Track-terrain modelling and traversability prediction for tracked vehicles on soft terrain

Skid-steered tracked vehicles are the favoured platform for unmanned ground vehicles (UGVs) in poor terrain conditions. However, the concept of skid-steering relies largely on track slippage to allow the vehicle to conduct turning manoeuvres potentially leading to overly high slip and immobility. It is therefore important to predict such vulnerable vehicle states in order to prevent their occurrence and thus paving the way for improved autonomy of tracked vehicles. This paper presents an analytical approach to track-terrain modelling and a novel traversability prediction simulator for tracked vehicles conducting steady-state turning manoeuvres on soft terrain. Traversability is identified by predicting the resultant track forces acting on the track-terrain interface and the adopted models are modified to provide an analytical generalised solution. The validity of the simulator has been verified by comparison with available data in the literature and through an in-house experimental study. The developed simulator can be employed as a traversability predictor and also as a design tool to test the performance of tracked vehicles with different vehicle geometries operating on a wide range of soil properties.     

Mobility of a lightweight tracked robot over deep snow

We designed and built a 24-kg tracked robot, named SnoBot, based on the performance of a 1400-kg manned vehicle scaled using Bekker mobility theory. We then documented the mobility of the robot for 10 cases of deep snow and four cases of shallow snow. The scaled predictions agreed well with average sinkage, resistance and traction measured in deep snow and thus gave useful design guidance. Nevertheless, large differences occurred between measured and predicted snow-compaction resistance on individual test days. The behavior of actual snow packs is difficult to capture using simple Bekker theory. Most deep-snow packs showed a linear relationship between pressure and sinkage for small indentation, followed by a steep rise in pressure as indentation compacted the snow against the ground. Also, small strength variations due to icy layers were important. SnoBot traveled easily over ice crusts that were much too weak to support foot travel. The results indicate that a lightweight tracked robot can display excellent deep-snow mobility when ground clearance, motor torque and energy storage allow for proportionally high sinkage and motion resistance compared with larger vehicles.     

An optimal method for the design of a robotic tracked vehicle to operate over fresh concrete under steering motion

The objective of this paper is to find an optimal method for the design of tracked base travel systems for special purpose vehicles and robotic machines that may be required to steer over a light bonded terrain composed of fresh concrete. For the case of a vehicle traveling on a weak fresh concrete during construction, the paper presents detailed comparative studies of the steering performances of a small model tracked test vehicle with alternative amount of steering ratio for various concrete slump values. For these studies a detailed simulation analytical method has been developed. From this work it is proven, in comparison to experiment, that the simulation analytical method is useful for predicting various steering performances of a test tracked vehicle running upon soft fresh concrete of various consistencies.     

Modeling of terrain impact caused by tracked vehicles

Analytical models that can predict the terrain impact caused by tracked vehicles on a horizontal plane were developed and tested. The models included a disturbed width model and an impact severity model. Inputs of the terrain impact models included vehicle static properties, vehicle dynamic properties, and terrain properties. The tested vehicles included an M1A1 tank, an M577 Armored Personal Carrier (APC), and an M548 cargo carrier. The models were verified with field tests conducted in Yakima Training Center in Yakima, WA, Fort Riley, KS, and Camp Atterbury, Indiana. The average percentage errors of the disturbed width model for the M1A1, M577, and the M548 were 10.0%, 27.3%, and 8.5%, respectively. The average percentage errors of the impact severity model of the M1A1 and M577 were 25.0% and 21.4%, respectively.     

Study of the influence of vehicle parameters on tractive performance in deep snow

This paper describes an experimental study of tractive performance in deep snow, carried out with a new special skid steered tracked vehicle, developed by Bodin [1]. The vehicle design parameters studied include the influence of the ground clearance of the vehicle belly and the longitudinal location of the centre of gravity on tractive performance in deep snow, as well as the effect of initial track tension. The most important results from the test show that an increase in the ground clearance has a positive effect on the drawbar pull, originating from a greater increase in the thrust than in the track motion resistance and a slight decrease in the belly drag. Tests of the longitudinal location of the centre of gravity show that a location ahead of the midpoint of the track contact length is to be preferred. The drawbar pull increases with the centre of gravity moving forward. This is due to a reduced track motion resistance, a slight decrease in the belly drag and an almost constant vehicle thrust. The reason for the decreased track motion resistance and belly drag with the centre of gravity located ahead of the midpoint of the track contact length is a decreased vehicle trim angle.     

