Review of terramechanics models and their applicability to real-time applications

ISTVS embarked on a project in 2016 that aims at updating the current ISTVS standards related to nomenclature, definitions, and measurement techniques for modelling, parameterizing, and, respectively, testing and validation of soft soil parameters and vehicle running gear-terrain interaction. As part of this project, a comprehensive literature review was conducted on the parameterization of fundamental terramechanics models. Soil parameters of the empirical models to assess off-road vehicle mobility, and parameters of the models to characterize the response of the terrain interacting with running gears or plates from the existing terramechanics literature and other researchers’ reports were identified. This review documents and summarizes the modelling approaches that may be applicable to real-time applications of terramechanics in simulation, as well as in controller design.     

Estimation of net traction for differential-steered wheeled robots

We present a method for estimating the net traction and resistive wheel torques for a suspensionless, differential-steered robot on rigid or deformable terrain. The method, based on extended Kalman-Bucy filtering (EKBF), determines time histories of net traction and resistive wheel torques and wheel slips during steady or transient maneuvers. This method assumes good knowledge of the vehicle dynamics and treats the unknown forces and moments due to terrain response as random variables to be estimated. A proprioceptive sensor suite renders a subset of the unknown forces and associated wheel slip and slip angles observable. This methodology decouples semi-empirical terramechanics models from the net effect of the vehicle-terrain interaction, namely the net traction developed by the vehicle on the terrain. By collecting sensor data and processing data off-line, force-slip characteristics are identified irrespective of the underlying terramechanics. These characteristics can in turn support development or validation of terramechanics models for the vehicle-terrain system. For autonomous robots, real-time estimates of force-slip characteristics can provide setpoints for traction and steering control, increasing vehicle performance, speed, and maneuverability. Finally, force-slip estimation is the first step in identifying terrain parameters during normal maneuvering. The methodology is demonstrated through both simulation and physical testing using a 13-kg robot.     

Next-generation NATO reference mobility model complex terramechanics – Part 1: Definition and literature review

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.     

Modelling of off-road wheeled vehicles for real-time dynamic simulation

Simulation of wheel-ground and vehicle-ground interactions is very important in many applications. Achieving accuracy and efficiency is challenging for both soft and hard terrains. This is not only because of the simulation and numerical challenges, but also due to the questionable nature of the existing terrain models. For example, the most widely used terramechanics model is not a representative constitutive relation for a full range of dynamic conditions and applications, but rather a parametrization of steady state conditions. In general, the selection and development of the proper constitutive model and the parametrization of the ground properties are very challenging. Here, we present a unified framework for general wheel-ground interaction which can be used with different terramechanics models. The framework is based on a complementarity formulation and also uses the concept of kinematic constitutive relations, beside the other known concepts for modelling and parametrizing the soil properties. The framework makes it possible to consider the appropriate modelling of the terrain for a broad range of dynamic behaviours and simulation conditions. We will illustrate the material with several examples for off-road conditions.     

Finite element modeling of tire/terrain interaction: Application to predicting soil compaction and tire mobility

Tire/terrain interaction has been an important research topic in terramechanics. For off-road vehicle design, good tire mobility and little compaction on terrain are always strongly desired. These two issues were always investigated based on empirical approaches or testing methods. Finite element modeling of tire/terrain interaction seems a good approach, but the capability of the finite element has not well demonstrated. In this paper, the fundamental formulations on modeling soil compaction and tire mobility issues are further introduced. The Drucker-Prager/Cap model implemented in ABAQUS is used to model the soil compaction. A user subroutine for finite strain hyperelasticity model is developed to model nearly incompressible rubber material for tire. In order to predict transient spatial density, large deformation finite element formulation is used to capture the configuration change, which combines with soil elastoplastic model to calculate the transient spatial density due to tire compaction on terrain. Representative simulations are provided to demonstrate how the tire/terrain interaction model can be used to predict soil compaction and tire mobility in the field of terramechanics.     

