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For the design of space missions in the Moon and planets, analysis of mobility in robots is crucial and poor planning has led to abortion of missions in the past. To mitigate the risk of mission failure, improved algorithms relying intrinsically on fusing visual odometry with other sensory inputs are developed for slip detection and navigation. However, these approaches are significantly expensive computationally and difficult to meet for future space exploration robots. Hence, today the central question in the field is how to develop a novel framework for in situ estimation of rover mobility with available space hardware and low-computational demanding terramechanics predictors. Ranging from pure simulations up to experimentally validated studies, this paper surveys dozens of existing methodologies for detection of vehicle motion performance (wheel forces and torques), surface hazards (slip-sinkage) and other parameters (soil strenght constants) using classical terramechanics maps, and compare them with novel approaches introduced by machine learning, allowing to establish future directions of research towards distributed exteroceptive and proprioceptive sensing for visionless exploration in dynamic environments. To avoid making it challenging to collect all relevant studies expeditiously, we propose a global classification of terramechanics according most common practices in the field, allowing to form an structured framework that condense most works in the domain within three estimator categories (direct/forward or inverse terramechanics, and slip estimators). Likewise, from the experiences collected in previous MER (Mars Exploration Rover) missions, five overlooked problems are documented that will need to be addressed in next generation of planetary vehicles, along three research questions and few hypothesis that will pave the road towards future applications of machine learning-based terramechanics.

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.

Planetary rovers are becoming indispensable for exploration activities and science missions. The rover used in such mission is often limited in its operation time owing to power and computational r...

The US army along with NATO member and partner nations’ militaries need an accurate software tool for predicting ground vehicle mobility (such as speed-made-good and fuel-consumption) on world-wide terrains where military vehicles may be required to operate. Currently, the NATO Reference Mobility Model (NRMM) is the only NATO recognized tool for assessing ground vehicle mobility. NRMM was developed from the 1960s to the 1980s and relies on steady-state empirical formulas which may not be accurate for new military ground vehicles. A NATO research task group (RTG-248) was established from 2016 to 2018 to develop the NG-NRMM (next-generation NRMM) software tool requirements and an NG-NRMM prototype which uses high-fidelity “simple” or “complex” terramechanics models for the terrain/soil along with modern 3D multibody dynamics software tools for modeling the vehicle. NG-NRMM Complex Terramechanics (CT) models are those that utilize full 3D soil models capable of predicting the 3D soil reaction forces on the vehicle surfaces (including tires, tracks, legs, and under body) and the 3D flow and deformation of the soil including both elastic and plastic deformation under any 3D loading condition. In Part 1 of this paper, an overview of the full spectrum of terramechanics models from the highest fidelity to the lowest fidelity is presented along with a literature review of CT ground vehicle mobility models.

In part 2 of this paper, the Complex Terramechanics (CT) software tools requirements recommended by the NATO research task group RTG-248 are presented along with example simulations from a CT prototype software tool which attempts to satisfy the requirements.

The soft ground and stones on the surface of Mars may cause sinkage of and damage to the wheels of a Mars rover. Therefore, we analyzed the performance of a wheel-step Mars rover from the perspective of terramechanics and structural mechanics. Using China’s Mars rover wheel prototype and wheel-soil interaction testbed, we obtained the driving performance of the wheels of a Mars rover under various conditions, including full skidding conditions. The vertical load set in the tests was determined using the gravity of Mars and the mass of the wheel-step Mars rover. The results indicate that the driving torque, sinkage, and resistance coefficient have a linear relationship with the wheel vertical load. An analysis of the structural mechanical characteristics of the wheel of the Mars rover was conducted by testing the radial, axial, torsional, and deflection stiffness. We found that the wheel ribs can improve the stiffness of the wheel but may reduce its driving performance. The analysis methods and evaluation indices can be used to analyze the performance of the wheels of other Mars rovers. Furthermore, the findings of this study can be used to optimize wheel design and motion control of wheel-step Mars exploration rovers.

Unmanned vehicles are a natural choice for accessing challenging or hazardous terrains, for instance oil sands tailings ponds, and performing tasks such as soil sampling and terramechanics investigations. In previously published work, an unmanned ground vehicle (UGV) named RTC-I was designed and built for this task by part of our group. The present article covers the design choices and technical details of a custom-built robotic manipulator, a soil sampler, and an instrumented wheel deployed onboard a second-generation UGV named RTC-II. The robotic manipulator is designed to provide the reach, payload capacity, ruggedness, and self-locking operation required for field operations. The soil sampler employs a curved scoop to minimize deformation of the collected sample. The instrumented wheel permits independent control of the normal load and the slip ratio during terramechanics investigations. Each of the three designs is deployed and successfully tested in field experiments. Measurements collected by the soil sampler and instrumented wheel will be used in future work dealing with sampler force modeling and real-time terrain parameter estimation, respectively.

