomotion strategies that actively adapt gait for autonomous terrain exploration.

Robot-aided exploration of planetary surfaces is essential for understanding geologic processes, yet many scientifically valuable regions, such as Martian dunes and lunar craters, remain hazardous due to loose, deformable regolith. We present a scout-rover cooperation framework that expands safe access to such terrain using a hybrid team of legged and wheeled robots. In our approach, a high-mobility legged robot serves as a mobile scout, using proprioceptive leg-terrain interactions to estimate regolith strength during locomotion and construct spatially resolved terrain maps. These maps are integrated with rover locomotion models to estimate traversal risk and inform path planning. We validate the framework through analogue missions at the NASA Ames Lunar Simulant Testbed and the White Sands Dune Field. Experiments demonstrate (1) online terrain strength mapping from legged locomotion and (2) rover-specific traversal-risk estimation enabling safe navigation to scientific targets. Results show that scout-generated terrain maps reliably capture spatial variability and predict mobility failure modes, allowing risk-aware path planning that avoids hazardous regions. By combining embodied terrain sensing with heterogeneous rover cooperation, this framework enhances operational robustness and expands the reachable science workspace in deformable planetary environments.

Locomotion on granular slopes such as sand dunes remains a fundamental challenge for legged robots due to reduced shear strength and gravity-induced anisotropic yielding of granular media. Using a hexapedal robot on a tiltable granular bed, we systematically measure locomotion speed together with slope-dependent normal and shear granular resistive forces. While normal penetration resistance remains nearly unchanged with inclination, shear resistance decreases substantially as slope angle increases. Guided by these measurements, we develop a simple robot-terrain interaction model that predicts anchoring timing, step length, and resulting robot speed, as functions of terrain strength and slope angle. The model reveals that slope-induced performance loss is primarily governed by delayed anchoring and increased backward slip rather than excessive sinkage. By extending the model to generalized terrain conditions, we construct failure phase diagrams that identify sinkage- and slippage-induced failure regimes, enabling quantitative risk estimation for locomotion on granular slopes. This physics-informed framework provides predictive insight into terrain-dependent failure mechanisms and offers guidance for safer and more robust robot operation on deformable inclines.

Deformable substrates such as sand and mud present significant challenges for terrestrial robots due to complex robot-terrain interactions. Inspired by mudskippers, amphibious animals that naturally adjust their tail morphology and movement jointly to navigate such environments, we investigate how tail design and control can jointly enhance flipper-driven locomotion on granular media. Using a bio-inspired robot modeled after the mudskipper, we experimentally compared locomotion performance between idle and actively oscillating tail configurations and found that tail oscillation increased forward speed by 17% while reducing body drag by 46%. Shear force measurements revealed that this improvement arises from oscillation-induced fluidization of the substrate, which lowers resistive forces acting on the body. Additionally, tail morphology strongly influenced the oscillation strategy: designs with larger horizontal surface areas leveraged the oscillation-induced reduction in shear resistance more effectively by limiting insertion depth. Based on these findings, we present a design principle to inform tail action selection based on substrate strength and tail morphology. Our results offer new insights into tail design and control for improving robot locomotion on deformable substrates, with implications for agricultural robotics, search and rescue, and environmental exploration.

Robots that traverse natural terrain must interpret contact forces generated under highly dynamic conditions. However, most terrain characterization approaches rely on quasi-static assumptions that neglect velocity- and acceleration-dependent effects arising during impact and rapid stance transitions. In this work, we investigate granular terrain interaction during high-speed hopping and develop a physics-based framework for dynamic terrain characterization using proprioceptive sensing alone. Through controlled hopping experiments with systematically varied impact speed and leg compliance, our measurements reveal that quasi-static based assumptions lead to large discrepancies in granular terrain property estimation during high-speed hopping, particularly upon touchdown and controller-induced stiffness transitions. Velocity-dependent drag alone cannot explain these discrepancies. Instead, acceleration-dependent added-mass effects-associated with grain entrainment beneath the foot-dominate transient force responses. We integrate this force decomposition with a momentum-observer-based estimator that compensates for rigid-body inertia and gravity, and introduce an acceleration-aware weighted regression to account for increased force variance during high-acceleration events. Together, these methods enable consistent recovery of granular stiffness parameters across locomotion conditions, closely matching linear-actuator ground truth. Our results demonstrate that accurate terrain inference during high-speed locomotion requires explicit treatment of acceleration-dependent granular effects, and provide a foundation for robots to characterize complex deformable terrain during dynamic exploration of terrestrial and planetary environments.