Cross-country mobility on various snow conditions for validation of a virtual terrain

Realistic simulation of on- and off-road vehicle performance in all weather conditions is needed by the U.S. Army for virtual training of personnel on existing vehicles, and for new vehicle design. The virtual test site is a computer simulation representing an actual terrain defined as having spatially distributed terramechanics properties and terrain interaction with vehicles. We developed a virtual test site for Ethan Allen Firing Range (EAFR) in northern Vermont. The virtual test site for EAFR is composed of terramechanics properties including spatially distributed snow depth and density, soil type, drainage class, slope, and vegetation type. Snow depth and density were spatially distributed with regard to elevation, slope, and aspect using a surface energy balance approach. This paper evaluates whether the terramechanics representation of a virtual test site is improved by adding spatially distributed snow and soil properties, rather than using uniform properties. The evaluation was accomplished by conducting a cross-country vehicle performance analysis using the North Atlantic Treaty Organization (NATO) Reference Mobility Model (NRMM) to validate the new algorithms for realistic spatial distribution of snow properties. The results showed that the percentage of No-Go areas for uniform snow is lower than the distributed snow by 4% for the CIV (CRREL Instrumented Vehicle), 8% for the HMMWV (High Mobility Multipurpose Wheeled Vehicle), and 5% for the Stryker vehicle. For both light vehicles, approximately 12% of the No-Go areas are classified as such because of slopes 29%. These results imply that spatial distribution of snow properties provides realistic vehicle response as opposed to having the snow properties distributed uniformly throughout the entire terrain. This represents an improvement over previous versions of the terramechanics properties.     

地面力学及其在行星探测研究中的应用

地面力学是研究越野行驶中机器与地面相互作用的一门力学学科,包括对机器通过性的预测和评价,行走机构的优化设计以及对地面可行驶性的预测判断等几个方面.首先简介地面力学的研究方法、试验仪器和设备以及主要的成果和结论,其中包括在这些方面的最新研究进展情况.之后重点介绍行星探测领域中所开展的地面力学研究,主要从行星探测器设计阶段对地面力学理论和方法的应用、行星模拟土壤研制和力学特性研究、行星就位土壤力学参数测量等几个方面进行了综述.最后对这一领域今后的研究方向进行了探讨.      

Reduced testing and modelling of the bearing capacity of rooted soil for wheeled forestry machines

The next generation of forestry machines must be developed to be gentler to soil and to the root mat than present machines, especially in thinning operations. The bearing capacity of the soil is a key property for determining the terrain trafficability and machine mobility. This asks for better and more general terramechanics models that can be used to predict the interaction between different machine concepts and real and complex forest soil.This paper presents results from terramechanics experiments of rooted soil with a new and small-scale testing device. The force–deflection results are analyzed and compared with analytical root reinforcement models found in literature. The presented study indicates that rooted soil properties obtained with the new laboratory test device can be used to create an augmented soil model that can be used to predict the bearing capacity of rooted soil and also to be used in dynamic machine–soil interaction simulations.     

Online terrain estimation for autonomous vehicles on deformable terrains

In this work, a terrain estimation framework is developed for autonomous vehicles operating on deformable terrains. Previous work in this area usually relies on steady state tire operation, linearized classical terramechanics models, or on computationally expensive algorithms that are not suitable for real-time estimation. To address these shortcomings, this work develops a reduced-order nonlinear terramechanics model as a surrogate of the Soil Contact Model (SCM) through extending a state-of-the-art Bekker model to account for additional dynamic effects. It is shown that this reduced-order surrogate model is able to accurately replicate the forces predicted by the SCM while reducing the computation cost by an order of magnitude. This surrogate model is then utilized in an unscented Kalman filter to estimate the sinkage exponent. Simulations suggest this parameter can be estimated within 4% of its true value for clay and sandy loam terrains. It is also shown in simulation and experiment that utilizing this estimated parameter can reduce the prediction errors of the future vehicle states by orders of magnitude, which could assist with achieving more robust model-predictive autonomous navigation strategies.     

