Digital image correlation techniques for measuring tyre-road interface parameters: Part 1 – Side-slip angle measurement on rough terrain

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.     

A roll stability performance measure for off-road vehicles

The roll stability is significant for both road and off-road commercial vehicles, while the majority of reported studies focus on road vehicles neglecting the contributions of uneven off-road terrains. The limited studies on roll stability of off-road vehicles have assessed the stability limits using performance measures derived for road vehicles. This study proposes an alternative performance measure for assessing roll stability limits of off-road vehicles. The roll dynamics of an off-road mining vehicle operating on random rough terrains are investigated, where the two terrain-track profiles are synthesized considering coherency between them. It is shown that a measure based on steady-turning root-mean-square lateral acceleration corresponding to the sustained period of unity lateral-load-transfer-ratio prior to the absolute-rollover, could serve as a reliable measure of roll stability of the vehicle operating on random rough terrains. The robustness of proposed performance measure is demonstrated considering sprung mass center height variations and different terrain excitations. The simulation results revealed adverse effects of terrain elevation magnitude on the roll stability, while a relatively higher coherency resulted in lower terrain roll-excitation and thereby enhanced vehicle roll stability. Terrains with relatively higher waviness increased the magnitude of lower spatial frequency components, which resulted in reduced roll stability limits.     

Stochastic vehicle mobility forecasts using the nato reference mobility model

The NATO Reference Mobility Model (NRMM) is a comprehensive means of predicting the speeds of military vehicles in on-road, off road, and gap-crossing contexts. The model has been in service for many years and helps user communities concerned with vehicle design, wargaming, and strategic planning. Recent developments in computer hardware and software are creating an opportunity for NRMM to serve a tactical role on the battlefield. Adaptation of NRMM to this role requires that its users come to grips with the collection of digital data to describe vehicle, terrain, and scenario data in a real-time environment. This paper discusses the performance of NRMM when selected inputs and algorithms contain random components. A developmental pathway is outlined that leads from current deterministic mobility forecasts to stochastic forecasts capable of suggesting the risks taken when speed predictions must be made in the presence of data and algorithm errors. Concepts that express measures of confidence for wide-area mobility forecasts when errors are known with small-area detail are described. Several numerical examples are given.     

The test and simulation of ABS on rough,non-deformable terrains

It is well known that the performance of many antilock braking systems (ABS) deteriorate on rough, non-deformable surfaces due to a number of factors such as axle oscillations, wheel speed fluctuations and deficiencies in the algorithms. Rough terrain excitation further contribute to dynamic tyre effects such as loss of vertical contact and poor contact patch generation that leads to reduced longitudinal force generation. In this study, a slightly modified version of the Bosch ABS algorithm is implemented in Matlab/Simulink using co-simulation with a validated full vehicle ADAMS model that incorporate a valid high-fidelity FTire model. A non-ABS test vehicle is fitted with a commercial ABS modulator controlled by an embedded computer. The co-simulation model is validated with vehicle test data on both smooth and rough terrains. Initial results show that wheel speed fluctuations on rough terrain cause inaccuracies in the estimation of vehicle velocity and excessive noise on the derived rotational acceleration values. This leads to inaccurate longitudinal slip calculation and poor control state decisions respectively. It is concluded that, although the correlation is not yet as desired, the combined use of a simulation model and test vehicle can be a useful tool in the research of ABS braking on rough terrains.     

Optimal control of the dynamic stability for robotic vehicles in rough terrain

In this paper, we mount semi-active suspensions between the wheels and platform of a robotic vehicle to absorb the vibrations caused by movement over rough terrain. The semi-active suspension consists of a spring and a magneto-rheological damper. By combining the dynamic model of the suspended robotic vehicle and the control model of the damper, we propose a new methodology to evaluate the dynamic stability of the vehicle. The model considers the configuration of semi-active suspensions and the road-holding ability of robotic vehicles. Based on the stability criterion, we use the particle swarm optimization method to search the optimum semi-active damping characteristics. The control model of the semi-active damper is checked by sinusoidal response analysis. To verify the dynamic stability criterion and the control method, we evaluate the proposed methodology by simulating a rough pavement condition and comparing the effectiveness of the method to a passive suspension. The results show that the proposed stability criterion is feasible, and the optimal control method yields a substantially improved dynamic stability when the vehicle moves through rough terrain.     

