Hybrid modelling is a concept that has been introduced in various fields of research but has yet to be explored in the field of terramechanics. The concept of a hybrid model is to find a middle ground between representing some system or process using traditional parametric models that are derived from first principles and data-based approaches that use statistical analysis or machine learning (ML) algorithms based on large amounts of experimental data gathered on the system that is being studied. The parametric models have the advantage of being based on known physical principles and provide a clear understanding of the system. Unfortunately, the systems being studied are often too complex to be accurately described by such models, and the necessary assumptions that are made in their development can also limit the scope of their applicability. Data-based methods can be used to represent systems that are difficult to model in other ways by simply using ML to map inputs to outputs. Given enough training data, this approach can be representative, but it provides no physical understanding of the system. A hybrid model combines both approaches to make up for each of their shortcomings. In such a model, a well-established parametric model is used to represent a system and a ML algorithm is trained to augment the model in an effort to represent the effects of phenomena that it does not capture. Training data is still required to train the ML component of the model, but the ML component learns only the necessary additions to the parametric model rather than the entire system. By using a hybrid model, the physical insights and understanding that the parametric model provides are maintained while ML is used to augment it in cases where its limitations prevent it from accurately describing the system being studied.

In traditional terramechanics theory, a pressure-sinkage equation is used to relate the pressure acting on a point along the wheel-soil contact surface to the wheel sinkage at that point. Another equation relates the normal pressure and the wheel slip to the shear stress acting at any point the wheel-soil interface. Because the normal soil reaction force is largely produced by the normal stress of the compacted soil, the wheel slip has very little effect on the predicted sinkage value. This means that, all other parameters being constant, the sinkage and compaction resistance force remain almost constant regardless of the slip. In practice, vehicles develop increasing sinkage with increasing slip and the true value of compaction resistance force can be up to double the force predicted using the traditional methods. Failing to capture this slip-sinkage effect can therefore lead to an over-estimation of vehicle performance indicators such as required power, traversability and maximum speed. This overestimation can lead to the design or selection of vehicles that are unable to perform the tasks that they are meant to complete. This problem was addressed in other works using analytical equations for the prediction of slip-sinkage that are based on experimental data. This work will present a detailed description of the application of the previously proposed slip-sinkage method as applied to a full vehicle performance prediction model.

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.

In this work, a simulation framework for testing of a tandem tractor-trailer is developed. The multibody dynamics engine Vortex Studio is used as the platform for modeling and simulation. The framework includes a configurable vehicle model, Simulink controller integration, an autonomous driver model, an automated vehicle test suite, and a test scene with a complex driving track. The framework provides a platform to evaluate the stability and maneuverability of a tandem tractor-trailer equipped with different active and passive trailer steering controllers.

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 com-ponent 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.(c) 2023 ISTVS. Published by Elsevier Ltd. All rights reserved.

The Nepean Wheeled Vehicle Performance Model (NWVPM) software has been in use for decades as a tool for engineers in industry and governmental agencies to predict the performance of off-road wheeled vehicles. It is based on the Bekker-Wong wheel-terrain interaction model which takes into account both the normal pressure and shear stress distributions at the wheel-terrain interface and uses the BekkerWong terrain parameters to characterize the terrain behavior. Using terrain and vehicle parameters as inputs, NWVPM computes various traction indicators such as drawbar pull, tractive effort, sinkage, and external motion resistance as functions of wheel slip by solving a set of equilibrium equations. This paper describes a novel method for predicting vehicle speed-made-good mobility maps and fuel consumption through an analytical approach using NWVPM. To evaluate the proposed method for predicting speedmade-good, a comparison is made with predictions obtained using Vortex, a commercial multibody dynamic simulation software that performs dynamic simulations of vehicles on soft terrain. In addition, a comparison of the capabilities of NWVPM and Vortex in predicting off-road vehicle performance over a range of terrains is presented and the results of the drawbar pull traction test from both software are compared with experimental data. Crown Copyright (C) 2022 Published by Elsevier Ltd on behalf of ISTVS. All rights reserved.