Torque distribution influence on tractive efficiency and mobility of off-road wheeled vehicles

Off-road vehicle performance is strongly influenced by the tire-terrain interaction mechanism. Soft soil reduces traction and significantly modifies vehicle handling; therefore tire dynamics plays a strong role in off-road mobility evaluation and needs to be addressed with ad-hoc models. Starting from a semi-empirical tire model based on Bekker–Wong theory, this paper, analyzes the performance of a large four wheeled vehicle driving on deformable terrain. A 14 degree of freedom vehicle model is implemented in order to investigate the influence of torque distribution on tractive efficiency through the simulation of front, rear, and all wheel drive configuration. Results show that optimal performance, regardless vertical load distribution, is achieved when torque is biased toward the rear axle. This suggests that it is possible to improve tractive efficiency without sacrificing traction and mobility. Vehicle motion is simulated over dry sand, moist loam, flat terrain and inclined terrain.     

Tractive performance analysis of a lugged wheel by open-source 3D DEM software

Open-source software (OSS) is free to use and has accessible source codes, thus, it can be modified by various users. By using OSS, it is possible to easily and economically develop a target program for interaction studies in terramechanics. Yet Another Dynamic Engine (YADE) is an OSS for the 3D discrete element method (DEM), but its applicability to various contact interaction problems in terramechanics is not well-known. To investigate the applicability of YADE in terramechanics, the tractive performance of a lugged wheel was analyzed in this study. An idea of a proportional-integral-differential control model was applied to realize the constant rotation of the wheel in YADE. Our previous experiments on the locomotion of a small lugged wheel on a lunar-soil simulant were analyzed by YADE, and the results were found to be qualitatively similar to the obtained experimental results when considering the effects of the lug height, lug thickness, lug number, and wheel diameter. By applying a quasi-2D analysis with the same soil bin width and wheel width, the computational load of 3D DEM by YADE can be reduced up to 36.8% with similar net traction behavior against the wheel slip in a 3D analysis.     

Algorithm and implementation of soil–tire contact analysis code based on dynamic FE–DE method

One of the fundamental problems in terramechanics is soil–tire system. Past achievements on this topic can be observed in various literatures. Fast development on CPU power of PC system enables us to apply numerical methods to this basic subject. Among others, finite element method (FEM) has been applied to simple problems of soil–tire system not only in 2D but also in 3D approach. However, it is noted that the current FEM technology cannot handle “singular” boundary conditions with sufficient accuracy of analysis. Typical example of this limitation can be seen in an application to traction tire–soil contact problems, where the contact point of tire lug tip behaves as the singular point of stress field. On the other hand, distinct or discrete element method (DEM) has in essence the capability of analyze microscopic deformation (or flow) of soil as many researchers have already been demonstrated. It is noted that DEM suffers large calculation time that is consumed not only at contact check between particulate elements but also at incremental time step. In our present study, we try to combine both merit of FEM and DEM together in order to analyze the soil–tire system interaction, where, for example, a tire and deep soil layer are modeled as FEM and soil surface layer as DEM. We propose simple algorithm of this FE–DE coupled method and sample program is developed that can solve some basic terramechanics problems in order to verify our idea. The obtained result shows qualitatively sufficient accuracy.     

Investigation of elemental shape for 3D DEM modeling of interaction between soil and a narrow cutting tool

Discrete Element Method (DEM) has been applied in recent studies of soil cutting tool interactions in terramechanics. Actual soil behavior is well known to be inexpressible by simple elemental shapes in DEM, such as circles for 2D or spheres for 3D because of the excessive rotation of elements. To develop a more effective model for approximating real soil behavior by DEM, either the introduction of a rolling resistance moment for simple elemental shape or the combination of simple elements to form a complex model soil particle shape cannot be avoided. This study was conducted to investigate the effects of elemental shape on the cutting resistance of soil by a narrow blade using 3D DEM. Six elemental shapes were prepared by combining unit spheres of equal elemental radius. Moreover, cutting resistance was measured in a soil bin filled with air-dried sand to collect comparative data. The elemental shape, with an axial configuration of three equal spheres overlapped with each radius, showed similar results of soil cutting resistance to those obtained experimentally for the six elemental shapes investigated.     