Parameterization and modelling of large off-road tyres for ride analyses: Part 2 – Parameterization and validation of tyre models

Every mathematical model used in a simulation is an idealization and simplification of reality. Vehicle dynamic simulations that go beyond the fundamental investigations require complex multi-body simulation models. The tyre–road interaction presents one of the biggest challenges in creating an accurate vehicle model. Many tyre models have been proposed and developed but proper validation studies are less accessible. These models were mostly developed and validated for passenger car tyres for application on relatively smooth roads. The improvement of ride comfort, safety and structural integrity of large off-road vehicles, over rough terrain, has become more significant in the development process of heavy vehicles. This paper investigates whether existing tyre models can be used to accurately describe the vertical behaviour of large off road tyres while driving over uneven terrain. [1] Presented an extensive set of experimentally determined parameterization and validation data for a large off-road tyre. Both laboratory and field test are performed for various loads, inflation pressures and terrain inputs. The parameterization process of four tyre models or contact models are discussed in detail. The parameterized models are then validated against test results on various hard but rough off-road terrain and the results are discussed.     

Aeroelastic stability consideration of supersonic flight vehicle using nonlinear aerodynamic response surfaces

Aeroelastic stability of a flexible supersonic flight vehicle is considered using nonlinear dynamics, nonlinear aerodynamics, and a linear structural model. Response surfaces including global multivariate orthogonal modeling functions are invoked to derive applied nonlinear aerodynamic coefficients. A modified Gram–Schmidt method is utilized to orthogonalize the produced polynomial multivariate functions, selected and ranked by predicted squared error metric. Local variation of angle-of-attack and side-slip angle is applied to the analytical model. Identification of nonlinear aerodynamic coefficients of the flight vehicle is conducted employing a CFD code and the required analytical model for simulation purposes is constructed. The method is used to determine the aeroelastic instability and response of a selected flight vehicle.     

Tyre rubber friction on a rough road

One of the most challenging aspects of vehicle dynamics is accurate modelling of the tyre-road interface. Forces between the tyre and road need to be accurately represented in simulation. This is challenging over rough roads since the friction changes along the road due to large surface asperities.The Heinrich/Klüppel friction coefficient estimation model has been implemented on smooth roads in the past. However, this study investigates the applicability of using this model over a rough but hard terrain, such as Belgian paving or cobblestones. The model is based on physical properties that can be determined mathematically or experimentally. The study includes detailed terrain topography and the difference between the top and bottom topography is used to determine the radially averaged PSD. Emphasis is placed on finding and implementing the flash temperature in a practical manner that could also be used in further studies.An experimental setup is built to validate the model. The experimental friction coefficient is compared to the friction coefficient calculated using the Heinrich/Klüppel model. The relative percentage error difference between experimental and friction model results is found to be less than 10% on a smooth concrete road and 20% on a rough road (concrete Belgian paving).     

Off-road tyre modelling II: effect of camber on tyre performance

The problem of off-road vehicle tyre-terrain interaction is that it is difficult to model accurately. For an off-road vehicle over medium to firm terrain, the tyre load may be entirely supported by the tips of the lugs, or with a minimum carcass contact with the terrain. In this case, the effect of the lugs should be taken into consideration. The forces at the interface between lugged tyre and the soil, including normal and shear stresses, are discussed in this paper. The multi-spoke tyre model was developed to study the effect of tyre lugs on the forces between tyre and terrain and it has been extended to predict the tyre forces and moments in the case of combined lateral and longitudinal slip for a cambered tyre. The influence of slip angle, camber angle and soil hardness on off-road tyre performance has been investigated. A computer program was developed using MATLAB software. The results were derived as tyre forces and moments in the three directions along the tyre contact length. A comparison between the results of the multi-spoke tyre model of a smooth off-road tyre and an off-road tyre with straight lugs, in the cambered case, has been made. The results indicated that slip angle, camber angle and soil characteristics have a strong effect on off-road tyre performance. The modified mathematical model results help the off-road tyre engineering designers to predict accurate values of tyre forces and moments in this complex case.     

