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To provide the necessary theoretical models of sphere–soil interaction for the structural design, motion control, and simulation of spherical robots, this paper derives analytical expressions for traction force and driving torque when spherical robots slide and sink into sandy terrain, based on terramechanics and multibody dynamics. Furthermore, orthogonal experimental analysis identifies the load, joint angular acceleration, and maximum joint angular velocity of spherical robots as influencing factors, highlighting that the load significantly affects their longitudinal motion performance. Experimental results indicate that rolling friction and additional resistance on sandy terrain cannot be ignored. The corrected theoretical model effectively replicates the temporal variation of driving torque exerted by spherical robots on sandy terrain. Numerical computations and experimental analyses demonstrate that increasing the radius of the sphere shell, the load, and the slip ratio all lead to increased traction force and driving torque. However, traction force and driving torque begin to decrease once the slip ratio reaches approximately 0.5. Therefore, in the design of spherical robot structures and control laws, appropriate parameters such as load and slip ratio should be chosen based on the established sphere–soil interaction theoretical model to achieve high-quality longitudinal motion performance on sandy terrain. [ABSTRACT FROM AUTHOR]

In the development of lunar and planetary exploration rovers, risk assessment in on-site environments comprising fine regoliths and unevenly distributed rocks is essential. To prevent a rover from being stuck during its operation, one must understand the behavior of its wheel when it climbs over rigid obstacles in off-road environments. In this study, we apply an extended terramechanics model, which can reasonably describe the interaction between soft ground and vehicles, to analyze the obstacle-climbing behavior of rigid wheels. To describe the interaction between the wheel and a hard obstacle, we combine the penalty method with the extended terramechanics model. Subsequently, we verify the effectiveness of the proposed method by comparing its results with those of a traversing single wheel obtained from a laboratory experiment. Furthermore, we use the model to perform a multibody dynamics analysis on a simple rover, where its applicability to the examination of the overall performance of obstacle climbing is demonstrated. [ABSTRACT FROM AUTHOR]

In order to investigate the soil reactions influenced by the single plate with the inclination angles from 0° to 75°, an in-house code of 2D DEM has been developed in this study. An iron flat plate penetrated soil by a constant velocity of 1 mm/s in the study. In the penetration test, the maximum vertical force was 753.8 N which was generated by the 0° plate. In addition, it was found that the less the inclination angle, the greater the vertical force. Furthermore, a greater force in the horizontal direction has been generated at 45° of the inclination angle. This research can provide a theoretical reference for optimizing tools that contact soil, for example, patterns/lugs on wheels, earthmoving blades (such as rotary cultivators, bulldozers, weeding machines etc.) and grouser of tracks. [ABSTRACT FROM AUTHOR]

The soil contact model (SCM) is widely used in practice for off‐road wheeled vehicle mobility studies when simulation speed is important and highly accurate results are not a main concern. In practice, the SCM parameters are obtained via a bevameter test, which requires a complex apparatus and experimental procedure. Here, we advance the idea of running a virtual bevameter test using a high‐fidelity terramechanics simulation. The latter employs the "continuous representation model" (CRM), which regards the deformable terrain as an elasto‐plastic continuum that is spatially discretized using the smoothed particle hydrodynamics method. The approach embraced is as follows: a virtual bevameter test is run in simulation using CRM terrain to generate "ground truth" data; in a Bayesian framework, this data is subsequently used to calibrate the SCM terrain. We show that (i) the resulting SCM terrain, while leading to fast terramechanics simulations, serves as a good proxy for the more complex CRM terrain; and (ii) the SCM‐over‐CRM simulation speedup is roughly one order of magnitude. These conclusions are reached in conjunction with two tests: a single wheel test, and a full rover simulation. The SCM and CRM simulations are run in the open‐source software Chrono. The calibration is performed using PyMC, which is a Python package that interactively communicates with Chrono to calibrate SCM. The models and scripts used in this contribution are available as open source for unfettered use and distribution in a public repository. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of contact parameters (slippage and sinkage) estimation for multi-modal robot locomotion on granular terrains. To describe the contact events in the same framework for robots operated at different modes (e.g., wheel, leg), we propose a unified description of contact parameters for multi-modal robots. We also provide a parameter estimation method for multi-modal robots based on CNN and DWT (discrete wavelet transformation) techniques and verify its effectiveness over different types of granular terrains. Besides motion modes, this paper also considers the influence of slope angles and the robot's handing angles over contact parameters. Through comparison and analysis of the prediction results, our method can not only effectively predict the contact parameters of multi-modal robot locomotion on a granular medium (better than $96\%$ accuracy) but also achieves the same or better performance when compared to other (direct) contact measurement methods designed for individual motion modes, that is, single-modal robots such as quadruped robots and mars rovers. Our proposed unified contact parameter estimation method can be useful for studying the interaction mechanics between multi-modal robots and granular terrains as well as terrain classification tasks due to its superior sensitivity which is analyzed in the experiments. [ABSTRACT FROM AUTHOR]

Due to the numerous variables that may influence the soil-machine interaction systems, predicting the mechanical response of soil interacting with off-road traction equipment is challenging. In this study, deep neural networks (DNNs) are chosen as a potential solution for explaining the varying soil sinkage rates because of their ability to model complex, multivariate, and dynamic systems. Plate sinkage tests were carried out using a Bevameter in a fixed-type soil bin with a 24 m length, 2 m width, and 1 m depth. Experimental tests were conducted at three sinkage rates for two plate sizes, with a soil water content of 10%. The provided empirical data on the soil pressure-sinkage relationship served as the basis for an algorithm capable of discerning the soil-machine interaction. From the iterative process, it was determined that a DNN, specifically a feed-forward back-propagation DNN with three hidden layers, is the optimal choice. The optimized DNN architecture is structured as 3-8-15-10-1, as determined by the Grey Wolf Optimization algorithm. While the Bekker equation had traditionally been employed as a widely accepted method for predicting soil pressure-sinkage behavior, it typically disregarded the influence of sinkage velocity of the soil. However, the findings revealed the significant impact of sinkage velocity on the parameters governing the soil deformation response. The trained DNN successfully incorporated the sinkage velocity into its structure and provided accurate results with an MSE value of 0.0871.

