Justin Madsen

A Physics-Based Vehicle/Terrain Interaction Model for Soft Soil Off- Road Vehicle Simulations

In the context of off-road vehicle simulations, deformable terrain models mostly fall into three categories: simple visualization of an assumed terrain deformation, use of empirical relationships for the deformation, or finite/discrete element approaches for the terrain. A real-time vehicle dynamics simulation with a physics-based tire model (brush, beam-based or Finite Element models) requires a terrain model that accurately reflects the deformation and response of the soil to all possible inputs of the tire in order to correctly simulate the response of the vehicle. The real-time requirement makes complex finite/discrete element approaches unfeasible, and the use of a ring or beam -based tire model excludes purely empirical terrain models. We present the development of a three-dimensional vehicle/terrain interaction model which is comprised of a tire and deformable terrain model to be used with a real-time vehicle dynamics simulator. The governing equations of both models are physics-based, rather than utilizing popular terramechanics models that are empirical. The tire draws on a lumped-mass model based on a radial spring-damper-mass distribution. The terrain model utilizes Boussinesq and Cerruti soil mechanics equations to determine the pressure distribution and deformation of a volume of soil as a function of normal and tangent forces applied at the soil surface by the tire. The soil volume that describes the terrain is discretized as a set of vertical columns of soil, and the deformation of each is modeled using visco-elasto-plastic compressibility relationships that relate subsoil pressures to a change in bulk density of the soil, which in turn produces soil displacements. Different loading combinations applied by a tire passing over a column of soil will be reflected in the state of each volume of soil contained in the column, rather than treating the column of soil as homogeneous in the vertical direction and only associating one set of parameters with the entire column, e.g. a Bekker type model. Furthermore, the time-dependent elastic and plastic response of the soil to repetitive compression/rebound tire loads is also taken into account. Horizontal soil force/displacement produced by tractive and turning forces will also be incorporated into the model. Both the vertical and horizontal force/displacement relationships allow the calculation of total energy and power required to deform the terrain. These physics-based models will be integrated into a real-time vehicle dynamics simulator and is anticipated to lead to a realistic vehicle dynamic response when driving on off-road, deformable terrain conditions, especially when repeated loading occurs or non-homogeneous soil conditions are present. Additionally, the changes in soil states can be used to directly compute the energy and power required to deform the terrain. In order to retain the ability to run real-time simulations, a GPU-accelerated approach is considered to leverage the inherently parallel nature of performing multiple independent terrain geometry queries and soil-mechanics calculations. Numerical experiments include a single soil volume node under a known load and a simplified tire model applying normal forces on the surface of the terrain. Results are given for the vertical plastic soil deformation, and for the power and energy required to perform the deformations.

A Stochastic Approach to Integrated Vehicle Reliability Prediction

This paper addresses some aspects of an on-going multiyear research project of GP Technologies in collaboration with University of Wisconsin-Madison for US Army TARDEC. The focus of this research project is to enhance the overall vehicle reliability prediction process. A combination of stochastic models for both the vehicle and operational environment are utilized to determine the range of the system dynamic response. These dynamic results are used as inputs into a finite element analysis of stresses on subsystem components. Finally, resulting stresses are used for damage modeling and life and reliability predictions. This paper describes few selected aspects of the new integrated ground vehicle reliability prediction approach. The integrated approach combines the computational stochastic mechanics predictions with available statistical experimental databases for assessing vehicle system reliability. Such an integrated reliability prediction approach represents an essential part of an intelligent virtual prototyping environment for ground vehicle design and testing.Copyright

