汽车外文翻译---驾驶者的转向感

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Driver perception of steering feel

Abstract: Steering feel is optimized at a late stage of vehicle development, using prototype vehicles and expert opinion. An understanding of human perception may assist the development of a good 'feel' earlier in the design process. Three psychophysical experiments have been conducted to advance understanding of factors contributing to the feel of steering systems. The first experiment, which investigated the frames of reference for describing the feel (tic properties) of a steering wheel, indicated that subjects focused on the steady state force that they applied to the wheel rather than the steady state torque, and on the angle that they turned the wheel rather than the displacement of their hands. In a second experiment thresholds for detecting changes in both steady state steering-wheel force and steady state steering-wheel angle were determined as about 15 per cent. The rate of growth in the perception of steady state steeringwheel force and steady state steering-wheel angle were determined using magnitude estimation and magnitude production. It was found that, according to Stevens' power law, the sensation of steady state steeringwheel force increases with a power of 1.39 with increased force, whereas the perception of steady state steeringwheel angle increases with a power of 0.93 with increased steeringwheel angle. The implications for steering systems are discussed steering feel, proprioceptive, haptic feedback INTRODUCTION

Driving a car is a complex task and involves many interactions between the driver and the vehicle through the various controls. Good performance of the system depends on how well a car 1 s able to create the driver's tensions, and how well differ- ences between those in-u-ns and the vehicle's response can be detected the driver. The steering system is one of the primary controls in a car, allowing the driver to control the direction of the vehicle. The steering system not only allows the driver to control the car but also provides the driver with feedback through haptic (i.e. touch) senses, giving cues to the state of the road-tyre interface

Forces originating at the road tyre interface (and related to the road wheel angle, vehicle red, and road adhesion), present themselves at the steering wheel (subject to kinematic losses through the steer-ing system, and subject to various assist methods in steering systems, e.g. hydraulic and electric power assist) where the driver can interact with them and develop an internal model of the steering propertiesand the environment

The relationship between the steering-wheel torque and the steering-wheel angle has been considered a useful means of describing steering feel Various metrics' of the relationship are used to define steering feel, and experiments have found that changing the relation between the steering-wheel force and steering-wheel angle can alter the driving experience. Knowledge of the way in which haptic stimuli at the steering wheel are

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perceived by drivers may therefore assist the development of steering-system designs.

The perception of stiffness and the perception of viscosity seem to come from force, position, and velocity cues. Psychophysiological studies indicate that muscle spindle receptors, cutaneous mechano-receptors, and joint receptors provide the neural.inputs used in the perception of the movement and force applied by a limb

Psychophysics provides techniques to describe how subjects perceive stimuli. Classic measures include the difference threshold (the minimum change needed to detect a change in a stimulus) and the psychophystcal function (the relationship between changes in stimulus magnitude and the perception of those changes). However, the first step in quanti-fying steering feel using psychophysical methods is to identify what aspects of the haptic feedback at the steering wheel are used by drivers.

Steering torque and steering angle describe the steady state characteristics of steering systems and their relationships have been identified as influencing steering feel. It seems appropriate to check whether subjects are judging what the experimenter 15 measuring. It has not been shown whether the properties of steering system should be described in rotational frames of reference or translation frames of reference

This paper describes three experiments designed to study how drivers perceive the steady state properties of steering wheels. The first experiment investigated whether rotational or translation frames of reference are more intuitive to subjects. It was hypothesized that, if asked to 'match' different steering-wheel sizes, either the rotational or the translation frame of reference would be matched more consistently. The second experiment deter- mined difference thresholds for the perception of steering-wheel force and angle, with the hypothesis that Weber's law would apply for both stimuli. The third experiment investigated the psychophysical scales for the perception of the physical properties at steering wheels determining relationships between steering-wheel force and the perception of steering-wheel force, and between steering-wheel angle and the perception of steering-wheel angle. It was hypothesized that Stevens' power law provides an adequate model for describing the psychophysical scales 2 APPARATUS

A rig was built to simulate the driving position of a 2002 model year Jaguar S-type saloon car as shown. The framework provided a heel point for subjects and supported a car seat and steering column assembly. The cross-section of a Jaguar S-type steering wheel was used to create the grips of the experimental steering wheel, which was formed by a rapid prototype polymer finished with production quality leather glued and stitched on to the subject posture was constrained the seat steering wheel, and heel point. The joint angle at the elbow~monitored and adjusted to 1100 for all subjects to ensure that they did not sit too close or too far from the steering wheel.