Vehicles often experience low tire pressures and high torques in off-road operations, making tire–rim slip likely. Tire–rim slip is undesirable relative rotation between the tire and rim, which, in this study, is measured by the relative tire–rim slip rate. There is little research on the effect of different terrains on tire–rim slip despite its significance for off-road driving; therefore, this topic was explored through Finite Element Analysis (FEA) simulations. An upland sandy loam soil was modelled and calibrated using Smoothed-Particle Hydrodynamics (SPH), and then a Regional Haul Drive (RHD) truck tire was simulated driving over this terrain, with a drawbar load added to increase drive torque. To examine their effects, five parameters were changed: tire–rim friction coefficient, longitudinal wheel speed, drawbar load, vertical load, and inflation pressure. The simulations showed that increasing the tire–rim friction coefficient and the inflation pressure decreased the tire–rim slip while increasing the vertical and drawbar loads increased the tire–rim slip. Varying the longitudinal wheel speed had no significant effect. Tire–rim slip was more likely to occur on the soil because it happened at lower drawbar loads on the soil than on the hard surface. These research results increased knowledge of tire–rim slip mechanics and provided a foundation for exploring tire–rim slip on other terrains, such as clays or sands.

Vehicles often experience low tire pressures and high torques in off-road operations, making tire–rim slip likely. Tire–rim slip is undesirable relative rotation between the tire and rim, which, in this study, is measured by the relative tire–rim slip rate. There is little research on the effect of different terrains on tire–rim slip despite its significance for off-road driving; therefore, this topic was explored through Finite Element Analysis (FEA) simulations. An upland sandy loam soil was modelled and calibrated using Smoothed-Particle Hydrodynamics (SPH), and then a Regional Haul Drive (RHD) truck tire was simulated driving over this terrain, with a drawbar load added to increase drive torque. To examine their effects, five parameters were changed: tire–rim friction coefficient, longitudinal wheel speed, drawbar load, vertical load, and inflation pressure. The simulations showed that increasing the tire–rim friction coefficient and the inflation pressure decreased the tire–rim slip while increasing the vertical and drawbar loads increased the tire–rim slip. Varying the longitudinal wheel speed had no significant effect. Tire–rim slip was more likely to occur on the soil because it happened at lower drawbar loads on the soil than on the hard surface. These research results increased knowledge of tire–rim slip mechanics and provided a foundation for exploring tire–rim slip on other terrains, such as clays or sands. [ABSTRACT FROM AUTHOR]

A planetary exploration rover has been employed for scientific endeavors or as a precursor for upcoming manned missions. Predicting rover traversability from its wheel slip ensures safe and efficient autonomous operations of rovers on deformable planetary surfaces; path planning algorithms that reduce slips by considering wheel-soil interaction or terrain data can minimize the risk of the rover becoming immobilized. Understanding wheel-soil interaction in transient states is vital for developing a more precise slip ratio prediction model, while path planning in the past assumes that slips generated at the path is a series of slip ratio in steady state. In this paper, we focus on the transient slip, or slip rate the time derivative of slip ratio, to explicitly address it into the cost function of path planning algorithm. We elaborated a regression model that takes slip rate and traction force as inputs and outputs slip ratio, which is employed in the cost function to minimize the rover slip in path planning phase. Experiments using a single wheel testbed revealed that even with the same wheel traction force, the slip ratio varies with different slip rates; we confirmed that the smaller the absolute value of the slip rate, the larger the slip ratio for the same traction force. The statistical analysis of the regression model confirms that the model can estimate the slip ratio within an accuracy of 85% in average. The path planning simulation with the regression model confirmed a reduction of 58% slip experienced by the rover when driving through rough terrain environments. The dynamics simulation results insisted that the proposed method can reduce the slip rate in rough terrain environments. [ABSTRACT FROM AUTHOR]

• Counter-rotating Archimedean screws enable locomotion across challenging terrains. • Only a few terramechanics models for screws have been published and have limitations. • We present a novel testing apparatus to perform scroll terramechanics experiments. • Hardware tests show system will be useful for future terramechanics model development. Modeling the force interaction between a wheel and the ground is necessary when evaluating the effectiveness of a vehicle's mobility on challenging terrain. Soft soils with low bearing strength are a particularly difficult medium for wheeled vehicles. Helical scrolls have shown promise as an alternative to wheels which can work across a range of terrains, warranting a detailed terramechanics study to model their capabilities. Most of the existing terramechanics literature is limited to wheels and often employs an apparatus to study single wheels in a fixed geometry. This paper describes the design and implementation of a novel apparatus capable of housing a range of scroll geometries and configurations. The apparatus is comprised of a soil container, carriage to drive the scroll in two operating configurations, and a surrounding frame that enables both vertical and horizontal motions of the carriage. The carriage is outfitted with a drive system and instrumentation to measure the sinkage, stress, and drawbar pull values required for a terramechanics characterization. Initial stress-sinkage curves for three different scroll configurations align with expected results and provide a proof of concept that the proposed apparatus can successfully measure differing geometric parameters and can be used for further terramechanics characterizations. [ABSTRACT FROM AUTHOR]