This paper proposes a wheel with a deployable leg that can change the apparent wheel radius to improve the runnability of a rover traversing a lunar surface covered with regolith. The driving force of the wheel was formulated according to terramechanics, and relations for the changing driving force with the different configurations were clarified. The simulated driving forces with the original wheel configuration and extended leg configuration were compared in a single-wheel experiment, and the results confirmed that the proposed extendable leg system exhibited a higher driving force than the original circular wheel. With this system, the rover can use the original wheel state for flat ground surfaces that do not require a high driving force and then switch to the proposed extendable leg system when a high driving force is required, such as escaping from local concave ground or climbing on steep slope. The proposed system is potentially applicable to efficiently traversing irregular surfaces not only on the Moon but also on other planets.

This paper extends the analysis of empirical methods for describing vehicle–terrain interactions in lunar terrain. Given analytical formulation to predict mobility performance in extraterrestrial environments requires reliable in situ testing campaigns, this imposes fundamental restrictions to conceive a more consolidated theory, and further any possibility to use improved empirical methods to design better space hardware. Hence, we propose an analytical approach to extrapolate data taken in parabolic flights to model vehicle performance in multiple gravity regimes. The extrapolation technique and respective reported uncertainties can be used, therefore, to tune fitting parameters of a set of general formulas in the domain of Terramechanics, allowing to have empirical estimates of the wheel mobility in cases where testing is inherently very complex. Finally, by the analysis of previous Moon and Mars rover missions with the fitted equations, we report an empirical design criterion that allows to generate first estimates of the optimal wheel dimensions, taking into account the eventual longitudinal slip of the rover and including the desired mass of the payload. The introduced rules for geometry optimization can be important for future space rover missions in remote soils.

This paper presents a suite of dynamic models enhanced by mem-models. A prototypical pogo stick model might mimic a space hopper or a segmented telescope mirror actuator, while an extension of that prototype could simulate the terramechanics problem of a deformable soil model interacting with a penetrator. The inclusion of mem-models, including memristor and memcapacitor models, introduces an increased level of fidelity and a new and effective means of modeling memory effects and path dependence of nonlinear interacting dynamical systems. This challenging class of problems, which involves non-smooth dynamical systems posed as differential-algebraic equations, is formulated here as a hybrid dynamical system with both continuous and discrete states, and a state event location algorithm is successfully applied to track discontinuous changes in the system states.

The parameterization of terramechanics model for the tire off-road traction dynamics modeling relies exclusively on the plate-sinkage test and shear test (not using a tire as the shear tool), according to the existing literature. However, the plate-soil interaction cannot be considered the same as the tire-soil interaction (Plackett, 1985). Part II of this paper investigates whether the tire-soil test can be used to parameterize terramechanics model. The parameterization of the modified Bekker’s model, the Magic Formula tire model, and a bulk density estimation model, using the data from the series of tire and soil tests presented in Part I of this paper (He et al., 2019), is discussed in detail herein. The parameterization approach presented herein can be used to develop tire off-road dynamics models.

Tire performance over soft soil is of interest for automotive and geotechnical engineers; the automotive engineers are mainly interested in tire tractive performance, and geotechnical engineers are concerned with the effects of the traffic brought by the tire to the soil. This two-part paper documents a series of tire and soil tests (Part I) and the application of their test data to the study of tire tractive performance over soft soil (characterized by drawbar pull) and to the model parameterization (Part II). Part I of this paper details the series of tests that are comprised of static tire deflection tests, static tire-soil tests, soil properties tests, and dynamic tire-soil tests, and describes the influence of tire inflation pressure or soil compaction level on the test data. The experimental approach presented herein produces parameterization and validation data that can be used in tire off-road traction dynamics modeling and terramechanics modeling.

An important parameter in terramechanics is the rut depth produced when a vehicle traverses deformable soil. The rut depth provides a measure of vehicle tractability as well as the impact on the environment. Rut depth is not uniform on natural terrain and typically only a few manual points are measured. Synchronizing rut depth with other measurements is also problematic. This paper investigates the feasibility of using cameras to measure 3D terrain profiles from which a single rut depth measurement is obtained. Tests were performed on different vehicles, for various dynamic vehicle manoeuvres, over varying terrains including sand, mud, grassland, snow and ice. Results were validated using the traditional stick ruler method. Measurement frequencies of 58 Hz were obtained using affordable commercially off the shelf computational hardware and dedicated software. Determining whether a vehicle can traverse a terrain can significantly improve the vehicle mobility. Therefore, real time measurements of rut depth can be used to determine the mobility of vehicles in off-road conditions that can change rapidly due to environmental conditions e.g. rain or snow. The techniques described can assist in gathering terrain and vehicle mobility data that can be used directly to assist the driver in making safety related decisions.

The ISTVS Research Award , the U.S. Army Engineer Research and Development Center (ERDC), the European Union Horizon 2020 Framework Program , Marie Sklodowska Curie actions , Project EVE, “ Innovative Engineering of Ground Vehicles with integrated Active Chassis Systems ”, the Vehicle Dynamics Group at University of Pretoria , the Terramechanics, Multibody, and Vehicle Systems (TMVS) Laboratory at Virginia Tech, and the NSF I/UCRC Center for Tire Research (CenTiRe).