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. (c) 2021 ISTVS. Published by Elsevier Ltd. All rights reserved.

The discrete element method (DEM) is widely seen as one of the more accurate, albeit more computationally demanding approaches for terramechanics modelling. Part of its appeal is its explicit consideration of gravity in the formulation, making it easily applicable to the study of soil in reduced gravity environments. The parallel particles (P-2) approach to terramechanics modelling is an alternate approach to traditional DEM that is computationally more efficient at the cost of some assumptions. Thus far, this method has mostly been applied to soil excavation maneuvers. The goal of this work is to implement and validate the P-2 approach on a single wheel driving over soil in order to evaluate the applicability of the method to the study of wheel-soil interaction. In particular, the work studies how well the method captures the effect of gravity on wheel-soil behaviour. This was done by building a model and first tuning numerical simulation parameters to determine the critical simulation frequency required for stable simulation behaviour and then tuning the physical simulation parameters to obtain physically accurate results. The former were tuned via the convergence of particle settling energy plots for various frequencies. The latter were tuned via comparison to drawbar pull and wheel sinkage data collected from experiments carried out on a single wheel testbed with a martian soil simulant in a reduced gravity environment. Sensitivity of the simulation to model parameters was also analyzed. Simulations produced promising data when compared to experiments as far as predicting experimentally observable trends in drawbar pull and sinkage, but also showed limitations in predicting the exact numerical values of the measured forces. (C) 2020 ISTVS. Published by Elsevier Ltd. All rights reserved.

Wheel-soil interaction modelling can be approached with continuum-based or discrete elements based methods. The traditional semi-empirical methods and also the finite element models are all based on the concept of the continuum approach. On the other hand detailed discrete element models are also used to model the soil for wheel-soil interaction studies. But, this is usually a computationally demanding task. However, the explicit consideration of gravity in discrete element formulations is straightforward. This can be particularly important for planetary exploration operations where effects of different gravitational conditions can be dominant. In this work we discuss a discrete element technique, called position-based (PB) approach, and its application to wheel-soil interaction and particularly the study of gravitational effects. We will also use experimental results obtained under reduced gravity conditions using Martian soil simulant to analyze the computational results. The PB approach is based on using particles only and considering their interactions in an implicit way via formulating a time stepping problem with constraints first and then relaxing these constraints to bring in constitutive relations. This makes the approach computationally more efficient as opposed to traditional explicit discrete element formulations. We analyzed a single wheel driving over soil in order to evaluate the applicability and performance of the method. This was achieved by building a model and first tuning numerical simulation parameters to determine the critical simulation frequency then tuning the physical parameters to obtain accurate results. The former were tuned via the convergence of particle settling energy and soil settling level plots for various frequencies. The physical parameters were tuned via comparison to drawbar pull and wheel sinkage data collected from experiments carried out on a single wheel testbed in both Earth-based and reduced gravity environments. The simulations have produced promising results when compared to experiments. We will present these results and comparisons.

The definition of performance indicators is a useful tool in the design and operation of planetary exploration rovers. These robots are intended to operate in unstructured environments, often with unknown mechanical properties, which makes it difficult to accurately predict the behaviour of the vehicle in realworld conditions. On the other hand, it is also possible to define performance indicators based on an alternative approach, where the qualitative effect of changes in the design and operation parameters on the performance of the rover becomes the primary goal of the analysis. The use of performance indicators in the analysis of planetary exploration vehicles was demonstrated in an earlier paper [1]. Wheel radius, vehicle centre-of-mass position, and torque distribution among the wheels were selected as design and operation parameters. The effect of their variation on the performance indicator, i.e. the overall traction developed by the rover, was studied with simulations and experiments. A similar approach was used by Thueer and Siegwart [2], where several performance indicators were defined for a step-climbing manoeuvre. Different vehicle suspension concepts were compared using static analysis in terms of the torque required to climb the obstacle and the ratio between normal and tangent forces at the contact points between wheels and ground. (a) -0.5 0 0.5 1 1.5 2 2.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 R at io T an g en t / R ad ia l F o rc e