The steering-column assembly included an optical incremental encoder to measure

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angle (resolution, 0.0440), a strain gauge torque transducer to measure torque (0.01 N accuracy), bearings to allow the wheel to rotate freely (isotonic control), and a clamp to lock the column in position (isometric control). 3 EXPERIMENTS

Three experiments were performed to investigate the response of the driver to steady state steering-wheel properties and to determine, firstly, the driver frame of reference, secondly; the difference thresholds for the perception of force and angle, and, thirdly, the rate of growth of sensations of force and angle.

The experiments were approved the Human Experimentation, Safety and Ethics Committee of the Institute of Sound and Vibration Research at the University of Southampton

3.1 Driver's frame of reference

Frames of reference provide means for representing the locations and motions of entities in space. There are two principal classifications for reference frames in spatial perception: the allocentric (a framework external to the person), and the egocentric (a frame- work centred on the person). For some tasks, the choice of reference frame may be merely a matter of convenience. In human spatial cognition and navigation the reference frame determines human perception. The haptic perception of steering-wheel position and motion is influenced by the spatial constraint imposed on the wheel, which can only rotate about a column.

In engineering terms, it is convenient to describe the motion of a steering wheel in a rotational frame of reference using steering-wheel torque and steering- wheel angle. However, drivers may use a different frame of reference when perceiving the feel of a steering system; they may perceive steering-wheel force rather than steering-wheel torque, and steering-wheel displacement rather than steering-wheel angle

Alternatively, drivers may use neither allocentric nor egocentric frames of reference and instead may employ some intermediate reference frame as suggested by Kappers

This experiment aims to test whether drivers sense steering-wheel force or torque, and whether they sense angle or displacement. The relationships between these properties are

T=rF (1) x=rB (2)

To investigate which variable is intuitively used by drivers, it is necessary to uncouple the relationship between rotational and translation frames of referece. This can be achieved by altering the radius of the steering wheel. It was hypothesized that, when asked to 'match' a reference condition using isometric steering wheels (i.e. wheels chat do not rotate)with varying radii, subjects would match either the force applied by the hand or the torque applied to the steering wheel. It was similarly hypothesized that,when using isotonic steering wheels (i.e. wheels that rotate without resistance to movement) with varying radu,

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subjects would match either the displacement of the hand on the steering wheel or the angle through which the steering wheel was turned. 'match the sensation experienced with the reference wheel. Subjects were required to achieve the reference or match within 6 s, and to hold the force or angle for 4 s. Subjects were required to move their hands to the test condition within the 6 s given to achieve the match. The total time for one reference and match trial was 20 s

Subjects attended two sessions, one with isometric steering wheels and one with isotonic steering wheels. Four reference conditions were presented in each session: 5 N, 15 N, 1.5 N m, and 3 N m with the isometric steering wheels, and 3`, 90, 10 mm, and 30 mm with the isotonic steering wheels. The forces and distances refer to the forces and dist-es at the hm of the steering wheel.

For this experiment, 12 male subjects, aged between 18 and 26 years, took part using a within-subjects experimental design where all subjects participated in all conditions. The order of presentation of the reference conditions was balanced across subjects

For six subjects, the first session used the isometric steering wheels; for the other six subjects, the first session used the isotonic steering wheels

For each reference condition, a total of 18 trials were undertaken: nine trials to account for each combination of three reference wheels and three diameters of test wheel (small, medium, and large) including matching to the same wheel, and a repeat of these nine conditions.