2D FE–DEM analysis of tractive performance of an elastic wheel for planetary rovers

We have been developing a simulation program for use with soil–wheel interaction problems by coupling Finite Element Method (FEM) and Discrete Element Method (DEM) for which a wheel is modeled by FEM and soil is expressed by DEM. Previous two-dimensional FE–DEM was updated to analyze the tractive performance of a flexible elastic wheel by introducing a new algorithm learned from the PID-controller model. In an elastic wheel model, four structural parts were defined using FEM: the wheel rim, intermediate part, surface layer, and wheel lugs. The wheel rigidity was controlled by varying the Young’s Modulus of the intermediate part. The tractive performance of two elastic wheels with lugs for planetary rovers of the European Space Agency was analyzed. Numerical results were compared with experimentally obtained results collected at DLR Bremen, Germany. The FE–DEM result was confirmed to depict similar behaviors of tractive performance such as gross tractive effort, net traction, running resistance, and wheel sinkage, as in the results of experiments. Moreover, the tractive performance of elastic wheels on Mars was predicted using FE–DEM. Results clarified that no significant difference of net traction exists between the two wheels.     

Design and development of a new transformable wheel used in amphibious all-terrain vehicles (A-ATV)

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.     

Efficient generation of accurate mobility maps using machine learning algorithms

U.S Army’s mission is to develop, integrate, and sustain the right technology solutions for all manned and unmanned ground vehicles, and mobility is a key requirement for all ground vehicles. Mobility focuses on ground vehicles’ capabilities that enable them to be deployable worldwide, operationally mobile in all environments, and protected from symmetrical and asymmetrical threats. In order for military ground vehicles to operate in any combat zone, the planners require a mobility map that gives the maximum predicted speeds on these off-road terrains. In the past, empirical and semi-empirical techniques (Ahlvin and Haley, 1992; Haley et al., 1979) were used to predict vehicle mobility on off-road terrains such as the NATO Reference Mobility Model (NRMM). Because of its empirical nature, the NRMM method cannot be extrapolated to new vehicle designs containing advanced technologies, nor can it be applied to lightweight robotic vehicles.The mobility map is a function of different parameters such as terrain topology and profile, soil type (mud, snow, sand, etc.), vegetation, obstacles, weather conditions, and vehicle type and characteristics.A physics-based method such as the discrete element method (DEM) (Dasch et al., 2016) was identified by the NATO Next Generation NRMM Team as a potential high fidelity method to model the soil. This method allows the capture of the soil deformation as well as its non-linear behavior. Hence it allows the simulation of the vehicle on any off-road terrain and have an accurate mobility map generated. The drawback of the DEM method is the required simulation time. It takes several weeks to generate the mobility map because of the large number of soil particles (millions) even while utilizing high performance computing.One approach to reduce the computational time is to use machine learning algorithms to predict the mobility map. Machine learning (Boutell et al., 2004; Burges, 1998; Barber et al., 1997) can lead to very accurate mobility predictions over a wide range of terrains. Machine learning is divided into two categories: the supervised and the unsupervised learning. Supervised learning requires the training data to be labeled into predetermined classes, while the unsupervised learning does not require the training data to be labeled. Machine learning can help generate mobility maps using trained models created from a minimum number of simulation runs. In this study different supervised machine learning algorithms such as the support vector machine (SVM), the nearest neighbor classifier (k-NN), decision trees, and boosting methods were used to create trained models labeled as 2 classes for the ‘go/no-go’ map, 5 classes for the 5-speed map, and 7 classes for the 7-speed map. The trained models were created from the physics-based simulation runs of a nominal wheeled vehicle traversing on a cohesive soil.     