On the numerical solution of tracked vehicle dynamic equations

In this investigation, the solution of the nonlinear dynamic equations of the multibody tracked vehicle systems are obtained using different procedures. In the first technique, which is based on the augmented formulation that employes the absolute Cartesian coordinates and Lagrange multipliers, the generalized coordinate partitioning of the constraint Jacobian matrix is used to determine the independent coordinates and the associated independent differential equations. An iterative Newton-Raphson algorithm is used to solve the nonlinear constraint equations for the dependent variables. The numerical problems encountered when one set of independent coordinates is used during the simulation of large scale tracked vehicle systems are demonstrated and their relationship to the track dynamics is discussed. The second approach employed in this investigation is the velocity transformation technique. One of the versions of this technique is discussed in this paper and the numerical problems that arise from the use of inconsistent system of kinematic equations are reported. In the velocity transformation technique, the tracked vehicle system is assumed to consist of two kinematically decoupled subsystems; the first subsystem consists of the chassis, the rollers, the sprocket and the idler, while the second subsystem consists of the track which is represented as a closed kinematic chain that consists of rigid links connected by revolute joints. It is demonstrated that the use of one set of recursive equations leads to numerical difficulties because of the change in the track configuration. Singular configurations can be avoided by repeated changes in the recursive equations. The sensitivity of the predictor-corrector multistep numerical integration schemes to the method of formulating the state equations is demonstrated. The numerical results presented in this investigation are obtained using a planner tracked vehicle model that consists of fifty four rigid bodies.     

An optimum design method for robotic tracked-vehicles operating over fresh concrete during straight-line motion

This paper addresses the general problem of the design of tracked base travel systems for special purpose vehicles and/or robotic machines that may be required to move over weak surfaces or over a lightly bonded terrain composed of fresh concrete. For the special case of a vehicle travelling on a very soft fresh concrete during construction, the paper presents detailed comparative studies of the tractive performance of several tracked vehicles with alternative slump values and mean contact pressure configurations. To complete these studies a detailed simulation-analytical method was used. From this, it was established that the simulation analysis method is useful for predicting land locomotion performance of specially designed small tracked vehicles running over fresh concrete of different consistencies during driving and braking action. This work was done for straight-line motion. Some possibilities for the real-time optimum control method of the tractive and braking performance of automated and robotic vehicles are also outlined.     

A method for predicting the internal motion resistance of rubber-tracked undercarriages,Pt. 1. A review of the state-of-the-art methods for modeling the internal resistance of tracked vehicles

This article summarizes the known methods for calculating the internal resistance of tracked undercarriages. The values of the coefficient of internal resistance for sample tracked vehicles are available in the literature and presented in this paper. Although they are suitable for simple computations, they cannot be used to optimize the energy efficiency of new generation tracked undercarriages. This problem might be solved by the models where every phenomenon leading to energy dissipation during vehicle motion is described by a separate submodel as a function of vehicle speed, track tension, undercarriage layout, design features of the undercarriage components, etc. This kind of model is still missing for vehicles with conventional rubber tracks. The article presents multiple state-of-the-art models describing rolling resistance of road wheels, bending resistance of rubber belts, etc., including the models of belt conveyors resistance. A vast majority of the phenomena discussed herein are described by several incompatible models whose parameters have not yet been determined for conventional rubber tracks. Consequently, in the second and the third part of the article, the authors have undertaken a theoretical and experimental studies on the methods for calculating and optimizing the internal motion resistance of vehicles with conventional rubber tracks.     

Ride dynamics mathematical model for a single station representation of tracked vehicle

Tracked vehicles are exposed to severe ride environment due to dynamic terrain-vehicle interactions. Hence it is essential to understand the vibration levels transmitted to the vehicle, as it negotiates different types of terrains at different speeds. The present study is focused on the development of single station representation of tracked vehicles with trailing arm hydro-gas suspension systems, simulating the ride dynamics. The kinematics of hydro-gas suspension system have been derived in order to determine the non-linear stiffness characteristics at various charging pressures. Then, incorporating the actual suspension kinematics, non-linear governing equations of motion have been derived for the sprung and unsprung masses and solved by coding in Matlab. Effect of suspension non-linear dynamics on the single station ride vibrations have been analyzed and validated with a multi-body dynamics model developed using MSC.ADAMS. The above mathematical models would help in estimating the ride vibration levels of the tracked vehicle, negotiating different types of terrains at various speeds and also enable the designers to fine-tune the suspension characteristics such that the ride vibrations are within acceptable limits. The mathematical ride model would also assist in development of non-linear ride vibration model of full tracked vehicle and estimate the sprung mass dynamics.     