Exploring and traversing extreme terrain with surface robots is difficult, but highly desirable for many applications, including exploration of planetary surfaces, search and rescue, among others. For these applications, to ensure the robot can predictably locomote, the interaction between the terrain and vehicle, terramechanics, must be incorporated into the model of the robot's locomotion. Modeling terramechanic effects is difficult and may be impossible in situations where the terrain is not known a priori. For these reasons, learning a terramechanics model online is desirable to increase the predictability of the robot's motion. A problem with previous implementations of learning algorithms is that the terramechanics model and corresponding generated control policies are not easily interpretable or extensible. If the models were of interpretable form, designers could use the learned models to inform vehicle and/or control design changes to refine the robot architecture for future applications. This paper explores a new method for learning a terramechanics model and a control policy using a model-based genetic algorithm. The proposed method yields an interpretable model, which can be analyzed using preexisting analysis methods. The paper provides simulation results that show for a practical application, the genetic algorithm performance is approximately equal to the performance of a state-of-the-art neural network approach, which does not provide an easily interpretable model., Published in: 2019 IEEE Aerospace Conference Date of Conference: 2-9 March 2019 Date Added to IEEE Xplore: 20 June 2019

It is important to further improve the traveling performances of the moon/planetary exploration rovers. To achieve this, we investigated the grouser shape of rigid wheels for use in such rovers, focusing particularly on rectangular and trapezoidal grousers. First, simple intrusion tests were carried out using the discrete element method. Grousers having a trapezoidal cross-sectional shape exerted a “packing effect” through which particles between grousers were strongly compressed. Next, single-wheel experiments were conducted, and the results show that sinkage was suppressed by the trapezoidal-shaped grousers. In addition, it was confirmed that trapezoidal-shaped grousers exhibited a drawbar-pull equivalent to that generated by the widely used rectangular-shaped grousers. Furthermore, we performed theoretical analysis using the resistive force theory to clarify the packing effect, and the results indicate that the use of a wheel with a trapezoidal-shaped grouser could be an effective method to improve the traveling performance of a rigid wheel.

Granular media (GM) present locomotor challenges for terrestrial and extraterrestrial devices because they can flow and solidify in response to localized intrusion of wheels, limbs, and bodies. While the development of airplanes and submarines is aided by understanding of hydrodynamics, fundamental theory does not yet exist to describe the complex interactions of locomotors with GM. In this paper, we use experimental, computational, and theoretical approaches to develop a terramechanics for bio-inspired locomotion in granular environments. We use a fluidized bed to prepare GM with a desired global packing fraction, and use empirical force measurements and the Discrete Element Method (DEM) to elucidate interaction mechanics during locomotion-relevant intrusions in GM such as vertical penetration and horizontal drag. We develop a resistive force theory (RFT) to account for more complex intrusions. We use these force models to understand the locomotor performance of two bio-inspired robots moving on and within GM.

In this paper, the realisation of a multibody model of a tracked machine is described. A new compact modelling of the tracks–soil interaction is presented and soil mechanics laws for terrain response are implemented. Tracked vehicles can be used in different fields such as agriculture, military and construction. The conditions of the terrain on which they operate may vary a lot, in terms of soil composition, slope and roughness. For this reason, performance of tracked vehicles is difficult to predict without a great number of field tests. The model is developed in a multibody code that makes it possible to investigate its dynamic and kinematic behaviour in several operating conditions. A specific routine is implemented in the multibody model in order to simulate the behaviour of the tracked vehicle on deformable terrains. The main hypothesis of this paper is that the terrain deformation could be in a narrow zone affected by the vehicle. Thus, the deformation of the soil is kinematically correlated to the vehicle. Soil mechanics equations are implemented on each track portion and solved only for track links in contact with the soil. The latter is modelled as a rigid body and terrain stress or deformation are not directly computed, thus simplifying solution and terrain modelling despite obtaining coherent results in terms of vehicle traction force, slip and sinkage. Results are reported pointing out performance of the tracked machine on different ground conditions.

To successfully deploy a wheeled mobile robot on deformable rough terrains, the wheel-terrain interaction mechanics should be considered. Skid terramechanics is an essential part of the wheel terramechanics and has been studied by the authors based on the wheel sinkage obtained using a linear displacement sensor that does not consider soil bulldozing effect. The sinkage measured by a newly developed wheel via detecting the entrance angle is about 2 times of that measured by the linear displacement sensor. On the basis of the wheel sinkage that takes the soil bulldozing effect into account, a linear function is proposed to the sinkage exponent. Soil flow in the rear region of wheel-soil interface is considered in the calculation of soil shear displacement, and its average velocity is assumed to be equal to the tangential velocity component of the transition point of shear stress. To compute the normal stress in the rear region directly, the connection of the entrance and leaving points is supposed as the reference of wheel sinkage. The wheel performance can be accurately estimated using the proposed model by comparing the simulation results against the experimental data obtained using two wheels and on two types of sands.