Due to the numerous variables that may influence the soil-machine interaction systems, predicting the mechanical response of soil interacting with off-road traction equipment is challenging. In this study, deep neural networks (DNNs) are chosen as a potential solution for explaining the varying soil sinkage rates because of their ability to model complex, multivariate, and dynamic systems. Plate sinkage tests were carried out using a Bevameter in a fixed-type soil bin with a 24 m length, 2 m width, and 1 m depth. Experimental tests were conducted at three sinkage rates for two plate sizes, with a soil water content of 10%. The provided empirical data on the soil pressure-sinkage relationship served as the basis for an algorithm capable of discerning the soilmachine interaction. From the iterative process, it was determined that a DNN, specifically a feed-forward backpropagation DNN with three hidden layers, is the optimal choice. The optimized DNN architecture is structured as 3-8-15-10-1, as determined by the Grey Wolf Optimization algorithm. While the Bekker equation had traditionally been employed as a widely accepted method for predicting soil pressure-sinkage behavior, it typically disregarded the influence of sinkage velocity of the soil. However, the findings revealed the significant impact of sinkage velocity on the parameters governing the soil deformation response. The trained DNN successfully incorporated the sinkage velocity into its structure and provided accurate results with an MSE value of 0.0871. [ABSTRACT FROM AUTHOR]

Three parameters of soil, vertical load and tire play a role in determining vehicle traction force in the process of soil and tire interaction. The complexity of the situation and the variability of variables such as the soil-tire contact area and contact pressure make it difficult to develop traction force estimation models. In this study, the first step involved developing a traction force prediction model under the assumption of a variable contact area and contact pressure, and developing a mathematical model to predict off-road vehicle traction force. The obtained model includes seven parameters related to tire, load, soil and tire dynamics of wheel movement, which are vertical load, soil-tire contact length, tire width, slip, soil cohesion, soil shear deformation parameter and angle of internal shear resistance. A statistical population with five levels for each of its component parameters was created to study the impact of those parameters. The Taguchi method was used to examine the relationship between parameters and traction force. The Taguchi method is employed to determination the key factors that significantly impact a process, also it employs a systematic experimental design, to minimize the number of experiments needed. The results confirmed that all seven parameters had a significant impact on the amount of traction force and established the relative importance of their effects on one another. As a result, the tire width and slip parameters played the most and the least roles in improving traction force, respectively.

To provide the necessary theoretical models of sphere–soil interaction for the structural design, motion control, and simulation of spherical robots, this paper derives analytical expressions for traction force and driving torque when spherical robots slide and sink into sandy terrain, based on terramechanics and multibody dynamics. Furthermore, orthogonal experimental analysis identifies the load, joint angular acceleration, and maximum joint angular velocity of spherical robots as influencing factors, highlighting that the load significantly affects their longitudinal motion performance. Experimental results indicate that rolling friction and additional resistance on sandy terrain cannot be ignored. The corrected theoretical model effectively replicates the temporal variation of driving torque exerted by spherical robots on sandy terrain. Numerical computations and experimental analyses demonstrate that increasing the radius of the sphere shell, the load, and the slip ratio all lead to increased traction force and driving torque. However, traction force and driving torque begin to decrease once the slip ratio reaches approximately 0.5. Therefore, in the design of spherical robot structures and control laws, appropriate parameters such as load and slip ratio should be chosen based on the established sphere–soil interaction theoretical model to achieve high-quality longitudinal motion performance on sandy terrain.

• Grouser in coastal terrains. • Experimental tests on physical and mechanical properties of costal terrains. • Effect of grouser shape ratio on thrust. • Discrete element method (DEM) for optimal shape ratio of a grouser. • Terramechanical experiment to validate DEM model. Using the discrete element method (DEM), this study derived the optimal shape ratio of a grouser driving in a coastal terrain. To develop a DEM model that considers the properties of the coastal terrain, experiments were performed on the physical and mechanical properties of the terrain, and parameters of the DEM model were calibrated using the experimental results. In addition, a terramechanical experiment was performed to validate the DEM model, for which parameters were calibrated. Furthermore, simulations were performed on the change in thrust according to the existence or nonexistence of the grouser and the change in thrust and sinkage according to the shape ratio using the validated DEM model. Consequently, the track with grouser generated a larger thrust than that without the grouser. Thus, the optimal shape ratio range of coastal terrain was derived using the DEM model, considering the mechanical properties of the terrain. [ABSTRACT FROM AUTHOR]

Three parameters of soil, vertical load and tire play a role in determining vehicle traction force in the process of soil and tire interaction. The complexity of the situation and the variability of variables such as the soiltire contact area and contact pressure make it difficult to develop traction force estimation models. In this study, the first step involved developing a traction force prediction model under the assumption of a variable contact area and contact pressure, and developing a mathematical model to predict off-road vehicle traction force. The obtained model includes seven parameters related to tire, load, soil and tire dynamics of wheel movement, which are vertical load, soil-tire contact length, tire width, slip, soil cohesion, soil shear deformation parameter and angle of internal shear resistance. A statistical population with five levels for each of its component parameters was created to study the impact of those parameters. The Taguchi method was used to examine the relationship between parameters and traction force. The Taguchi method is employed to determination the key factors that significantly impact a process, also it employs a systematic experimental design, to minimize the number of experiments needed. The results confirmed that all seven parameters had a significant impact on the amount of traction force and established the relative importance of their effects on one another. As a result, the tire width and slip parameters played the most and the least roles in improving traction force, respectively. [ABSTRACT FROM AUTHOR]

Penetration detection is an important method for in-situ scientific exploration of planetary surfaces, and is used to indirectly detect the mechanical properties of planetary subsurface soil. In this study, four ogive-nosed penetrators with different radii were simulated to penetrate planetary soil of varying compactness under different impact velocities using a nonlinear finite element (FE) method based on HyperMesh/LS-DYNA. A nonparametric estimation method was proposed through analysis of the corresponding results. Three main characteristic parameters in the penetration process were adopted in the method: maximum deceleration a m , penetration depth z , and trajectory deviation x p. Twenty parameters for identifying planetary soil properties were derived based on these three characteristic parameters. The terrain consisted of simulant soil classified non-parametrically and artificially defined as three states (low, medium, and high compactness) based on different harnesses, and five estimation criteria (slack, ideal, partially strict, relatively strict, and strict) were proposed. Three identification parameters were derived through the analysis of the evaluation indices (identification rate η i , accurate rate η a , and conservative rate η c) under different estimation criteria. a m 2 x p 2 was selected as the optimal identification parameter and the superior estimation criterion is the ideal criterion. The verification results of simulation tests show that the accurate success rate and conservative success rate of the final evaluation are 60% and 80%, respectively, indicating that the nonparametric estimation method in this study can be used to estimate the mechanical properties of planetary soil effectively. [ABSTRACT FROM AUTHOR]