A comparison of ground vehicle mobility analysis based on soil moisture time series datasets from WindSat,LIS, and in situ sensors

Soil moisture is a key terrain variable in ground vehicle off-road mobility. Historically, models of the land water balance have been used to estimate soil moisture. Recently, satellites have provided another source of soil moisture estimates that can be used to estimate soil-limited vehicle mobility. In this study, we compared the off-road vehicle mobility estimates based on three soil moisture sources: WindSat (a satellite source), LIS (a computer model source), and in situ ground sensors (to represent ground truth). Mobility of six vehicles, each with different ranges of sensitivity to soil moisture, was examined in three test sites. The results demonstrated that the effect of the soil moisture error on mobility predictions is complex and may produce very significant errors in off-road mobility analysis for certain combinations of vehicles, seasons, and climates. This is because soil moisture biases vary in both direction and magnitude with season and location. Furthermore, vehicles are sensitive to different ranges of soil moistures. Modeled vehicle speeds in the dry time periods were limited by the interaction between soil traction and the vehicles’ powertrain characteristics. In the wet season, differences in soil strength resulted in more significant differences in mobility predictions.     

Design of manned lunar rover wheels and improvement in soil mechanics formulas for elastic wheels in consideration of deformation

Most of the current lunar rover vehicle wheels are inconvenient for changing broken wheels and have poor shock absorbing in driving, so they cannot be used to carry people on the moon. To meet the demands for manned lunar transportation, a new wheel possessing a woven metal wire mesh tire and using hub-rim combination slide mechanism is designed in this article. The characteristics of the new wheel is analyzed by comparing with the same-size conventional rover wheels after demonstrating the validity of FEM simulation. The new wheel possesses lighter structure and superior shock absorbing. It also provides stronger traction because the deformation of the designed wheel increases the contact area between the tire and lunar terrain. In order to establish an on-line soil parameter estimation algorithm for low cohesion soil, the stress distribution along a driven deformable wheel on off-road terrain is simplified. The basic mechanics equations of the interaction between the wheel and the lunar soil can be used for analytical analysis. Simulation results show that the soil estimation algorithm can accurately and efficiently identify key soil parameters for loose sand.     

Discrete element method-based studies on dynamic interactions of a lugged wheel with granular media

Terramechanics plays an important role in determining the design and control of autonomous robots and other vehicles that move on granular surfaces. Traction capabilities, slippage, and sinkage of a robot are governed by the interaction of a robot’s appendage with the operating terrain. It is important to understand how the terrain flows under this appendage during such an interaction. In this work, dynamics of soil performance and locomotion performance of a lugged wheel travelling on soft soil are numerically investigated. Studies are conducted with a two-dimensional model by using the discrete element method to analyze the interactions between a lugged wheel and the soil. The soil performance is studied by examining the force distribution and evolution of force networks during the course of the wheel travel. For two different control modes, namely, slip-based wheel control and angular velocity-based wheel control, the performance parameters such as, sinkage, traction, traction efficiency, and power consumption of the wheel are compared for various wheel configurations. The findings of this work are expected to be useful for optimal design and control of the lugged wheel travelling on deformable surfaces.     

Simulation on mechanical behavior of cohesive soil by Distinct Element Method

Analysis in the dynamic mechanical behavior of cohesive soils subjected to external forces is very important in designing and optimizing terrain machines. Distinct Element Method (DEM) is an ideal method to analyze large discontinuous deformations of soil, but the conventional DEM model is difficult in simulating the complex behavior of cohesive soil. In order to simulate and analyze the behavior of cohesive soil accurately, the DEM mechanical model of cohesive soil with parallel bonds between particles was established by considering the capillary and the dynamic viscous forces induced by the presence of water between soil particles. During the excavation process by a bulldozing plate, the dynamic behavior of cohesive soil was simulated by DEM software PFC2D. The phenomena that the discrete particles were bonded into clusters initially, and the clusters were broken into smaller clusters or discrete particles during the excavation process, are consistent with the ruptures and separations of the actual cohesive soils subjected to external forces.