Deformable granular terrains introduce significant locomotion and immobilization risks in planetary exploration and are difficult to detect via remote sensing (e.g., vision). Legged robots can sense terrain properties through leg-terrain interactions during locomotion, offering a direct means to assess traversability in deformable environments. How to systematically exploit this interaction-derived information for navigation planning, however, remains underexplored. We address this gap by presenting PSANE, a Proprioceptive Safe Active Navigation and Exploration framework that leverages leg-terrain interaction measurements for safe navigation and exploration in unknown deformable environments. PSANE learns a traversability model via Gaussian Process regression to estimate and certify safe regions and identify exploration frontiers online, and integrates these estimates with a reactive controller for real-time navigation. Frontier selection is formulated as a multi-objective optimization that balances safe-set expansion probability and goal-directed cost, with subgoals selected via scalarization over the Pareto-optimal frontier set. PSANE safely explores unknown granular terrain and reaches specified goals using only proprioceptively estimated traversability, while achieving performance improvements over baseline methods.

The ability to efficiently and effectively explore planetary surfaces is currently limited by the capability of wheeled rovers to traverse challenging terrains, and by pre-programmed data acquisition plans with limited in-situ flexibility. In this paper, we present two novel approaches to address these limitations: (i) high-mobility legged robots that use direct surface interactions to collect rich information about the terrain's mechanics to guide exploration; (ii) human-inspired data acquisition algorithms that enable robots to reason about scientific hypotheses and adapt exploration priorities based on incoming ground-sensing measurements. We successfully verify our approach through lab work and field deployments in two planetary analog environments. The new capability for legged robots to measure soil mechanical properties is shown to enable effective traversal of challenging terrains. When coupled with other geologic properties (e.g., composition, thermal properties, and grain size data etc), soil mechanical measurements reveal key factors governing the formation and development of geologic environments. We then demonstrate how human-inspired algorithms turn terrain-sensing robots into teammates, by supporting more flexible and adaptive data collection decisions with human scientists. Our approach therefore enables exploration of a wider range of planetary environments and new substrate investigation opportunities through integrated human-robot systems that support maximum scientific return.

Muddy terrains present significant challenges for terrestrial robots, as subtle changes in composition and water content can lead to large variations in substrate strength and force responses, causing the robot to slip or get stuck. This paper presents a method to estimate mud properties using proprioceptive sensing, enabling a flipper-driven robot to adapt its locomotion through muddy substrates of varying strength. First, we characterize mud reaction forces through actuator current and position signals from a statically mounted robotic flipper. We use the measured force to determine key coefficients that characterize intrinsic mud properties. The proprioceptively estimated coefficients match closely with measurements from a lab-grade load cell, validating the effectiveness of the proposed method. Next, we extend the method to a locomoting robot to estimate mud properties online as it crawls across different mud mixtures. Experimental data reveal that mud reaction forces depend sensitively on robot motion, requiring joint analysis of robot movement with proprioceptive force to determine mud properties correctly. Lastly, we deploy this method in a flipper-driven robot moving across muddy substrates of varying strengths, and demonstrate that the proposed method allows the robot to use the estimated mud properties to adapt its locomotion strategy, and successfully avoid locomotion failures. Our findings highlight the potential of proprioception-based terrain sensing to enhance robot mobility in complex, deformable natural environments, paving the way for more robust field exploration capabilities.