The mobility of vehicles in off-road environments is critical for many applications. Predicting the tire-soil interaction is a challenge, especially in non-linear deformable terrain. This paper presents an overview of the bibliographic references on tires–deformable soil interactions after the 2000's, identifying the gaps in the literature. The capabilities and challenges of different modeling frameworks used for mobility (i.e., empirical, semi-empirical, and physics-based) are discussed; special emphasis is given to continuum-based frameworks. A summary of terrain material models used to approximate the behavior of coarse and fine-grained soils is provided with practices used to characterize such materials. A review of tire models for deformable soil navigation and the tire-soil interfaces is provided. Strategies to validate all these models are presented. Finally, the application of these studies for assessing the sensitivity concerning input parameters (e.g., velocity, inflation pressure, and normal load), multi-pass, multi-layered soils, wet soils, and fully integrated multi-body vehicle models are discussed. The final contribution of this review paper is a summary table that synthesizes the extensive bibliographic review. Overall, this work highlights a lack of physics-based trafficability studies in wet and plastic deformable soils. Moreover, studies on contact adhesion, stone picking, multipass, and cornering also need improvement. [ABSTRACT FROM AUTHOR]

A planetary exploration rover has been employed for scientific endeavors or as a precursor for upcoming manned missions. Predicting rover traversability from its wheel slip ensures safe and efficient autonomous operations of rovers on deformable planetary surfaces; path planning algorithms that reduce slips by considering wheel-soil interaction or terrain data can minimize the risk of the rover becoming immobilized. Understanding wheel-soil interaction in transient states is vital for developing a more precise slip ratio prediction model, while path planning in the past assumes that slips generated at the path is a series of slip ratio in steady state. In this paper, we focus on the transient slip, or slip rate the time derivative of slip ratio, to explicitly address it into the cost function of path planning algorithm. We elaborated a regression model that takes slip rate and traction force as inputs and outputs slip ratio, which is employed in the cost function to minimize the rover slip in path planning phase. Experiments using a single wheel testbed revealed that even with the same wheel traction force, the slip ratio varies with different slip rates; we confirmed that the smaller the absolute value of the slip rate, the larger the slip ratio for the same traction force. The statistical analysis of the regression model confirms that the model can estimate the slip ratio within an accuracy of 85% in average. The path planning simulation with the regression model confirmed a reduction of 58% slip experienced by the rover when driving through rough terrain environments. The dynamics simulation results insisted that the proposed method can reduce the slip rate in rough terrain environments.

We present EMBUR-EMerita BUrrowing Robot-the first legged robot inspired by the Pacific mole crab, Emerita analoga, capable of burrowing vertically downward. We choose Emerita analoga as a model organism for its rapid downward burrowing behaviors, as it is four times as fast as the most rapid bivalve mollusk. Vertical burrowing in granular media is a challenging endeavor due to the tendency for the media to create upwards resistive forces on an intruder, even during purely horizontal motions. Our robot is capable of vertically burrowing its body in granular substrate primarily through excavation using two leg pairs, which are functionally analogous to groupings of leg pairs of the mole crab. We implement a novel leg mechanism with a sweeping trajectory, using compliant fabric to enable an anisotropic force response. The maximum resistive force during the power stroke is 6.4 times that of the return stroke. We compare robot body pitch and spatial trajectories with results from biomechanical studies of the mole crabs. We characterize the sensitivity of the robot to initial depth, body pitch and leg pose, and propose bounds on initial conditions which predict various burrowing failure modes. Parametric studies utilizing Granular Resistive Force Theory inform our understanding of robot behavior in response to leg phasing and orientation. Not only does this robotic platform represent the first robophysical model of vertical mole crab-inspired burrowing, it is also one of the first legged, primarily excavative small-scale burrowing agents.

• Paper reviews operation and parameters of archimedean scroll propulsion systems. • A thorough review of literature on scroll propulsion vehicles is presented. • An emerging application of screw propulsion are uncrewed ground vehicles. This paper provides a comprehensive review of the published literature on screw propulsion for off-road vehicles and amphibious transportation, from its origins in the 18th century to the present day. Additionally, this work describes the basis and elements of an archimedean scroll propulsion mechanism and discusses the most developed dynamic models available in the literature and their limitations. The paper also examines the need for a tested terramechanics dynamic model and explores potential future applications of screw propulsion technology for uncrewed ground vehicles and robotic planetary exploration. [ABSTRACT FROM AUTHOR]

Trafficability gives tracked vehicles adaptability, stability, and propulsion for various purposes, including deep-sea research in rough terrain. Terrain characteristics affect tracked vehicle mobility. This paper investigates the soil mechanical interaction dynamics between rubber-tracked vehicles and sedimental soils through controlled laboratory-simulated experiments. Focusing on Bentonite and Diatom sedimental soils, which possess distinct shear properties from typical land soils, the study employs innovative user-written subroutines to characterize mechanical models linked to the RecurDyn simulation environment. The experiment is centered around a dual-tracked crawler, which in itself represents a fully independent vehicle. A new three-dimensional multi-body dynamic simulation model of the tracked vehicle is developed, integrating the moist terrain’s mechanical model. Simulations assess the vehicle’s trafficability and performance, revealing optimal slip ratios for maximum traction force. Additionally, a mathematical model evaluates the vehicle’s tractive trafficability based on slip ratio and primary design parameters. The study offers valuable insights and a practical simulation modeling approach for assessing trafficability, predicting locomotion, optimizing design, and controlling the motion of tracked vehicles across diverse moist terrain conditions. The focus is on the critical factors influencing the mobility of tracked vehicles, precisely the sinkage speed and its relationship with pressure. The study introduces a rubber-tracked vehicle, pressure, and moisture sensors to monitor pressure sinkage and moisture, evaluating cohesive soils (Bentonite/Diatom) in combination with sand and gravel mixtures. Findings reveal that higher moisture content in Bentonite correlates with increased track slippage and sinkage, contrasting with Diatom’s notable compaction and sinkage characteristics. This research enhances precision in terrain assessment, improves tracked vehicle design, and advances terrain mechanics comprehension for off-road exploration, offering valuable insights for vehicle design practices and exploration endeavors.