A previous three-dimensional discrete element method (DEM) model of Mars Exploration Rovers (MERs) wheel mobility demonstrated agreement with test data for wheel drawbar pull and sinkage for wheel slips from 0.0 to 0.7. Here, results from the previous model are compared with wheel mobility data for non-MER wheels that cover the range of wheel slip from 0.0 to 1.0. Wheel slips near 1.0 are of interest for assessing rover mobility hazards. DEM MER wheel model predictions show close agreement with weight-normalized wheel drawbar pull data from 0.0 to 0.99 wheel slip and show a similar trend for wheel sinkage. The nonlinear increase in MER wheel drawbar pull and sinkage for wheel slips greater that 0.7 is caused by development of a tailings pile behind the wheel as it digs into the regolith. Classical terramechanics wheel mobility equations used in the ARTEMIS MER mobility model are inaccurate above wheel slips of 0.6 as they do not account for the regolith tailings pile behind the wheel. To improve ARTEMIS accuracy at wheel slips greater that 0.6 a lookup table of drawbar pull, wheel torque, and sinkage derived from DEM mobility simulations can be substituted for terramechanics equation calculations.

The success of NASA's Mars missions has generated a renewed interest in planetary exploration, along with a need for better mobility of wheeled mobile robots (WMRs)—steering performance, in particular, has not yet reached an acceptable benchmark in high-precision models. This study focuses on the steering mechanics of WMRs, as it can enrich the terramechanics of planetary rovers. An improved sinkage model based on the variable sinkage exponent is proposed, and the sinkage exponent is derived as a function of steering angle. Furthermore, a high-precision steering moment model is proposed based on the steering-sinkage model, which considers the interaction area and the lug effect. The model can fit the results obtained by all of the experimental wheels, based on soil parameter identification. Most of the max relative errors (MREs) for the sinkage are within 5%, and the coefficients of determination are more than 0.97. The MREs of moment increase with increasing vertical load but remain within 10%. This technique can also be applied to other WMRs with rigid wheels steering on deformable terrain.

Characterization of planetary soils in past space missions has been a task confined mostly to specific instruments developed to assess the terrain. However, the non-standard techniques introduced by Sojourner Pathfinder and Mars Exploration Rovers (MER), have shown that analytical modeling of the wheel-soil interactions, combined with suspension-related telemetry acquired from the rovers, was sufficient to reveal natural restrictions of Mars terrains and strength properties, without the need of in-situ samplers. The progress on this field established since then is briefly summarized in this paper. Although dozens of approaches for in-situ characterization of planetary grounds with terramechanics have evolved over the years (defined here as inverse terramechanics estimators, or IT), most techniques are achievable in controlled environments but unsuitable for application in planetary rovers. This is because they generally require intensive onboard processing to obtain teal-time estimations like slip, which is not straightforward to perform in real conditions (MER must stop all functions to perform visual odometry). Consequently, beyond previous MER approaches, detection of martian or lunar terrain constants will not be realizable with most proposed empirical methods and available rover hardware. However, novel developments based in machine learning (ML) can quickly change this paradigm. ML-regression models can provide the available measurements (e.g. slip) for IT-approaches to work, even in challenging conditions such as dim light or eclipses. Nevertheless, ML-based methods typically do not include uncertainty and may require to incorporate gaussian process regression models to perform better. Hence we recommend novel research directions for IT to become achievable in practical applications. We further discuss how methods for planetary soil strength detection by IT have grouped over the years into basically three classifications (pure-empirical, learning-based, or combined frameworks), and relate the advantages of each according to the environment.

The three-dimensional finite-discrete element method (FEM/DEM) is applied to the simulation of tire-sand interactions, where the tire is discretized into hexahedron finite elements and sand is modeled by using the discrete element method. The feasibility and effectiveness of the method are proven by comparing the simulation results with the current reported results. Since long test roads are usually required for investigating tire running behaviors, which lead to large-scale simulation models and time consuming problems, the alternately moving road method is proposed to handle this problem. It can simulate tire running behaviors on an arbitrary length sand road with a constant road length value. The numerical model of a lug tire running on a bisectional road with fine and coarse sand is established to verify the feasibility of the method.

Recently, the study of machinery/medium interaction is becoming increasingly important in terramechanics. In order to maximise the performance of existing equipment and obtaining desired compaction density in road construction, reasonable and effective paving operations are essential. However, the operations always depend on empirical approaches. In this paper, a model based on vibration compaction theory was used to describe the deformation property of asphalt mixture, which can lay a foundation for future analysis. And then, a dynamic model of tamper/asphalt mat interaction, based on the principles of resonance, was developed to predict asphalt mat density during paving operation. The model inputs included excitation frequency, tamper stroke, paver forward speed and asphalt mixture properties parameters for different tamper or asphalt mixture. The numerical simulations are provided to demonstrate how the tamper/asphalt mat interaction model can be used to predict asphalt mixture compaction in th...

Wheeled mobile robots are often used on high risk rough terrain. Sandy terrains are widely distributed and tough to traverse. To successfully deploy a robot in sandy environment, wheel-terrain interaction mechanics in skid should be considered. The normal and shear stress is the basis of wheel-soil interaction modeling, but the normal stress in the rear region on the contact surface is computed through symmetry in classical terramechanics equations. To calculate that directly, a new reference of wheel sinkage is proposed. Based on the new reference, both the wheel sinakge and the normal stress can be given using a quadratic equation as the function of wheel-soil contact angle. Moreover, the normal stress can be expressed as a linear function of the wheel sinkage by introducing a constant coefficient named as sand stiffness in this paper. The linearity is demonstrated by the experimental data obtained using two wheels and on two types of sands. The sand stiffness can be estimated with high accuracy and it decreases with the increase of skid ratio due to the skid-sinkage phenomenon, but increases with the increase of vertical load. Furthermore, the sand stiffness can be utilized directly to compare the stiffness of various sandy terrains.