Granular friction μ is a sensitive and poorly understood function of packing fraction ϕ. Every granular material has a distinct critical volume fraction ϕc that delineates two mechanical deformation modes – compaction for ϕ < ϕc, and dilation for ϕ > ϕc. Here we examine the relation(s) between friction and packing fraction, using quasi-static penetration tests in materials ranging from glass beads to highly heterogeneous lunar regolith simulant. Noncohesive materials collapse onto a master curve that relates changes in friction to the distance from ϕc, confirming that the handoff from compaction to dilation is a phase transition. The mechanical distinction between compaction and dilation regimes is highlighted with the addition of cohesive dust – relevant for lunar regolith – which has little effect for ϕ < ϕc, but drastically enhances strength for ϕ > ϕc. Our simple model improves predictions of granular resistance to intrusion, which can help to explore and manipulate soils on Earth and regolith on other planets. A reanalysis of Apollo era lunar penetration tests demonstrates the promise of our approach.

In-situ robotic exploration is an important tool for advancing knowledge of geological processes that describe the Earth and other Planetary bodies. To inform and enhance operations for these roving laboratories, it is imperative to understand the terramechanical properties of their environments, especially for traversing on loose, deformable substrates. Recent research suggested that legged robots with direct-drive and low-gear ratio actuators can sensitively detect external forces, and therefore possess the potential to measure terrain properties with their legs during locomotion, providing unprecedented sampling speed and density while accessing terrains previously too risky to sample. This paper explores these ideas by investigating the impact of gait on proprioceptive terrain sensing accuracy, particularly comparing a sensing-oriented gait, Crawl N' Sense, with a locomotion-oriented gait, Trot-Walk. Each gait's ability to measure the strength and texture of deformable substrate is quantified as the robot locomotes over a laboratory transect consisting of a rigid surface, loose sand, and loose sand with synthetic surface crusts. Our results suggest that with both the sensing-oriented crawling gait and locomotion-oriented trot gait, the robot can measure a consistent difference in the strength (in terms of penetration resistance) between the low- and high-resistance substrates; however, the locomotion-oriented trot gait contains larger magnitude and variance in measurements. Furthermore, the slower crawl gait can detect brittle ruptures of the surface crusts with significantly higher accuracy than the faster trot gait. Our results offer new insights that inform legged robot "sensing during locomotion" gait design and planning for scouting the terrain and producing scientific measurements on other worlds to advance our understanding of their geology and formation.

Legged robots have the potential to leverage obstacles to climb steep sand slopes. However, efficiently repositioning these obstacles to desired locations is challenging. Here we present DiffusiveGRAIN, a learning-based method that enables a multi-legged robot to strategically induce localized sand avalanches during locomotion and indirectly manipulate obstacles. We conducted 375 trials, systematically varying obstacle spacing, robot orientation, and leg actions in 75 of them. Results show that movement of closely-spaced obstacles exhibit significant interference, requiring joint modeling. In addition, different multi-leg excavation actions could cause distinct robot state changes, necessitating integrated planning of manipulation and locomotion. To address these challenges, DiffusiveGRAIN includes a diffusion-based environment predictor to capture multi-obstacle movements under granular flow interferences and a robot state predictor to estimate changes in robot state from multi-leg action patterns. Deployment experiments (90 trials) demonstrate that by integrating the environment and robot state predictors, the robot can autonomously plan its movements based on loco-manipulation goals, successfully shifting closely located rocks to desired locations in over 65% of trials. Our study showcases the potential for a locomoting robot to strategically manipulate obstacles to achieve improved mobility on challenging terrains. Supplementary material is available at https://sites.google.com/view/diffusivegrain/home.

The capability of effectively moving on complex terrains such as sand and gravel can empower our robots to robustly operate in outdoor environments, and assist with critical tasks such as environment monitoring, search-and-rescue, and supply delivery. Inspired by the Mount Lyell salamander's ability to curl its body into a loop and effectively roll down hill slopes, in this study we develop a sand-rolling robot and investigate how its locomotion performance is governed by the shape of its body. We experimentally tested three different body shapes: Hexagon, Quadrilateral, and Triangle. We found that Hexagon and Triangle can achieve a faster rolling speed on sand, but exhibited more frequent failures of getting stuck. Analysis of the interaction between robot and sand revealed the failure mechanism: the deformation of the sand produced a local “sand incline” underneath robot contact segments, increasing the effective region of supporting polygon (ERSP) and preventing the robot from shifting its center of mass (CoM) outside the ERSP to produce sustainable rolling. Based on this mechanism, a highly-simplified model successfully captured the critical body pitch for each rolling shape to produce sustained rolling on sand, and informed design adaptations that mitigated the locomotion failures and improved robot speed by more than 200%. Our results provide insights into how locomotors can utilize different morphological features to achieve robust rolling motion across deformable substrates.