A GAUSSIAN PROCESS BASED APPROACH FOR HANDLING UNCERTAINTY IN VEHICLE DYNAMICS SIMULATION

Advances in vehicle modeling and simulation in recent years have led to designs that are safer, easier to handle, and less sensitive to external factors. Yet, the potential of simulation is adversely impacted by its limited ability to predict vehicle dynamics in the presence of uncertainty. A commonly occurring source of uncertainty in vehicle dynamics is the road-tire friction interaction, typically represented through a spatially distributed stochastic friction coefficient. The importance of its variation becomes apparent on roads with ice patches, where if the stochastic attributes of the friction coefficient are correctly factored into real time dynamics simulation, robust control strategies could be designed to improve transportation safety. This work concentrates on correctly accounting in the nonlinear dynamics of a car model for the inherent uncertainty in friction coefficient distribution at the road/tire interface. The outcome of this effort is the ability to quantify the effect of input uncertainty on a vehicle’s trajectory and the associated escalation of risk in driving. By using a space-dependent Gaussian process, the statistical representation of the friction coefficient allows for consistent space dependence of randomness. The approach proposed allows for the incorporation of noise in the observed data and a nonzero mean for inhomogeneous distribution of the friction coefficient. Based on the statistical model considered, consistent friction coefficient sample distributions are generated over large spatial domains of interest. These samples are subsequently used to compute and characterize the statistics associated with the dynamics of a nonlinear vehicle model. The information concerning the state of the road and thus the friction coefficient is assumed available (measured) at a limited number of points by some sensing device that has a relatively homogeneous noise field (satellite picture or ground sensors, for instance). The methodology proposed can be modified to incorporate information that is sensed by each individual car as it advances along its trajectory.Copyright

Compaction-Based Deformable Terrain Model as an Interface for Real-Time Vehicle Dynamics Simulations

This paper discusses the development of a deformable terrain database to be used in a co-simulation environment with a multibody dynamics vehicle model. The implementation of the model includes a general tire-terrain traction model which is modular to allow for any type of tire model that supports the Standard Tire Interface[1] to operate on the terrain. Rather than utilizing empirical terramechanics models that only consider the pressure/sinkage directly under the tire, the governing equations of the terrain are based on a soil compaction model that includes both the propagation of subsoil stresses due to vehicular loads, and the resulting visco-elastic-plastic stress/strain on the affected soil volume. Pedo transfer functions allow for the calculation of the soil mechanics model parameters from existing soil measurements. This terrain model was implemented in a way that maps well to Graphics Processor Unit, which allows the model to run in realtime, enabling operator in the loop full vehicle simulations. Test simulations are run using a rigid tire with lugs to show the capability of the model to predict tire and terrain responses. Run times and scaling analyses are presented to gauge the relative speedup of utilizing GPUs for computational acceleration.

Chrono: A Parallel Physics Library for Rigid-Body, Flexible-Body, and Fluid Dynamics

This contribution discusses a multi-physics simulation engine, called Chrono, that relies heavily on parallel computing. Chrono aims at simulating the dynamics of systems containing rigid bodies, flexible (compliant) bodies, and fluid-rigid body interaction. To this end, it relies on five modules: equation formulation (modeling), equation solution (simulation), collision detection support, domain decomposition for parallel computing, and post-processing analysis with emphasis on high quality rendering/visualization. For each component we point out how parallel CPU and/or GPU computing have been leveraged to allow for the simulation of applications with millions of degrees of freedom such as rover dynamics on granular terrain, fluid-structure interaction problems, or large-scale flexible body dynamics with friction and contact for applications in polymer analysis.

Using a Granular Dynamics Code to Investigate the Performance of a Helical Anchoring System Design