TERCOM地形高程辅助导航系统发展及应用研究

介绍了地形轮廓匹配（TERCOM）地形高程辅助导航系统的工作原理、系统组成和技术应用，分析了地形轮廓匹配算法的性能指标；着重介绍了地形轮廓匹配辅助导航系统中数字地图、地形相关适配性、匹配搜索算法、实测高程数据采集、组合导航、数字相关器等几项关键技术，有针对性地提出了基于地形信息熵的匹配区域选择、序贯相似度检测搜索（SSDA）、等间距高程数据采集、多组合导航等比较适用的解决方案和应用实例，并通过数据统计和分析进行了论证。     

3D contact patch measurement inside rolling tyres

This paper presents a novel method for capturing the 3D profile of the inside of a rolling off-road vehicle tyre at the tyre-road contact region. This method captures the contact region at all times as the vehicle negotiates obstacles. The system uses a pair of inexpensive digital cameras (capable of capturing up to 300 frames per second) and features a purely mechanical stabilisation system to ensure that the cameras capture the contact region at any wheel speed or vehicle acceleration.The captured images are processed using 3D computer vision techniques using an open source computer vision library called OpenCV. Stereo image pairs are used to create clouds of 3D points showing the profile of the inside surface with good accuracy. Various obstacles were traversed with the deformed tyre profile being compared to the undeformed profile. The system improves on current measurement techniques used to measure the contact patch by capturing a large region of the contact patch, providing full 3D surface geometry, as well as remaining centred on the contact patch irrespective of wheel rotation. The system also enables other imaging techniques to be used such as digital image correlation to determine velocity profiles as well as strain measurements.     

Rough terrain profiling using digital image correlation

Road profiling is an important aspect of vehicle dynamics simulations especially over rough terrains. The accurate measurement of rough terrains allows for more accurate multi body simulations. Three dimensional road profiles are usually performed by utilising a line scan sensor which measures several points lateral to the road. The sensors range from simple road following wheels to LiDAR sensors. The obtained line scans are longitudinally stitched together using the orientation and position of the sensor to obtain a full three dimensional road profile. The sensor’s position and orientation therefore needs to be accurately determined in order to combine the line scans to create an accurate representation of the terrain. The sensor’s position and orientation is normally measured using an expensive inertial measurement unit or Inertial Navigation System (INS) with high sensitivity, low noise and low drift. This paper proposes a road profiling technique which utilises stereography, based on two inexpensive digital cameras, to obtain three-dimensional measurements of the road. The system negates the use of an expensive INS system to determine orientation and position. The data sets also require subsampling which can be computationally expensive. A simple subsampling routine is presented which takes advantage of the structure of the data sets to significantly speed up the process.     

A free gait algorithm for quadrupedal walking machines

A free gait is a computer generated, rule-based gait for a walking machine to walk on rough terrain. Based on a given terrain map, the gait algorithm selects footholds for leg placements and determines the movements of legs and body. In the past, a few free gaits for hexapods have been developed. For quadrupeds, the only report on free gait was briefly mentioned in a paper by Hirose [Int. J. Robotics Res., 3(2) (1984)]. In this paper, a free gait algorithm for a quadrupedal walking chair is developed. For quadrupeds, the stability margin is small due to a small number of legs and the choices of a leg to be lifted are limited. Hence, deadlock situations may occur quite often. Many special techniques are incorporated into the algorithm in order to reduce deadlocks. This free gait algorithm adopts the wave-crab gaits as the primary gait because they are periodic and can provide good stability. The algorithm also adopts a non-periodic free gait to handle terrain with higher concentration of forbidden areas. This algorithm is evaluated under different terrain conditions using computer simulations. The results show that the performance is satisfactory on randomly generated rough terrain and needs improvement on manually generated rough terrain.     

Analysis of the vibration-excitation effect caused by deformable soil surfaces

Terrain roughness induces vibrations in the chassis of vehicles moving cross-country. These vibrations affect the comfort of the occupants detrimentally and, when a certain rough ride condition is exceeded, the vehicle can no longer be controlled by the driver. This study deals with the relationship between terrain roughness and the vehicle traveling over it. In the case of deforming soil, the so called original soil profile is altered significantly by the vehicle. This study determines the original as well as the modified profiles, the latter being caused by the vehicle traveling over the former. The vehicle's transfer function is used to compute the effective profile, which generates the actual vibrations of the vehicle. These investigations are presented for several soil types and for a number of vehicles whose mass and running gear design are known.     