Terrain traversability is critical for developing Go/No-Go maps for ground vehicles, which significantly impact a mission's success. To predict the mobility of terrain, one must understand the soil characteristics. In-situ measurements performed in the field are the current method of collecting this information, which is time-consuming, costly, and can be lethal for military operations. This paper investigates an alternative approach using thermal, multispectral, and hyperspectral remote sensing from an unmanned aerial vehicle (UAV) platform. Remotely sensed data combined with machine learning (linear, ridge, lasso, partial least squares (PLS), support vector machines (SVM), and k nearest neighbors (KNN)) and deep learning (multi-layer perceptron (MLP) and convolutional neural network (CNN)) are used to perform a comparative study to estimate the soil properties, such as the soil moisture and terrain strength, used to generate prediction maps of these terrain characteristics. This study found that deep learning outperformed machine learning. Specifically, a multi-layer perceptron performed the best for predicting the percent moisture content (R2/RMSE = 0.97/1.55) and the soil strength (in PSI), as measured by a cone penetrometer for the averaged 0–6" (CP06) (R2/RMSE = 0.95/67) and 0–12" depth (CP12) (R2/RMSE = 0.92/94). A Polaris MRZR vehicle was used to test the application of these prediction maps for mobility purposes, and correlations were observed between the CP06 and the rear wheel slip and the CP12 and the vehicle speed. Thus, this study demonstrates the potential of a more rapid, cost-efficient, and safer approach to predict terrain properties for mobility mapping using remote sensing data with machine and deep learning algorithms. [ABSTRACT FROM AUTHOR]

• A framework for a hybrid terramechanics modelling method is presented. • The method involves using ML to augment existing semi-empirical models. • Model presented in a general way that can be applied to any semi-empirical model. • Method applied to a blade simulation with the Fundamental Earthmoving Equation. • Method applied to a wheel simulation with the Bekker-Wong terramechanics formulation. The field of terramechanics focuses largely on two types of simulation approaches. First, the classical semi-empirical methods that rely on empirically determined soil parameters and equations to calculate the soil reaction forces acting on a wheel, track or tool. One major drawback to these methods is that they are only valid under steady-state conditions. The more flexible modelling approaches are discrete or finite element methods (DEM, FEM) that discretize the soil into elements. These computationally demanding approaches do away with the steady state assumption at the cost of including more model parameters that can be difficult to accurately tune. Model-free approaches in which machine learning algorithms are used to predict soil reaction forces have been explored in the past, but the use of these models comes at the cost of the valuable insight that the semi-empirical models provide. In this work, we presume that in a dynamic simulation, the soil reaction forces can be divided into a steady state component that can be captured using semi-empirical models and a dynamic component that cannot. We propose an augmented modelling approach in which a neural network is trained to predict the dynamic component of the reaction forces. We explore how this theory can be applied to the simulation of a soil-cutting blade using the Fundamental Earthmoving Equation and of a wheel driving over soft soil using the Bekker wheel-soil model. [ABSTRACT FROM AUTHOR]

Wheeled locomotion mechanisms can traverse even terrains with high velocity, while tracked locomotion mechanisms can traverse rough terrains. Since different locomotion mechanisms are suitable for different terrains, there has always been a problem to choose appropriate modes according to terrains for all-terrain unmanned ground vehicles (UGVs). In order to make UGVs can traverse various terrains efficiently, based on the concept of mechanism reconfiguration, the reconfigurable deformable tracked wheel (RDTW) is proposed, which can realize wheeled mode and tracked mode. The mechanical design of RDTW is introduced, and the kinematic of reconfigurable rims is investigated. The nonlinear terramechanics model is established by coupling with the deformation parameter of reconfigurable mechanisms. Further, this model is validated by Multibody Dynamics-Discrete Element Method (MBD-DEM) co-simulation and experiments. Based on the theoretical model, the passing ability can be improved by changing the configuration of the mechanism. The simulation and test prove that the structural design of RDTW is reasonable and effective, and the optimal deformation strategy obtained from the terramechanics based on its structure is effective and can be applied in practice. The analysis results show that the nonlinear sinkage curves and traction performance of UGVs can be effectively improved by configuring RDTW. The proposed locomotion mechanism is an important attempt in improving the design of multi-locomotion-mode UGVs. [ABSTRACT FROM AUTHOR]

Adjusting the roll angle of a rover's body is a commonly used strategy to improve its traversability over sloped terrains. However, its range of adjustment is often limited, due to constraints imposed by the rover design and geometry factors such as suspension, chassis, size, and suspension travel. In order to improve the rover's traversability under these constraints, this paper proposes a reconfigurable rover design with a two-level (sliding and rolling) mechanism to adjust the body's roll angle. Specifically, the rolling mechanism is a bionic structure, akin to the human ankle joint which can change the contact pose between the wheel and the terrain. This novel adjustment mechanism can modulate the wheel–terrain contact pose, center-of-mass projection over the supporting polygon, wheel load, and the rover driving mode. Combining the wheel–load model and terramechanics-based wheel–terrain interaction model, we develop an integrated model to describe the system dynamics, especially the relationship between rover pose and wheel slippage parameters. Using this model, we develop an associated attitude control strategy to calculate the desired rover pose using particle swarm algorithm while considering the slip rate and angle constraints. We then adjust the sliding and rolling servo angles accordingly for slope traversing operations. To evaluate the proposed design and control strategies, we conduct extensive simulation and experimental studies. The results indicate that our proposed rover design and associated control strategy can double the maximum slope angles that the rover can negotiate, resulting in significantly improved traversability over soft sloped terrains. [ABSTRACT FROM AUTHOR]