Evaluation of drawbar performance of winter tyres for special purpose vehicles

Driving on ice is still a risky activity. Research has investigated the factors contributing to the friction mechanism and has reported experimental studies of pneumatic tyres on ice in order to develop models that predict tractive and braking performance on ice/snow. Therefore, developing testing methods to obtain relevant experimental data for the validation of models is equally important.There are agricultural and industrial vehicles which are also designed for pulling but there are no specific studies reporting experimental tests on traction force of such machines in snowy conditions. However, this issue is very topical, as demonstrated by the appearance on the market of winter tyres for such vehicles.This study presents a method for testing winter tyres in outdoor test facilities with a focus on traction performance. The conclusions will serve in future investigations as a concise knowledge source to develop improved testing facilities and tyre–ice interaction models, aiding the development of better tyre designs and improved vehicle safety systems.The functional tests hereafter described have been carried out with the aim of evaluating the possibility of measuring the influences of different technique solutions on the performance of certain 17.5 R25 sized industrial tyres.     

Effects of a roller and a tracked vehicle on the compaction of a high lifted decomposed granite sandy soil

The aim of this research was to innovate a new compaction machinery by comparing experimentally the effects of a two-axle, two wheel road roller and a tracked vehicle on the compaction of a decomposed granite sandy soil with a high spreading lift. By measuring the amount of sinkage of the terrain surface, the dry density distribution versus depth using a cone penetrometer, the normal earth pressure distribution versus depth using a stress state transducer (SST), the effects of the road roller and the tracked vehicle on the increment of the soil dry density were considered theoretically. It was observed that the tracked vehicle showed a larger amount of sinkage and a larger dry density distribution versus depth than the roller. The ratio of shear stress to normal stress was still large enough at the deep stratum, so that an optimal shear strain was developed on the whole range of the high lifted stratum and it increased the soil compaction density due to the dilatancy effect.     

The applicability of the MMP concept in specifying off-road mobility for wheeled and tracked vehicles

A review is given of the use of mean maximum pressure (MMP) in specifying off-road performance of vehicles. The need to quote a single mobility criterion which is unbiased in favour of either wheeled or tracked vehicles is recognised. The difficulties which researchers have encountered in developing expressions for MMP for both wheeled and tracked vehicles which correctly describe their relative performance are highlighted. Predictions of MMP for wheeled vehicles are compared with ground pressure measurements for a number of vehicles and it is shown that the MMP parameter does not actually represent the ground pressure accurately. Finally it is argued that the only safe route for the specifier is to quote a range of soil types, conditions and gradients on which the vehicle is to operate. This shifts the responsibility to the designer but also clears the way for innovative design, beyond the constraints of the MMP formulae.     

膜扑翼飞行器的变形研究

最近昆虫翼的变形成了研究热点,而扑翼飞行器的变形力学研究却几乎无人问津.然而,无论昆虫、鸟类还是扑翼飞行器在飞行时,翼的变形都是存在的,要精确计算翼扑动产生的气动力,必须考虑其变形.本文比较了导致变形产生的膜扑翼飞行器的惯性力和气动力在一个周期中的变化情况,发现它们的峰值比值为2左右,然后提出了在随体坐标系中的固支边界条件,采用有限元法计算了惯性力和气动力分别对变形的影响,发现扑翼飞行器的气动力对变形的影响是不可忽略的重要因素,而惯性力与气动力的合力引起的最大正变形发生在下扑初始阶段,最大负变形发生在上扑初始阶段.本文为扑翼飞行器的设计提供了力学分析基础.     

Mobility analysis of off-road vehicles: Benefits for development, procurement and operation

Nowadays the requirements on off-road vehicles are rising steadily. The ideal vehicle has to provide excellent off-road capability with low fuel consumption, offer a high customizability for each specific mission and, last but not least, it has to be easy to operate. To meet these demands, on the development side a lot of parameter studies have to be carried out. The customer has to compare offers from a multiplicity of suppliers to decide which vehicle fulfills the designated mission task best. And finally, the operator needs the best training on the vehicle to cope with all possible situations in off-road mobility. In response to these needs, the presented simulation program WinMaku was developed to offer a tool to facilitate development, procurement and operator training. Exemplary simulation results show, on the one hand, the influence of specific design parameters, e.g. tire size, engine power, torque characteristics, gear shifting, and engine working conditions, and on the other hand the (beneficial or adverse) effects of operational parameters like driving with maximum/partial engine load, gear selection, engine speed, tire inflation pressure or track tension, on mobility performance. Furthermore results of vehicle comparison analysis are presented. These types of analysis show comparisons of mobility performance of different vehicle types or vehicle concepts (e.g. wheel vs. track) in fulfilling a certain mission profile, characterized by passing a sequence of different soils with various inclines. Endowed with such capability, the presented simulation tool serves as a training tool for operators, provides a cost effective method to assess possible development steps, allows customers to run a pre-selection process prior to expensive and time-consuming field tests, and finally supports mission planning by providing data like expected fuel consumption or time needed to pass a certain mission profile.     