The length of time that subjects were required to hold a force or torque was minimized to prevent fatigue. Typically, subjects took 10s to reach the desired force or angle. The view of their hands was obscured so that subjects did not receive visual feedback of their position or movement.

3.1.1 Method

Using the 'method of adjustment' [11l, subjects 'matched' sensations from a 'reference' steering wheel to a 'test' steering wheel. When grasping the reference wheel, subjects were required to achieve a desired stimulus magnitude师acting on the wheel in a clockwise

direction using visual feedback from a fixed 11-point indicator scale on a computer monitor. Instructions on the computer monitor then instructed the subjects to move their hands to either the'small','medium; or'large steering wheel, and to The results for a typical subject in the experiment with isometric control are shown in terms of force in. The results for a typical subject in the experiment with isotoniccontrol are shown in terms of angle in Fig. 4 and in terms of displacement in Fig. 5

Correlation coefficients between the physical magnitudes of the reference condition and the test condition are presented for each subject in Table 1 For isometric control,

correlation coefficients were obtained for both torque and force at the steering- wheel rim. For isotonic control, correlation coefficients were obtained for both angle and displace

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ment at the steering-wheel rim. It was assumed that the variable with the greater correlation (i.e. either force or torque, or angle or displacement) is the most efficient engineering term to represent the data.

Over the 12 subjects, for isometric control, the correlation coefficients obtained for force were significantly higher than those obtained for torque (p<0.01, Wilcoxon matched-pairs signed-ranks test) Por isotonic control, the correlation coefficients obtained for angle were significantly higher than those obtained for displacement (p<0.01) 3.1.3 Discussion

Lines of best fit to the data had gradients of less than unity for 11 subjects. The single subject that achieved a slope greater than 1.0 did so only for angle data. The effect could have arisen from the reference being presented first (i.e. an order effect) Alternatively, it could indicate that the physical variables do not reflect the parameters adjusted by is described in terms of a'Weber fraction' or percentage. Weber proposed that the absolute difference threshold is a linear function of stimulus intensity and can therefore be described as a constant per- centage, or fraction, of the stimulus intensity. This is expressed in Wbet's law Subject rwque Farce the subjects. Regardless of the deviations of references and 'matches' from the 450 line, the Spearman correlations ranked the reference and 'match' data according to magnitude without making any ass umptions about the reset values of the reference and the 'match'.

The results suggest that with idealized isometric and isotonic controls, drivers have a better sense of steering-wheel force than steering-wheel torque and a better sense of steering wheel-angle than steeringwheel displacement. It seems that subjects used the forces in their muscles and the angles at the joints of their hands and arms to position the steeringwheels.

To judge torque, subjects would need to combine estimates of force with knowledge of the distance between their hands and the centre of the steering wheel. To judge the displacement of the steeringwheel rrn， subjects would need to combine estimates of their joint angles with the length of their limbs. The estimation of torque and distance requires

more information and greater processing than the estimation offorce and angle. Consequently,it is not surprising that torque and distance result in less accurate judgements and are not preferred or‘natural. 3.2 Difference thresholds

A difference threshold is the smallest change in a stimulus required to produce a just noticeable difference in seusation 111]. Differencecuts,山resholds can be described in absolute terms, where the threshold is described in the physical units of the variable under test, or in relative terms, where the threshold often expressed as a percentage

Difference thresholds for the perception of force are available in a variety of forms. Jones 1121 reported (7 per cent) for forces generated at the elbow flexor muscles.