In this study, the design and driving performance evaluation of a driving system for driving on deformable terrain was performed using terramechanics theory and multi-body dynamics simulation. For the design of the driving system, the mechanical interaction of track-terrain was analyzed using a Bekker-based model. Based on the analyzed results, the design of a track suitable for the deformable terrain to be driven and selection of a power source (engine, transmission, etc.) were carried out. A multi-body simulation model of the tracked vehicle reflecting the designed track and the selected power source was developed, and a ground model reflecting the mechanical property of terrain was also developed to analyze the mechanical interaction of the track-terrain through simulation. In addition, each link constituting the track was modeled as a 6 DOF spring/damper system to consider the track's tension force and load distribution under the track, and through this, different ground pressure and soil thrust were applied according to the motion state of each link. Finally, driving performance analyses were performed using the developed tracked vehicle, and as a result, it was confirmed that the driving requirements of the tracked vehicle were satisfied. [ABSTRACT FROM AUTHOR]

Tracks and wheels are the most widely used running gear for the locomotion of agricultural vehicles. The main difference between the two systems is the contact area with the ground and, consequently, the pressure distribution. Evaluating the pressure distribution on the ground is important because soil damage and vehicle performance depend on it. This analysis is especially difficult for tracked vehicles, owing to their complexity compared with wheeled systems. In this paper, we describe a multibody model of a flexible track to evaluate the pressure distribution upon contact with soft terrain. The track considered in this study is part of a reconfigurable locomotion system of a small farming vehicle, which can vary the pressure distribution by switching from a wheeled vehicle to a half-tracked vehicle. The aim of such a vehicle is to minimize soil damage in addition to optimizing its performance. The model is used to characterize this vehicle and evaluate the pressure distribution with varying characteristic parameters, such as track tension, the position of the vehicle's center of gravity, the weight distribution on the track itself, and the stiffness of the suspension system. [ABSTRACT FROM AUTHOR]

We present EMBUR—EMerita BUrrowing Robot—the first legged robot inspired by the Pacific mole crab, Emerita analoga, capable of burrowing vertically downward. We choose Emerita analoga as a model organism for its rapid downward burrowing behaviors, as it is four times as fast as the most rapid bivalve mollusk. Vertical burrowing in granular media is a challenging endeavor due to the tendency for the media to create upwards resistive forces on an intruder, even during purely horizontal motions. Our robot is capable of vertically burrowing its body in granular substrate primarily through excavation using two leg pairs, which are functionally analogous to groupings of leg pairs of the mole crab. We implement a novel leg mechanism with a sweeping trajectory, using compliant fabric to enable an anisotropic force response. The maximum resistive force during the power stroke is 6.4 times that of the return stroke. We compare robot body pitch and spatial trajectories with results from biomechanical studies of the mole crabs. We characterize the sensitivity of the robot to initial depth, body pitch and leg pose, and propose bounds on initial conditions which predict various burrowing failure modes. Parametric studies utilizing Granular Resistive Force Theory inform our understanding of robot behavior in response to leg phasing and orientation. Not only does this robotic platform represent the first robophysical model of vertical mole crab-inspired burrowing, it is also one of the first legged, primarily excavative small-scale burrowing agents.

Terrain traversability is critical for developing Go/No-Go maps for ground vehicles, which significantly impact a mission’s success. To predict the mobility of terrain, one must understand the soil characteristics. In-situ measurements performed in the field are the current method of collecting this information, which is time-consuming, costly, and can be lethal for military operations. This paper investigates an alternative approach using thermal, multispectral, and hyperspectral remote sensing from an unmanned aerial vehicle (UAV) platform. Remotely sensed data combined with machine learning (linear, ridge, lasso, partial least squares (PLS), support vector machines (SVM), and k nearest neighbors (KNN)) and deep learning (multi-layer perceptron (MLP) and convolutional neural network (CNN)) are used to perform a comparative study to estimate the soil properties, such as the soil moisture and terrain strength, used to generate prediction maps of these terrain characteristics. This study found that deep learning outperformed machine learning. Specifically, a multi-layer perceptron performed the best for predicting the percent moisture content (R2/RMSE = 0.97/1.55) and the soil strength (in PSI), as measured by a cone penetrometer for the averaged 0–6” (CP06) (R2/RMSE = 0.95/67) and 0–12” depth (CP12) (R2/RMSE = 0.92/94). A Polaris MRZR vehicle was used to test the application of these prediction maps for mobility purposes, and correlations were observed between the CP06 and the rear wheel slip and the CP12 and the vehicle speed. Thus, this study demonstrates the potential of a more rapid, cost-efficient, and safer approach to predict terrain properties for mobility mapping using remote sensing data with machine and deep learning algorithms.

In a complex off-road environment, due to the low bearing capacity of the soil and the uneven features of the terrain, generating a safe and effective global route for unmanned ground vehicles (UGVs) is critical for the success of their motion and mission. Most traditional global path planning methods simply take the shortest path length as the optimization objective, which makes it difficult to plan a feasible and safe route in complex off-road environments. To address this problem, this research proposes a global path planning method, which considers the influence of terrain factors and soil mechanics on UGV mobility. First, we established a high-resolution 3D terrain model with remote sensing elevation terrain data, land use and soil type distribution data, based on a geostatistical method. Second, we analyzed the vehicle mobility by the terramechanical method (i.e., vehicle cone index and Bakker's theory), and then calculated the mobility cost based on a fuzzy inference method. Finally, based on the calculated mobility cost, the probabilistic roadmap method was used to establish the connected matrix and the multi-dimensional traffic cost evaluation matrix among the sampling nodes, and then an improved A* algorithm was proposed to generate the global route. [ABSTRACT FROM AUTHOR]