A review of mobility metrics for next generation vehicle mobility models

In the United States, the NATO Reference Mobility Model (NRMM) has been used for evaluating military ground vehicle mobility and the Vehicle Cone Index (VCI) has been selected as a mobility metric. VCI represents the minimum soil strength required for a vehicle to consistently make a specific number of passes, usually one or fifty passes. In the United Kingdom, the Mean Maximum Pressure (MMP) has been adopted as a metric for assessing military vehicle cross-country mobility. MMP is the mean value of the maxima occurring under all the wheel stations of a vehicle. Both VCI and MMP are empirically based. This paper presents a review of the basis upon which VCI and MMP were developed, as well as their applications to evaluating vehicle mobility in practice. With the progress in terramechanics and in modelling and simulation techniques in recent years, there is a growing desire to develop physics-based mobility metrics for next generation vehicle mobility models. Based on the review, criteria for selecting physics-based mobility metrics are proposed. Following these criteria, metrics for characterizing military vehicle traction limits and traversability on a given operating area are recommended.     

Bayesian calibration of Vehicle-Terrain Interface algorithms for wheeled vehicles on loose sands

The Vehicle-Terrain Interface (VTI) model is commonly used to predict off-road mobility to support virtual prototyping. The Database Records for Off-road Vehicle Environments (DROVE), a recently developed database of tests conducted with wheeled vehicles operating on loose, dry sand, is used to calibrate three equations used within the VTI model: drawbar pull, traction, and motion resistance. A two-stage Bayesian calibration process using the Metropolis algorithm is implemented to improve the performance of the three equations through updating of their coefficients. Convergence of the Bayesian calibration process to a calibrated model is established through evaluation of two indicators of convergence. Improvements in root-mean square error (RMSE) are shown for all three equations: 17.7% for drawbar pull, 5.5% for traction, and 23.1% for motion resistance. Improvements are also seen in the coefficient of determination (R²) performance of the equations for drawbar pull, 2.8%, and motion resistance, 2.5%. Improvements are also demonstrated in the coefficient of determination for drawbar pull, 2.8%, and motion resistance, 2.5%, equations, while the calibrated traction equation performs similar to the VTI equation. A randomly selected test dataset of about 10% of the relevant observations from DROVE is used to validate the performance of each calibrated equation.     

Investigation of the soil thrust interference effect for tracked unmanned ground vehicles (UGVs) using model track tests

The traction force of a tracked unmanned ground vehicle (UGV) depends on the soil thrust generated by the shearing action on the soil-track interface. In the development of soil thrust, because the continuous-track system consists of a number of single-track systems connected to each other, interference occurs between the adjacent single-track systems through the surrounding soil. Thus, the total soil thrust of the continuous-track system is not equal to the sum of the soil thrust of each single-track system, and the interference effect needs to be carefully considered. In this study, model track tests were conducted on model single-, double-, and triple-track systems according to relative density of soil and shape ratio (i.e., the length of the track plate to grouser depth). The test results indicated that the interference effect reduced soil thrust due to the overlapping shear zones between adjoining single-track systems. The loss of soil thrust increased as the relative density of the soil increased and the shape ratio decreased. Based on these findings, a soil thrust multiplier that can be utilized to assess the soil thrust of a continuous-track system was developed.     

交通荷载下沥青路面车辙三维非线性有限元分析

建立了半刚性沥青路面和柔性沥青路面的三维有限元模型,采用非线性粘弹塑性理论分析了不同交通荷载对沥青路面车辙变形和切应力的影响,并考虑了刹车、路面纵坡对路面车辙的影响。结果表明:在相同荷载作用下,两种路面结构的车辙变形和切应力分布随着路面深度呈非线性分布,但不同路面结构对交通荷载变化的敏感性存在较大的差异;不同的胎压、轮载以及刹车产生的水平力对路面车辙变形有着较大的影响。当胎压为1 050 kPa及轮载为62.5 kN时,路面产生的车辙都大于在标准荷载及标准胎压时路面产生的车辙;在坡度为1%～6%时,路面纵坡对沥青路面车辙深度的影响不明显;在坡道上行车(特别是下行)时刹车是路面车辙过大的主要原因。