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Difference thresholds for lifted weights have been reported by Laming .based on an Experiment Fechner using weights from 300 to 3000 g, resulting in a Weber fraction of 0.059 (5.9 per cent), and Oberlin [151 measured difference thresholds for lifted weights from 50 to 550 gaving a Weber fraction of 0.043 (4.3 percent)

tic discrimination of finger span with widths varying from 17.7 to 100 mm have been reported as 0.021 (2.1 per cent) by Gaydos h61. Discrimination of elbow movement has been reported as 8 per cent by Jones et al. [17], while discrimination of sinusoidal movements of the finger studied Rinker et al. produced difference thresholds that ranged from the present experiment investigated difference thresholds for steady state steering-wheel force(using an isometric steering wheel), and difference thresholds for steady state steering-wheel angle (using an isotonic steering wheel). 3.2.1 Method

Difference thresholds were determined with a two alternative forced-choice procedure using an up-and-down transformed response (UDTR) method. Subjects were required to act on the steering wheel to achieve a reference force or reference angle, followed by a test stimulus. The required levels for both actions were presented on a character-less 11-point scale on a computer monitor. The reference stimulus and a test stimulus were presented sequentially, and in random order, to subjects who were required to report which of the two stimuli 'felt greater: The UDTR method was used with a three down one-up rule (i.e. three correct responses row caused the test stimulus to become closer to the reference stimulus whereas one incorrect response resulted in an increase in the difference between the reference and the test stimulus). The three-up one down rule means that the observed at a 79.4 percentdictated their responses. The sequence terminated after three 'up' and three 'down' reversals of direction. The difference thresholdwas measured as the mean value of the last two 'up' and the last two 'down' reversals.

For this experiment, 12 male subjects, aged between 18 and 28 years, took part using a within-subjects experimental design. The order of presentation for the refer-- conditions was balan-d across sub- jects with six subjects starting with isotonic control, and six starting with isometric control. 3.2.2 Results

The median absolute and relative difference thresh olds are shown in Table 2. For both force and angle, the absolute difference thresholds increased signifi- cantly with increasing magnitude of the reference(p < 0.01, Friedman test)

The median absolute and relative difference thresh- olds for both force and angle are shown in Fig. 6 andFig. 7 respectively. The median relative difference thresholds tended to decrease (from 16.5 per cent to 11.5 per cent) with increases in the reference force and decrease (from 17.0 per cent to 11.5 per cent)with increases in the reference angle. However, over-all, the relative difference thresholdsd not differ significantly over the three

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force references or over the three angle references (p > 0.4, Friedman tes law can be upheld for the Relativeforce arange)differenud angle thresholds for steady state(medians and interquardleMedian difference

Driver pereepfiun of.waring feel produce. The bias causes magnitude production to yield steeper slopes (i.e. higher values for n) than magnitude estimation.

The third experiment employed both magnitude estimation and magnitude production to develop a force

The mean relative difference thresholds across the magnitudes of the reference stimuli were 15 percent when detecting changes in force and 14 per cent when detecting changes in angle. This suggests no fundamental difference in the accuracy of detecting changes in force and angle, implying that force and angle provide equally discriminable changes in feedback.

For the perception of force, the 15 per cent relative difference threshold was obtained with a correct performance level of 79.4 per cent. Direct comparison with the aforementioned studies of the perception of force are not possible, as correct response levels are not presented in those studies. For the perception of angle, 14 per cent in the present study compares the a difference threshold for limb movement in the range 10-18 per cent (for a 71 per cent correct performance level) according to Rinker et al. [18], and 8 per cent (for a 71 per cent correct performance level) according to Jones of perception of steady state steering-wheel and steady state steering-wheel angle. 3.3 Rate of growth of sensation

The rate of growth of sensation of stimuli has often been determined using Stevens' power law Where is the sensation magnitude,is the stimulus intensity, k is a scalar constant depending on the conditions, and n is the value of the exponent that describes the rate of growth of sensation of the stimulus and depends on the sensory modality (e.g perception of force, or perception of loudness).

Previous studies have reported rates of growth of sensation of force and weight with exponents between。and 2.0 over a variety of experimental conditions 121-2引A study of the haptic sensation of finger span Steven. and Stone using widths of 2.3-63.7 mm reported an exponent of 1.33 using magnitude estimation.