Conventional ground-wheeled vehicles usually have poor trafficability, low efficiency, a large amount of energy consumption and possible failure when driving on soft terrain. To solve this problem, this paper presents a new design of transformable wheels for use in an amphibious all-terrain vehicle. The wheel has two extreme working statuses: unfolded walking-wheel and folded rigid wheel. Furthermore, the kinematic characteristics of the transformable wheel were studied using a kinematic method. When the wheel is unfolded at walking-wheel status, the displacement, velocity and acceleration of the wheel with different slip rates were analyzed. The stress condition is studied by using a classic soil mechanics method when the transformable wheel is driven on soft terrain. The relationship among wheel traction, wheel parameters and soil deformation under the stress were obtained. The results show that both the wheel traction and trafficability can be improved by using the proposed transformable wheel. Finally, a finite element model is established based on the vehicle terramechanics, and the interaction result between the transformable wheel and elastic–plastic soil is simulated when the transformable wheel is driven at different unfold angles. The simulation results are consistent with the theoretical analysis, which verifies the applicability and effectiveness of the transformable wheel developed in this paper.

In this paper, a three-dimensional multi-body dynamic model of a seafloor mining vehicle is developed in the RecurDyn simulation program by integrating the developed terramechanics model of the seafloor sediment. The discrete element method (DEM) is employed to model a mining pipeline as discrete rigid elements linked by flexible connectors. An innovative user-defined subroutine for parametrically and rapidly automatically building a DEM model for such long pipeline is developed in the C language in RecurDyn. A new 3D multi-body dynamic model of a total deep ocean mining vehicle-pipeline-ship system is established with the integration of developed models for subsystems. The integrated motion simulations are achieved and demonstrate that the synchronized stable motion of the total system can be well maintained during operation processes. Do danes še ni bil narejen opis kompleksne dinamike celotnih sistemov za rudarjenje na globokih morjih. Izvajanje preizkusov na oceanu bi bila draga in izjemno težavna naloga, zato s tem pristopom ni mogoče vrednotiti konstrukcijskih rešitev in njihove sposobnosti za trajno obratovanje. Učinkovit vpogled v te lastnosti pa je mogoče pridobiti s simulacijami dinamike sistema. Članek opisuje razvoj točnih in učinkovitih modelov dinamike podsistemov, ki so združeni v model celotnega sistema. V jeziku C je bila pripravljena inovativna uporabniška podrutina za popis posebnega teramehanskega modela sedimentov na morskem dnu, ki je bila dodana v paket za simulacije RecurDyn/Track in nato validirana z laboratorijskimi preizkusi.

Because of the unique lunar environment, a suitable wheel for lunar rover decides the rover’s trafficability on deformable terrains. The wire mesh wheel (hereinafter referred to as WMW) has the advantages of light weight and superior stability, been widely adopted for lunar rovers. But a comprehensive research on performance of WMW on deformable terrains has not been conduct. This paper would provide particular study on a type WMW, including quasi-static pressure-sinkage test and driving performance. A novel pressure-sinkage model for the WMW on deformable soils was presented. In order to investigate the sinkage characteristics of the WMW, tests were performed using a single-wheel testbed for the WMW with different loads and velocities. The effects of load and velocity on sinkage were analyzed, and the relationship between real and apparent sinkage was presented. The research on traction performance of WMW under different slip ratios (0.1–0.6) was also conducted, contrast tests were proceed by using a normal cylindrical wheel (hereinafter referred to as CW). The traction performance of WMW is analyzed using performance indices including wheel sinkage, drawbar pull, driving torque, and tractive efficiency. The experimental results and conclusions are useful for optimal WMW design and improvement/verification of wheel–soil interaction mechanics model.

Dynamic simulation is an important aspect of legged robotic research, which is essential for its design and control. However, the dynamics of the interaction between a soft terrain and a deformable leg (e.g., a spring) is hardly taken into account. In this paper, a high-fidelity, faster-than-real-time simulation system for hexapod robots has been developed based on Vortex. Foot-terrain interaction mechanics and flexible mechanical system are taken into account in order to improve the simulation precision. A general foot-terrain interaction model is presented based on terramechanics. Pseudo-rigid-body method is used to simulate the flexibility of the robot. A speed test shows that the simulation system is capable of real-time or faster simulation. The simulation system's fidelity was validated using two hexapod robots, which is found to be greater than 90%.