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This article presents a review of the equipment used in the process of determining the mechanical strength of soil, in particular with regards to the vertical loads applied. Here, devices incorporating the bevameter approach, i.e. medium and large-scale testers, are discussed. The bevameter technique is described in detail, along with the most common mathematical models relating to the vertical pressure applied to the soil and its compaction. The paper also highlights important phenomena for this type of experiment, such as the scale effect, wall effect, multipass effect, and slip sinkage effect. The article presents the reasons for which plate testers are currently the most commonly used tester type for soil penetration tests for the purpose of terramechanics, including the Next Generation NATO Reference Mobility Model that is currently under development. Investigations towards the influence of the penetration rate on soil penetration are also addressed. Furthermore, the authors also present a selection of their own results of currently ongoing research on the subject of potential influence of the plate grouser on plate sinkage. The results already obtained have made it possible to identify phenomena that are not taken into account in the current research methods, in turn resulting in the development of an innovative plate tester for investigating the sinkage of the running gear components of machines and vehicles in fragmented media. • Bevameters show a number of significant advantages over penetrometers. • Bevameters will be the leading soil testing method in the new NATO mobility model. • There are reasonable minimum dimensions for both tester plate and soil bin. • The grouser of the tester plate can also influence the soil penetration process. • Taking from already conducted bevameter tests can improve research pace. [ABSTRACT FROM AUTHOR]

Reliable assessment of soil mechanical parameters causes many problems due to its random nature, and therefore the literature on the subject provides many techniques in this area. The article presents an analysis of the state of the art in the field of process analogues (testers) for identifying soil compaction under external loads that are generated, for example, by the running gear components of off-road machinery and vehicles. A classification of these testers into three main groups is proposed: small-size (penetrometers), medium-size (plate testers), and large-size (chassis components). The cone index approach for small-scale testers is described in detail in the paper. Consequently, the bevameter approach, which is used for medium- and large-scale testers, is described in Part 2 of this pair of articles. The main application of penetrometers in terramechanics, which is to determine the mobility of off-road vehicles, mostly qualitatively, is highlighted, with a description of the most important mobility metrics, also in the context of the NATO Reference Mobility Model, also being presented. An overview of the devices is presented, with the tester area, applied pressure levels, types of soil tested, and field of use also being discussed. The analyses include static and dynamic testers. The pair of articles also presents the main issues with penetrometer testing, and the reasons for which bevameters are the most commonly used tester for determining quantitative soil parameters for the purpose of terramechanics. • Penetrometers are basic testers for evaluating the mobility of off-road vehicles. • Various tester shapes are used with cone penetrometers being the most common ones. • There are methods for dynamic and impact soil testing incorporating penetrometers. • Taking from already conducted penetration tests can improve research pace. [ABSTRACT FROM AUTHOR]

With the advent of artificial intelligence, the analysis of systems related to complex processes has become possible or easier. The interaction of the traction factor of off-road vehicles with soil or other uncommon surfaces is one of the complex mechanical problems, which has been very difficult to model and analyze in conventional and previous methods due to numerous and variable parameters. This review article delves into the imperative and progression of integrating AI algorithms within the realm of modeling and predicting target parameters in Terramechanics engineering. Such endeavors are especially pertinent to predicting various soil properties, including soil compaction, traction, energy consumption, deformation, and associated factors. The application of AI encompasses various facets, including modeling and predicting traction, soil sinkage, rut depth, contact area, soil stress, density, and energy wasted on the traction device's movement on the soil. The present study evaluates the solutions and benefits offered by AI-based methodologies in addressing soil-machine interaction challenges. Furthermore, the study investigates the constraints inherent in utilizing these methodologies. [ABSTRACT FROM AUTHOR]

The interaction between deformable terrain and wheels significantly affects wheel mobility. To accurately predict vehicle mobility or optimize wheel design, an analysis of this interaction is essential. This study develops a hybrid terramechanics model (HTM) that integrates the semi-empirical model (SEM) and the discrete element method (DEM) using artificial neural networks (ANNs). The model overcomes the limitations inherent in SEM and DEM approaches. We used DEM simulations to analyze the impact of wheel design parameters and slip ratio on terrain behavior. ANNs were subsequently developed to predict dynamic sinkage in real time based on these results. A new concept, termed bulldozing angle, was introduced to define additional terrain–wheel contact caused by dynamic sinkage. Based on this concept, we predicted the bulldozing resistance exerted on the wheel. By combining SEM, ANNs, and DEM, we developed an HTM capable of terrain behavior analysis. Lastly, we conducted a comparative analysis between the SEM, HTM, and actual test data. The results confirmed that the predictive accuracy of the HTM surpassed that of the SEM across all slip ratios. [ABSTRACT FROM AUTHOR]

• A semi-empirical terramechanics approach for complex terrain profiles is presented. • The approach is an extension of the semi-empirical models. • The terrain can be defined using an arbitrary heightfield. • The method can capture complex terrain geometries and gaps in the contact patch. • Comparison to the least square plane method highlight proposed approach's strengths. Dynamic simulations of various types of off-road vehicles, from planetary rovers to agricultural equipment, have long relied on well-established semi-empirical terramechanics models. While these models do have drawbacks and reliability issues that have been addressed by numerous works in the decades since the models were first introduced, semi-empirical approaches remain one of the few ways to simulate realistic wheel-soil interaction in real-time. One of their drawbacks is their assumption that the terrain is a flat plane. The models work by integrating normal and shear stresses along the wheel-terrain contact patch. The normal stress at each point along the contact patch is determined using an equation that computes soil pressure based on semi-empirical parameters, the dimensions of the wheel and the sinkage, which is determined based on the distance between the point and the plane that defines the terrain. Other works simplify the rough terrain contact problem by defining an equivalent contact plane at each time step in order to continue to be able to use semi-empirical models - modified to work with slanted planes - to compute the interaction forces. In this work, we propose a new, modified version of the semi-empirical model in which interaction forces for a wheel travelling on rough terrain can be computed without the need to use an equivalent contact plane. To highlight the advantages of our proposed approach, we compare our simulation results to the results of simulations using an existing approach for modelling a wheel travelling over rough terrain using traditional semi-empirical models. [ABSTRACT FROM AUTHOR]