The value of the exponent n may be determined by either magnitude estimation or magnitude production. Magnitude estimation requires subjects to make numerical estimations of the perceived magnitudes of sensations, whereas magnitude production requires subjects to adjust the stimulus to produce sensory magnitudes equivalent to given numbers These methods have systematic biases which Stevens called a 'regression effect. The biasese attributed to a tendency for subjects to limit the range of stimuli over which they have control; so with magnitude estimation they limit the range of numbers that they report, and in magnitude production they limit the range of stimuli that they For magnitude

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estimation, a subject first applied a reference force (or angle)acting on the steering wheel in a clockwise direction. The reference was 10.5 N on the isometric steering wheel and 9" on the isotonic steering wheel. Feedback was given on an 11-point scale, with the reference in the middle of the scale. Subjects were told that the reference corresponded to 100.

A subject then applied 11 different test forces (or angles) by applying a force or angle until the pointer was placed at the middle mark of the 11-point scale. The forces or angles required corresponded to 50 per cent, 60 per cent, 70 per cent, 80 per cent, 90 per cent, 100 per cent, 120 percent, 140 per cent, 160 per cent, 180 per cent, and 200 per cent of the reference force or angle. For force, these stimuli ranged from 5.25 N to 21 N while, for angle, they ranged from 4.5` to IS`. After the presentation of a test stimulus, a subject was asked to report a number considered to represent the test force (or angle) in proportion to the reference. The presentation order of the test stimuli was randomized. For magnitude production, a subject first applied a reference force (or angle) by acting on the steering wheel in a clockwise direction. The referencewas 10.5 N on the isometric steering wheel and 90 on the isotonic steering wheel. Feedback was given on an 11-point scale, with the reference in the middle of the scale. The subject was told that this corresponded to 1011. The scale was removed and a number was displayed instead (50, 60, 70, 80, 90 100, 120, 140, 160, 180, or 200) and the subject was asked to produce a force (or angle) corresponding to the given number in proportion to the reference The presentation order of the test stimuli was randomized.

For this experiment, 12 male subjects, aged between 18 and 26 years, took part using a within- subjects experimental design. Subjects attended two sessions with the order of presentation of the force angle, and magnitude estimation, and magnitude production conditions balanced across subjects.

The exponent indicating the rate of growth of sensation was determined by fitting Stevens' power law to the data. With the stimulus and sensation 3.3.2 Results

Exponents for the rate of growth of sensation were obtained from least-squares regression between the median judgements of the 12 subjects for each test magnitude and the actual test magnitude, with the apparent magnitude assumed to be the dependent variable (261. The calculated exponents were 1.14 (force magnitude estimation), 1.70 (force magnitude production), (1.91 (angle magnitude estimation), and 0.96 (angle magnitude production). The median data, and lines of best fit from all subjects, are shown in Figs 8, 9, 10, and 11 for force estimation, force production, angle estimation, and angle production respectively and are compared inFig. 12

The Spearman rank order correlation coefficients between the physical magnitudes and the perceived magnitudes were 0.89 for force magnitude estimation, 0.65 for force magnitude production, 0.89 for angle magnitude estimation, and 0.87 for angle magnitude

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production. All correlations were significant (p < 0.01; N=132), indicating high correlations between stimuli and the estimated or assigned magnitude. 3.3.3iscussfon

With magnitude estimation, the rank order of all median estimates of force and angle increased with of growth production apparent force using magnirude estimatml of apparent force using magni

Data from 12 subjects Incresing force and angle, except for the middle (100 and 120) force estimates. This deviation is assumed to have arisen by chance. To assess the impact that this deviation has on the exponent obtained from the median data, an exponent was regressed to all data points from all subjects. This yielded an exponent of 1.14, which is the same as the exponent determined from the median data. Similarly, with magnitude production, the median forces and angles

increased with increasing required value, except for the two lowest forces. The lowest median force was produced when subjects were asked to produce a rate of growth of sensation of apparent force and angle is taken as the geometric mean of the rates of growth for magnitude estimation and magnitude production. In this study, the means of the esti- mation and production slopes were 1.39 for steeringwheel force and 0.93 for steering-wheel angle.