This paper proposes a supporting force model of a Push-Pull Locomotion on the rough terrain. Planetary rovers should avoid many obstacles on the planetary surfaces, for instance, rocks, stones, and rough terrain. When planetary rovers become stuck, this typed rover can move by using a large supporting force of the wheel, which is generated by keeping a position of a supporting wheels relative to the ground and move to another position. Recently, planetary rovers need to be controlled autonomously, therefore, the interaction mechanics between supporting wheels and soil need to be investigated. The drawbar pull force of the rotational wheel model has been investigated in the terramechanics field, however, in the Push-Pull Locomotion, the supporting wheels are locked during bulldozing soil. Therefore, the conventional model cannot apply to the supporting wheels. As the initial step, this paper constructs the supporting force model of the locked wheels without considering normal force of a wheel by using the Coulomb and GLEM (Generalized Limit Equilibrium Method) theory. The validity of these models is confirmed by a single wheel bulldozing tests. The experimental results revealed that the proposed model based on the GLEM theory can predict the supporting force of the wheel without a normal force in each wheel size and sinkage.

Planetary exploration robots encounter challenging terrain during operation. Vision-based approaches have failed to reliably predict soil characteristics in the past, making it necessary to probe the terrain tactilely. We present a robust, haptic inspection approach for a variety of fine, granular media, which are representative of Martian soil. In our approach, the robot uses one limb to perform an impact trajectory, while supporting the main body with the remaining three legs. The resulting vibration, which is recorded by sensors placed in the foot, is decomposed using the discrete wavelet transform and assigned a soil class by a Support Vector Machine. We tested two foot designs and validated the robustness of this approach through the extensive use of an open-source dataset, which we recorded on a specially designed single-foot testbed. A remarkable overall classification accuracy of more than 98% could be achieved despite various introduced disturbances. The contributions of the different sensors to the classification performance are evaluated. Finally, we test the generalization performance on unknown soils and show that the interaction behavior can be anticipated., IEEE Robotics and Automation Letters, 4 (2), ISSN:2377-3766

The experimental execution, theoretical analysis, structural optimization and performance prediction of lunar rover wheels are subject to many limitations due to the particularity and complexity of the lunar environment. The numerical simulation has notable advantages in analyzing the interaction between wheels and lunar soil simulant and designing the lunar rover wheels applied to complex environments. In this paper, based on the theory of terramechanics, a three-dimensional (3D) dynamic system that simulated the interaction between irregular structure wheels and lunar soil simulant was established using the interface code and embedded FISH language of PFC3D. The rationality of the simulation system was verified by the wheel soil-bin test. Then, in order to improve and optimize the 3D dynamic simulation system, the interaction between wheel and lunar soil simulant was simulated in two different kinds of simulated lunar environments besides the flat ground, and the climbing property of the wheel was analyzed qualitatively. Finally, the mesoscopic changes of lunar soil stimulant particles were characterized by the color gradient variations, and the simulation results were processed in the IV program so that the distribution of lunar soil stimulant particles under the wheel could be observed more clearly. This research provided a reliable method for the study of the interaction between irregular wheel and loose lunar soil in complex environments and of designing the wheel structure.

Neural networks (NNs) have been widely implemented for identifying nonlinear models, and predicting the distribution of targets, due to their ability to store and learn training samples. However, for highly complex systems, it is difficult to build a robust global network model, and efficiently managing the large amounts of experimental data is often required in real-time applications. In this paper, an effective method for building local models is proposed to enhance robustness and learning speed in globally supervised NNs. Unlike NNs, Gaussian processes (GP) produce predictions that capture the uncertainty inherent in actual systems, and typically provides superior results. Therefore, in this study, each local NN is learned in the same manner as a Gaussian process. A mixture of local model NNs is created and then augmented using weighted regression. This proposed method, referred to as locally supervised NN for weighted regression like GP, is abbreviated as “LGPN”, is utilized for approximating a wheel–terrain interaction model under fixed soil parameters. The prediction results show that the proposed method yields significant robustness, modeling accuracy, and rapid learning speed.

A method is presented for the online prediction of the terrain-shearing parameters for a wheeled Unmanned Ground Vehicles (UGVs) traversing on an unknown terrain. The method uses a trained multiple-output least squares support vector machine (LS_SVM) to map engineering data and predict the terrain-shearing parameters such as cohesion, internal friction angle and shear deformation modulus without requiring information on wheel sinkage. The predicted terrain-shearing parameters can be used to predict vehicle drawbar pull which can be used for trafficability prediction, traction control and performance optimization. Experiments were performed using a single-wheel soil bin to measure the sinkage, drawbar pull and torque for a griddle net wheel under different slip ratio. An additional experiment was performed under a continuous slip ratio from 0.2 to 0.6 with a wheel load of 50 N to validate the method. The experimental results show that the multiple output LS_SVM model can accurately predict the terrain-shearing parameters using the slip ratio, torque and wheel load without the need of wheel sinkage.

The observation motivating this contribution was a perceived lack of expeditious deformable terrain models that can match in mobility analysis studies the level of fidelity delivered by today’s vehicle models. Typically, the deformable terrain-tire interaction has been modeled using Finite Element Method (FEM), which continues to require prohibitively long analysis times owing to the complexity of soil behavior. Recent attempts to model deformable terrain have resorted to the use of the Discrete Element Method (DEM) to capture the soil’s complex interaction with a wheeled vehicle. We assess herein a DEM approach that employs a complementarity condition to enforce non-penetration between colliding rigid bodies that make up the deformable terrain. To this end, we consider three standard terramechanics experiments: direct shear, pressure-sinkage, and single-wheel tests. We report on the validation of the complementarity form of contact dynamics with friction, assess the potential of the DEM-based exploration of fundamental phenomena in terramechanics, and identify numerical solution challenges associated with solving large-scale, quadratic optimization problems with conic constraints.