NASA is interested in designing a spacecraft capable of visiting a Near Earth Object (NEO), performing experiments, and then returning safely. Certain periods of this mission will require the spacecraft to remain stationary relative to the NEO. Due to the low gravity, such situations require an anchoring mechanism that is compact, easy to deploy and upon mission completion, easily removed. In the proposed approach, using Chrono::Engine (Tasora 2008; Negrut, Tasora et al. 2011; SBEL 2011), a simulation package capable of utilizing massively parallel GPU hardware, extensive validation experiments will first be performed. A set of parametric studies will concentrate on the simulation of the anchoring system. The outcome of this effort will be a systematic study that considers several different anchor designs, along with a recommendation on which anchor design is better suited to the task of anchoring. The anchors will be tested against a range of parameters relating to soil, environment and anchor penetration angles/velocities on a NEO to better understand their performance characteristics. SIMULATION CAPABILITY The simulation of very large collections of rigid bodies is prohibitively time consuming if done on sequential processors. Until recently, the high cost of parallel computing limited the analysis of such large systems to a small number of research groups. This is rapidly changing, owing in large part to general-purpose computing on the GPU (GP-GPU). GP-GPU computing has been vigorously promoted by NVIDIA since the release of the CUDA development platform (NVIDIA 2011), an application interface for software development targeted to run on NVIDIA GPUs. A large number of scientific applications have been developed using CUDA, most of them dealing with problems that are quite easily parallelizable such as molecular dynamics or signal processing. Very few GP-GPU projects are concerned though with the dynamics of multibody systems, the two most significant being the Havok (Havok 2011) and the NVIDIA PhysX (NVIDIA 2010) engines. Both are commercial and proprietary libraries used in the video-game industry and their algorithmic details are not public. Typically, these physics engines trade precision for efficiency as the priority is in speed rather than accuracy. In this context, the goal of this effort is to moderately de-emphasize the efficiency attribute and instead implement a free, general-purpose physics based GPU solver for multibody dynamics backed by convergence results that guarantee the accuracy of the numerical solution. Unlike the so-called penalty or regularization methods, where the frictional interaction can be represented by a collection of stiff springs combined with damping

OFF-ROAD VEHICLE DYNAMICS MOBILITY SIMULATION WITH A COMPACTION BASED DEFORMABLE TERRAIN MODEL

This paper discusses the terramechanics models developed to incorporate a physics-based, three dimensional deformable terrain database model with vehicle dynamics mobility simulation software. The vehicle model is contained in Chrono, a research-grade C++ based Application Programming Interface (API) that enables accurate multibody simulations. The terrain database is also contained in a C++ based API, and includes a general tire-terrain interaction model which is modular to allow for any tire model that supports the Standard Tire Interface (STI) to operate on the terrain. Furthermore, the ability to handle arbitrary, three dimensional traction element geometry allows for tracked vehicles (or vehicle hulls) to also interact with the deformable terrain. The governing equations of the terrain are based on a soil compaction model that includes both the propagation of subsoil stresses due to vehicular loads, and the resulting visco-elastic-plastic stress/strain on the affected soil volume. Non-flat, non-homogenous and non-uniform soil densities, rutting, repeated loading and strain hardening effects are all captured in the vehicle mobility response as a result of the general 3-D tire/terrain model developed. Pedo-transfer functions allow for the calculation of the soil mechanics model parameters from existing soil measurements. This terrain model runs at near real-time speed, due to parallel CPU and GPU implementation. Results that exercise the force models developed with the 3-D tire geometry are presented and discussed for a kinematically driven tire and a full vehicle simulation.Copyright

A Physics-Based Terrain Model for Off-Road Vehicle Simulations

We present the development of a three-dimensional Vehicle/Tire/Terrain Interaction Model (VTTIM) consisting of a general 3D tire-terrain traction model which operates on a novel deformable terrain representation that utilizes a soil compaction model. Rather than utilizing popular empirical terramechanics models that only consider the pressure/sinkage directly under the tire, the governing equations of the terrain are based on i) the propagation of subsoil stresses due to vehicular loads, and ii) the resulting stress/strain which is based on a visco-elastic-plastic soil model developed by Ayers and Bozdech. The implementation of the terrain model is modularized in the form of an API, as the vehicle and tire are assumed to be contained in commercial simulation software as to focus on the implementation of the deformable terrain model. A number of test simulations are run using a rigid tire with and without grousers to show the capability of the VTTIM to predict tire forces for use in vehicle mobility and traction performance simulations. Power and energy required to deform the terrain will also be presented with the simulation results, which allows the prediction of the extra power required by a vehicle traveling on off-road, deformable soil.Copyright