Legged robots can sense terrain through force interactions during locomotion, offering more reliable traversability estimates than remote sensing and serving as scouts for guiding wheeled rovers in challenging environments. However, even legged scouts face challenges when traversing highly deformable or unstable terrain. We present Safe Active Exploration for Granular Terrain (SAEGT), a navigation framework that enables legged robots to safely explore unknown granular environments using proprioceptive sensing, particularly where visual input fails to capture terrain deformability. SAEGT estimates the safe region and frontier region online from leg-terrain interactions using Gaussian Process regression for traversability assessment, with a reactive controller for real-time safe exploration and navigation. SAEGT demonstrated its ability to safely explore and navigate toward a specified goal using only proprioceptively estimated traversability in simulation.

Modeling and controlling legged robot locomotion on terrains with densely distributed large rocks and boulders are fundamentally challenging. Unlike traditional methods, which often consider these rocks and boulders as obstacles and attempt to find a clear path to circumvent them, in this study, we aim to develop methods for robots to actively utilize interaction forces with these "obstacles" for locomotion and navigation. To do so, we studied the locomotion of a quadrupedal robot as it traversed a simplified obstacle field with 12 different gaits and discovered that with each gait, the robot could passively converge to a distinct orientation. A compositional return map explained this observed passive convergence and enabled prediction of the steady-state orientation angles for each quadrupedal gait. We experimentally demonstrated that with these predictions, a legged robot could effectively generate the desired shape of trajectories among large, slippery obstacles, simply by switching between different gaits. Our study offered a novel method for robots to exploit traditionally-considered "obstacles" to achieve agile movements on challenging terrains.

Legged robot locomotion on sand slopes is challenging due to the complex dynamics of granular media and how the lack of solid surfaces can hinder locomotion. A promising strategy, inspired by ghost crabs and other organisms in nature, is to strategically interact with rocks, debris, and other obstacles to facilitate movement. To provide legged robots with this ability, we present a novel approach that leverages avalanche dynamics to indirectly manipulate objects on a granular slope. We use a Vision Transformer (ViT) to process image representations of granular dynamics and robot excavation actions. The ViT predicts object movement, which we use to determine which leg excavation action to execute. We collect training data from 100 real physical trials and, at test time, deploy our trained model in novel settings. Experimental results suggest that our model can accurately predict object movements and achieve a success rate >= 80% in a variety of manipulation tasks with up to four obstacles, and can also generalize to objects with different physics properties. To our knowledge, this is the first paper to leverage granular media avalanche dynamics to indirectly manipulate objects on granular slopes. Supplementary material is available at https://sites.google.com/view/grain- corl2024/home.

Moving down a hillslope from ridge to valley, soil develops and becomes increasingly weathered. Downslope variation in clay content, organic matter, and porosity should produce concomitant changes in soil strength that influence slope stability and erosion. This has yet to be demonstrated, however, because in-situ measurements of soil rheology are challenging and rare. Here we employ a robotic leg as a mechanically sensitive and time-efficient penetrometer to map soil strength along a canonical temperate hillslope profile. We observe a systematic downslope weakening, and increasing heterogeneity, of soil strength associated with a transition from sand-rich ridge materials to cohesive valley bottom soil aggregates. Weathering-induced changes in soil composition lead to physically distinct mechanical behaviors in cohesive soils that depart from the behavior observed for sand. We also demonstrate the promise that legged robots may use their limbs to sense and improve mobility in complex environments, with implications for planetary exploration.