A lunar roving vehicle is of great significance in the processing of manned lunar exploration for long-duration space exploration missions. The mechanical model of the lunar roving vehicle’s wheel directly affects the mobility performance. However, the wheel of lunar roving vehicle is a special one with the metal mesh surface, and the soil can penetrate through its surface. In this paper, the mechanical model of a rigid normal wheel is deduced, and four stress correction coefficients are introduced to obtain the mechanical model of the lunar roving vehicle’s wheel. These four stress correction coefficients are identified in several groups of experiment of the lunar roving vehicle’s wheel, and using the functional coefficients can have a high precision for the mechanical model of the lunar roving vehicle’s wheel.

Nowadays soft soil–wheel contact models are widely used for predicting the mobility of rovers in off-road applications. However, most of the contact models used in computer simulations are based on semi-empirical laws for which soil parameters can be assessed only with large uncertainty. This lack of knowledge results in significant uncertainty on the rover position predictions. Applied to a planetary rover model, this paper illustrates probabilistic and non-probabilistic techniques for efficient treatment of soil parameter uncertainty for rover position predictions.

Planetary rovers on rough terrain are likely to encounter hazards such as rocks as well as loose soil or regolith that causes the wheels to slip and potentially get stuck. These missions need autonomous navigation for avoiding these hazards. The slippage of the wheels depends dynamically on the wheel properties, soil mechanical properties, speed and pose of the rover. In this paper, we investigate the path finding problem for a planetary rover on rough sandy terrain. Insights from terramechanics, ie. the wheel soil interaction model, is used to determine path cost to be used for the A ∗ algorithm, which is used on a sample grid to determine the best path. The proposed model incorporates the slippage required to develop drawbar pull to climb up a slope, as well as steering angle needed to counter lateral force. The path thus found is evaluated based on the slip ratio and steering angle required to traverse it.

As an indispensable tool for astronauts on lunar surface, the lunar roving vehicle (LRV) is of great significance for manned lunar exploration. An LRV moves on loose and soft lunar soil, so the mechanical property of its wheels directly affects the mobility performance. The wheels used for LRV have deformable and mesh pattern, therefore, the existing mechanical theory of vehicle wheel cannot be used directly for analyzing the property of LRV wheels. In this paper, a new mechanical model for LRV wheel is proposed. At first, a mechanical model for a rigid normal wheel is presented, which involves in multiple conventional parameters such as vertical load, tangential traction force, lateral force, and slip ratio. Secondly, six equivalent coefficients are introduced to amend the rigid normal wheel model to fit for the wheels with deformable and mesh-pattern in LRV application. Thirdly, the values of the six equivalent coefficients are identified by using experimental data obtained in an LRV’s single wheel testing. Finally, the identified mechanical model for LRV’s wheel with deformable and mesh pattern are further verified and validated by using additional experimental results.

This paper presents inexpensive methods whereby the vehicle side-slip angle can be measured accurately at low speeds on any terrain using cameras. Most commercial side-slip angle sensor systems and estimation techniques rely on smooth terrain and high vehicle speeds, typically above 20 km/h, to provide accurate measurements. However, during certain in-situ tyre and vehicle testing on off-road conditions, the vehicle may be travelling at speeds slower than required for current sensors and estimation techniques to provide sufficiently accurate results. Terramechanics tests are typical case in point. Three algorithms capable of determining the side-slip angle from overlapping images are presented. The first is a simple fast planar method. The second is a more complex algorithm which can extract not only the side-slip angle but also its rotational velocities and scaled translational velocities. The last uses a calibrated stereo-rig to obtain all rotations and translational movement in world coordinates. The last two methods are aimed more at rough terrain applications, where the terrain induces motion components other than typical predominant yaw-plane motion. The study however found no discernible difference in measured side-slip angle of the methods. The system allows for accurate measurement at low and higher speeds depending on camera speed and lighting.

Wheeled exploration robots (WERs) used for applications such as planetary exploration have to traverse loose terrain, often, during which time they may suffer longitudinal slip and side slip owing to the interaction between their rigid wheels and the loose soil. Longitudinal slip and side slip are the main causes for WERs delay or deviate from the ideal trajectory. But the presented work is indeed focused on longitudinal slip. By analyzing and simplifying the wheel–soil interaction terramechanics model for this case, the algorithm for an adaptive fuzzy control law based on slip ratio optimization is designed to optimize the tractive efficiency and minimize energy consumption. Its stability is proved, and conditions for control parameters are derived. Analytical and simulation results demonstrate that the proposed control system significantly improves the mobile performance of the WER.