• Finish foot-terrain interaction experiments under large sinkage and dynamic sliding. • Establish mechanical models considering large sinkage and dynamic sliding effect. • Design a coronal foot with better anti-sinkage and tangential traction performance. Legged robots exhibit superior adaptability to complex extraterrestrial environments compared to wheeled mobile robots. However, legged robots employed in planetary exploration face challenges in dealing with soft terrains. This paper focuses on investigating the issues of large foot sinkage and slip encountered by legged robots on soft terrain. Extensive experiments on quasi-static loading, loading with impact and tangential force have been carried out for both spherical and cylindrical feet. The variations in normal force, tangential force, and sinkage are meticulously recorded and analyzed. Foot-terrain interaction mechanics models are established to address scenarios involving substantial sinkage and sliding sinkage, leveraging the stress distribution characteristics of deformable soil. Accurate models are obtained through parameter identification utilizing experimental data, which can aid in the foot design of legged robots intended for planetary exploration. Based on the developed models and experimental data, a design optimization scheme for the coronal foot is proposed, leading to performance enhancements that are validated through experimental verification. [ABSTRACT FROM AUTHOR]

Adjusting the roll angle of a rover’s body is a commonly used strategy to improve its traversability over sloped terrains. However, its range of adjustment is often limited, due to constraints imposed by the rover design and geometry factors such as suspension, chassis, size, and suspension travel. In order to improve the rover’s traversability under these constraints, this paper proposes a reconfigurable rover design with a two-level (sliding and rolling) mechanism to adjust the body’s roll angle. Specifically, the rolling mechanism is a bionic structure, akin to the human ankle joint which can change the contact pose between the wheel and the terrain. This novel adjustment mechanism can modulate the wheel–terrain contact pose, center-of-mass projection over the supporting polygon, wheel load, and the rover driving mode. Combining the wheel–load model and terramechanics-based wheel–terrain interaction model, we develop an integrated model to describe the system dynamics, especially the relationship between rover pose and wheel slippage parameters. Using this model, we develop an associated attitude control strategy to calculate the desired rover pose using particle swarm algorithm while considering the slip rate and angle constraints. We then adjust the sliding and rolling servo angles accordingly for slope traversing operations. To evaluate the proposed design and control strategies, we conduct extensive simulation and experimental studies. The results indicate that our proposed rover design and associated control strategy can double the maximum slope angles that the rover can negotiate, resulting in significantly improved traversability over soft sloped terrains.

Dimensional optimization is important for planetary rovers to reach good performance, such as high mobility, stability, and low energy consumption. The paper presents a dimensional optimization for a planetary rover with rocker-bogie suspension. During the optimization process, the influence of dimensions on the actuation requirements is studied based on kinetostatics and terramechanics. The objective function is built considering the average driving torque requirements in the most common type of windblown terrain in Mars called megaripples. The optimal dimension design is reached through the genetic algorithm, and the influences of dimensional parameters on rover performances are studied by drawing performance atlases. This work realizes the consideration of energy consumption in the design phase of a planetary rover. Finally, the results guide the design of a rover prototype and are validated by a series of experiments. [ABSTRACT FROM AUTHOR]

Abstract Planetary exploration rovers have required a high traveling performance to overcome obstacles such as loose soil and rocks. Push-pull locomotion rovers is a unique scheme, like an inchworm, and it has high traveling performance on loose soil. Push-pull locomotion uses the resistance force by keeping a locked-wheel related to the ground, whereas the conventional rotational traveling uses the shear force from loose soil. The locked-wheel is a key factor for traveling in the push-pull scheme. Understanding the sinking behavior and its resistance force is useful information for estimating the rover’s performance. Previous studies have reported the soil motion under the locked-wheel, the traction, and the traveling behavior of the rover. These studies were, however, limited to the investigation of the resistance force and amount of sinkage for the particular condition depending on the rover. Additionally, the locked-wheel sinks into the soil until it obtains the required force for supporting the other wheels’ motion. How the amount of sinkage and resistance forces are generated at different wheel sizes and mass of an individual wheel has remained unclear, and its estimation method hasn’t existed. This study, therefore, addresses the relationship between the sinkage and its resistance force, and we analyze and consider this relationship via the towing experiment and theoretical consideration. The results revealed that the sinkage reached a steady-state value and depended on the contact area and mass of each wheel, and the maximum resistance force also depends on this sinkage. Additionally, the estimation model did not capture the same trend as the experimental results when the wheel width changed, whereas, the model captured a relatively the same trend as the experimental result when the wheel mass and diameter changed.

• Two clutches allow for predictable transition from moving hub to moving tread. • Linear actuators facilitate transformation from circular track to triangular track. • Prototype testing shows promise for reconfigurable wheel-track. The National Robotics Engineering Center has conceived a novel system that is able to reconfigure from a track to a wheel while in motion. The purpose of this device is to combine the benefits of wheels and tracks to provide performance optimization on a variety of terrain. The first stage of development resulted in two benchtop prototypes: one to test a transition from rotating hub to rotating tread and another to test a constantly-oriented shape transition from circle to triangle. This paper documents the testing of these devices including current draw, temperature change, and braking characteristics. Through experimentation with the first testbed, desired speed was shown to be consistent within +/−6% when transitioning between wheel and track modes at an approximated ground speed between 5 and 35 km/h while transitioning in 5 to 60 seconds. Testing on the second system identified asymmetry in testbed construction and showed consistent loading patterns throughout a 42 mm-change in sprocket position between wheel and track mode while transitioning between 10 and 50 mm/s. The evaluation of these testbeds informed the design of the next process of the reconfigurable wheel-track project, which resulted in a larger prototype capable of propelling a small ground vehicle. [ABSTRACT FROM AUTHOR]