Digital image correlation techniques for measuring tyre–road interface parameters: Part 2 – Longitudinal tyre slip ratio measurement

Measurement of tyre longitudinal slip-ratio is often estimated from three independent measurements devices namely wheel rotation speed, vehicle speed and tyre rolling radius. This produces an expensive measurement system to indirectly determine the slip-ratio. This paper presents a method by which the slip-ratio is determined from a video camera using digital image correlation techniques. The camera, mounted in such a way that the contact patch region is captured, enables the system to measure the tyre tread speed and ground speed at the contact patch. The slip-ratio is then determined from these two measurements.     

新型汽车结构胶剪切实验研究

利用数字图像相关方法(DICM),分别测定了准静态单向剪切拉伸试验条件下,新型汽车结构胶粘接试件和传统点焊连接试件粘接部分的剪切力学性能。实验采用了非接触测量物体应变的方法,运用CCD及其计算机图像处理系统,实时获取变形前后试件表面图像。利用数字相关软件对变形前后的图像进行分析,从而获得试件该时刻的应变。最后确定了试件拉伸过程中的力-位移曲线及应力-应变关系曲线。测试结果及分析表明:采用新型结构胶粘接试件的力学性能与点焊结构相比有明显的优势。这为该结构胶进一步改进提供了一定的实验依据。测试中的数字图像相关法是非接触测量物体应变的方法,在实际应用中有很大的意义。     

Tracking the free surface of time-dependent flows: image processing for the dam-break problem

The dam-break problem (i.e., the sudden release of a given volume of fluid down a slope) has attracted a great deal of attention from mechanicians and physicists over the past few years, with particular interest devoted to the free-surface profile and the spreading rate. Experimentally, impediments to accurate measurements of the free-surface evolution are numerous because of the significant variations in its curvature and velocity. To accurately measure the surge’s free-surface variations with time, we have developed a new imaging system, consisting of a digital camera coupled with a synchronized micro-mirror projector. The object’s surface is imaged into a camera and patterns are projected onto the surface under an angle of incidence that differs from the imaging direction. From the deformed pattern recorded by the camera, the phase can be extracted and, by using unwrapping algorithms, the height can be computed and the free surface reconstructed. We were able to measure the free surface of the flow to within 1 mm over a surface of 1.8 × 1.1 m². Although the techniques used in our system are not new when taken individually, the system in its entirety is innovative and more efficient than most methods used to-date in practical applications.     

A spatial motion analysis model of tracked vehicles with torsion bar type suspension

A spatial motion analysis model for high-mobility tracked vehicles was constructed for evaluation of ride performance, steerability, and stability on rough terrain. Ordinary high-mobility tracked vehicles are equipped with independent torsion bar type suspension system, which consists of road arms and road wheels. The road arm rotates about the axis of torsion bar, and rigidity of the torsion bar and cohesion of damper absorb sudden force change exerted by interaction with the ground. The motion of the road arms should be considered for the evaluation of off-road vehicle performance in numerical analysis model. In order to obtain equations of motion for the tracked vehicles, the equations of motion for the vehicle body and for the assembly of a road wheel and a road arm were constructed separately at first. Two sets of equations were reduced with the constraint equations, which the road arms are mechanically connected to the vehicle body. The equations of motion for the vehicle have been expressed with minimal set of variables of the same number as the degrees of freedom for the vehicle motion. We also included the effect of track tension in the equations without constructing equations of motion for the tracks. Numerical simulation based on the vehicle model and experiment of a scale model passing over a trapezoidal speed bump were performed in order to examine the numerical model. It was found that the numerical results reasonably predict the vehicle motion.     

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.     

Calculating fractal parameters from low-resolution terrain profiles

Driver comfort on rough terrain is an important factor in the off-road performance of wheeled and tracked ground vehicles. The roughness of a terrain has typically been quantified by the U.S. Army as the root-mean-square elevation deviation (RMS) of the terrain profile. Although RMS is an important input into many mobility calculations, it is not scale invariant, making it difficult to estimate RMS from low resolution terrain profiles. Fractal parameters are another measure of roughness that are scale invariant, making them a convenient proxy for RMS. While previous work found an empirical relationship between fractal dimension and RMS, this work will show that, by including the cutoff length, an analytic relationship between fractal properties and RMS can be employed. The relationship has no free parameters and agrees very well with experimental data - thus providing a powerful predictive tool for future analyses and a reliable way to calculate surface roughness from low-resolution terrain data in a way that is scale invariant. In addition, we show that this method applies to both man-made ride courses and natural terrain profiles.