Physical space exploration missions usually include exploring craters that are composed of various slopes and covered with fine regolith. Wheeled mobile robots (WMRs), commonly known as rovers, are widely used in these missions to find a host of information on topography, mineralogy, geological processes, etc. In traditional terramechanics theories, at least seven experiments under various slip ratios are required to estimate the terrain parameters and drawbar pull that determines a WMR's slope climbing capability. Moreover, the wheel sinkage—an important index that indicates whether the fine and soft planetary regolith would become a dangerous trap—cannot be estimated in-situ currently. In this paper, highly coupled terramechanics equations are simplified into closed-form analytical models, whose effectiveness is experimentally validated after wheels enter quasi-static conditions. Based on these validated equations, the goal of in-situ estimation of terrain parameters, drawbar pull, and wheel sinkage can be accomplished by directly measuring physically measureable quantities. Thus, wheeled rovers will have the ability to perceive the planetary regolith's mechanical properties and the wheels’ running condition by mounting an instrumental wheel that contains a rotation force/torque sensor.

This research focuses on prediction of the rolling resistance coefficient of an agriculture tyre using finite element analysis (FEA) technique, and Bekker and Wismer-Luth models. The tyre-soil interaction is modelled using FEA and smoothed-particle hydrodynamics (SPH) techniques in Visual Environment's PAM-Crash software and validated based on experimental results. A single-wheel tester along with a controlled soil bin at Urmia University, Iran is used to investigate the effect of a tyre's multi-pass and vertical load on the rolling resistance coefficient of an off-road tyre. In order to calculate the rolling resistance of Bekker model, a bevameter device is installed on a carriage moving on clayey-loam soil and a digital penetrometer is used for obtaining the output of Wismer-Luth model. Analysis of experimental data shows that rolling resistance coefficient increases as the vertical load increases and decreases with each pass of tyre. These results are used to compare and evaluate the above-mentioned methods. The results of this study will be used in further research on the interaction between a tyre and soil.

In many designs of vehicle suspension anti-roll bars are used for body roll reduction (Cronje and Els, J Terramechanics 47:179–189, 2010; Her et al., IFAC Proc. 2013. https://doi.org/10.3182/20130904-4-JP-2042.00152). Such solutions are used in compact cars (C-segment), mid-size cars (D-segment), mid-size luxury car (E-segment) and even sports cars (S-segment). Antiroll bars are torsion bars connecting both sides of car suspension and they are connected with suspension arms. When car wheels move in vertical direction these torsion bars are twisted. Increasing torsional stiffness of front or rear suspension is the main role of sway bars. The use of these rods reduces tilting of the body while riding at high speed when the tilt of a car body is caused by the centrifugal force acting on the car. This force compress suspension spring with one side of the car, and extends on the other. The torque generated by the torsion bars reduce the difference in springs suspension. It reduces the compression of springs on one side of a car and extension on the other. Reduction of car body tilt improving handling and road holding and therefore improve safety. Antiroll bars also allow for the reduction of lateral vibrations caused by road roughness. During straight driving on equal road surface or under the same excitation of the wheels, the stabilizer doesn’t work. During overcoming high road irregularities, the force acting on one of a wheel is transferred to the other via the bar. Antiroll bars also allow for the reduction of lateral vibrations caused by road inequalities. This causes unwanted oscillations. This effect is more noticeable if angle stiffness of the stabilizer is higher. In order to avoid such phenomena, active anti-roll bars are used. The most commonly used solutions are two-part active disconnect anti-roll bar or just active antiroll bar. In case of a two-part disconnectable anti-roll bar a hydraulic actuator connected to the ends of the roll bars usually is used. In such case, wheels work independently of each other so that the reactions from one wheel are not transferred to the other. If necessary, the stabilizer is connected by means of an actuator and works just like the classic one. In an active stabilizer a hydraulic actuator connected to the ends of the antiroll rods usually is used. Controlling the pressure or flow rates of the oil gives wide possibilities for acting actively on the anti-swaying of the vehicle.

What does it make some sports such as off-road motorcycle to be perceived as non-environmentally-friendly? Are the activities themselves or the actual and/or traditional way of their fulfillment? How is it possible to make them more environmentally sustainable without giving up the fun? This paper aims to give an answer to these questions, analyzing the case of off-road motorcycling. It is clear that some of negative consequences of such sport are due to the bad behavior and scarce ecological awareness of its practitioners, while it is often neglected that other aspects are related to the present characteristics of its means: the motorcycles. The present work, starting with the analyses of the environmental damages related to this sport, tries to give an answer focusing on the technical aspects of actual motorcycles that can be related to such damages. In particular, the authors propose the application of an integrated eco-innovation and technical contaminated approach for the design and development of a new concept of off-road motorcycle to meet the requirements of low environmental impact and light weight of the vehicle, while maintaining the pleasure of riding in the nature.

One of the key tasks of mobile robotics is navigation, which for Outdoor-type robots is exacerbated by the functioning in an environment with a priori of unknown characteristics of underlying surfaces. In this paper, for the first time, the learning navigation system for mobile robot based on the group method of data handling (GMDH) is presented. The paper presents the results of training of models both for evaluating the robot’s pose (coordinates and angular orientation) in heterogeneous environment and classification of the type of underlying surfaces. In addition to the direct readings of the on-board sensors, additional parameters (reflecting how the robot perceives the surface terramechanics) were introduced to train the models. The results of testing of the obtained models demonstrate their performance in an essentially heterogeneous environment, when areas of the underlying surfaces are comparable with the robot’s dimensions. This testifies the operability of developed GMDH-based learning system for mobile robot navigation.