Truly collaborative scientific field data collection between human scientists and autonomous robot systems requires a shared understanding of the search objectives and tradeoffs faced when making decisions. Therefore, critical to developing intelligent robots to aid human experts, is an understanding of how scientists make such decisions and how they adapt their data collection strategies when presented with new information in situ . In this study we examined the dynamic data collection decisions of 108 expert geoscience researchers using a simulated field scenario. Human data collection behaviors suggested two distinct objectives: an information-based objective to maximize information coverage, and a discrepancy-based objective to maximize hypothesis verification. We developed a highly-simplified quantitative decision model that allows the robot to predict potential human data collection locations based on the two observed human data collection objectives. Predictions from the simple model revealed a transition from information-based to discrepancy-based objective as the level of information increased. The findings will allow robotic teammates to connect experts’ dynamic science objectives with the adaptation of their sampling behaviors, and in the long term, enable the development of more cognitively-compatible robotic field assistants.

Moving on natural muddy terrains, where soil composition and water content vary significantly, is complex and challenging. To understand how mud properties and robot-mud interaction strategies affect locomotion performance on mud, we study the terrestrial locomotion of a mudskipper-inspired robot on synthetic mud with precisely-controlled ratios of sand, clay, and water. We observed a non-monotonic dependence of the robot speed on mud water content. Robot speed was the largest on mud with intermediate levels of water content (25%–26%), but decreased significantly on higher or lower water content. Measurements of mud reaction force revealed two distinct failure mechanisms. At high water content, the reduced mud shear strength led to a large slippage of robot appendages and a significantly reduced step length. At low water content, the increased mud suction force caused appendage entrapment, resulting in a large negative displacement in the robot body during the swing phase. A simple model successfully captured the observed robot performance, and informed adaptation strategies that increased robot speed by more than 200%. Our study is a beginning step to extend robot mobility beyond simple substrates towards a wider range of complex, heterogeneous terrains.

Effective human-robot collaboration requires robot to adopt their roles and levels of support based on human needs, task requirements, and complexity. Traditional human-robot teaming often relies on a pre-determined robot communication scheme, restricting teamwork adaptability in complex tasks. Leveraging strong communication capabilities of Large Language Models (LLMs), we propose a Human-Robot Teaming Framework with Multi-Modal Language feedback (HRT-ML), a framework designed to enhance human-robot interaction by adjusting the frequency and content of language-based feedback. HRT-ML framework includes two core modules: a Coordinator for high-level, low-frequency strategic guidance, and a Manager for subtask-specific, high-frequency instructions, enabling passive and active interactions with human teammates. To assess the impact of language feedback in collaborative scenarios, we conducted experiments in an enhanced Overcooked environment with varying levels of task complexity (easy, medium, hard) and feedback frequency (inactive, passive, active, superactive). Our results show that as task complexity increases relative to human capabilities, human teammates exhibited a stronger preference towards robotic agents that can offer frequent, proactive support. However, when task complexities exceed the LLM's capacity, noisy and inaccurate feedback from superactive robotic agents can instead hinder team performance, as it requires human teammates to increase their effort to interpret and respond to a large number of communications, with limited performance return. Our results offer a general principle for robotic agents to dynamically adjust their levels and frequencies of communications to work seamlessly with humans and achieve improved teaming performance.

Our analysis of human sampling decision data reveals that scientists adapt their sampling strategies to balance multiple objectives based on two key factors: the current level of information about the environment, and the availability of sampling location options with large potential rewards. While this work is only a beginning step towards the development of cognitive-compatible robotic decision algorithms, our findings show by better understanding human decision processes, robots can use extremely simple algorithms to connect experts' high-level objectives to desired sampling locations while balancing multiple objectives. Going forward, exploring how humans coordinate and prioritize multiple objectives under more sophisticated scientific exploration scenarios, such as with multiple competing hypotheses, with hypotheses regarding multiple variables, or with additional sampling objectives, would be helpful to explore. These understandings could help our robots produce explainable sampling strategies that are well-aligned with humans' high level goals, and improve humans' trust and confidence during teaming. These cognitive understandings could also allow robots to identify potential vulnerabilities in human decisions, such as biases and fatigue, and provide targeted support to enhance scientific outcomes. In addition, we expect that these cognitive insights could complement existing robotic decision methods by informing which algorithms to use, and eventually empower robots to become intelligent teammates that can truly participate in the decision-making process.