The rate of growth of sensation of steering wheel force ties within the range previously reported for force. A rate of growth of 1.39 means the sensation of force growmore rapidly than the force causing the sensation. For example, a doubling of force will give rise to a 162 per cent increase in the perception of force. Steering-wheel angle had a mean rate of growth of 0.93; so the sensation of angle grows at a slower rate than the angle. For example, a doubling of angle would give rise to only a 91 percent increase in the perception of angle force corresponding to an apparent magnitude of 70'; the median force was slightly higher (although not significantly different) for apparent magnitudes of '60' and '50'. This deviation from the expected order, which is assumed to have arisen chance means that the exponent for force production (1.70) was higher than it would have been without the two lowest forces. Regression to all the data from all subjeers for force production (instead of the median judgement) yielded an exponent of 1.38

The regression effect was present in both the force and the angle data. An estimate of the 'unbiased' Although it is desired to optimize 'steering feel', there has been little systematic investigation of what drivers feel, the differences that they can detect, or the way that sensations change with variations in force or angle of turn of steering wheels. The first experiment addressed the appropriate terminology for steering feel, in anticipation of the subsequent two studies. The results of the first study imply that the hotic properties of steering systems in vehicles should take account of the radius of the steering wheel when considering the load applied by the driver. Variations in the steering-wheel radius will scale

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force perception and change the feel.

The second experiment determined the differences required in steering-wheel force and angle for the differences to be detected. A difference of 15 percent for force and 14 per cent for angle was required for the difference to be detected 79.4 per cent of the time. Difference thresholds can be described using the theory of signal detection, with no one value for the threshold but values that vary according to the corect response rate. A 'receiver-operating characteristic' (ROC) curve would describe the difference threshold over all response rates. The experiment provided one point on the ROC curve; it would be desirable to measure other points and to construct a full ROC curve so that the relation between the difference threshold and the probability of detecting

a difference can be seen. The conditions in which the difference thresholds were determined may have influenced the thresholds determined. In the present study, subjects 'relaxed' between the force trials and returned the wheel to the centre between the angle trials, representative

of successive presentations of individual stimuli rather than incremental changes in force or angle as will occur during driving. Notwithstanding the limitations of the experiment, the results may be useful in various areas. For example, they provide insight into the differences that may be acceptable from asymmetries in a steering system, and the differences acceptable during repeated turns

The results of the third experiment show that neither the perception of steering wheel force nor the perction of steering wheel angle is 'linear. Understanding of how drivers perceive the feed back of steering-wheel force and steering-wheel angle requires recognition that their feel is not linearly related to either the force or the angle

The studies reported in this paper investigated how the perception of steering-wheel force and steeringwheel angle depend on force and angle respectively. There may be limitations in the application of the findings to vehicle steering systems where the force applied to a steering wheel and the steering wheel-angle vary together. The perception of force or angle may be altered by variations in angle or force respectively. Additionally, auditory, visual and other somatosensory stimuli present in vehicles but not in this laboratory study may affect the perception of force and angle at a steering wheel 5 CONCLUSIONS

Steering-wheel force rather than steering-wheel torque， and steering-wheel angle rather than the translational displacement ofthe hands on the steering wheel, are more efficient descriptors of'steering feel'. When judged in successive presentations, the median difference threshold for the perception of steering-wheel force was found to be 15 per cent and the median difference threshold for the perception of steering-wheel angle was 14 per cent. The rate of grow of sensation of steering-wheel force follows a power law function with an exponent of 1.39; so erceptions of steering force increase more rapidly han

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increases in force. In contrast, the rate of growth of sensation of steering-wheel angle follows a power aw with an exponent of 0.93; so perceptions of steering-wheel angle increase less rapidly than increases n steering-wheel angle

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驾驶者的转向感

摘要:最近随着汽车技术的发展，利用原型车和专业方法，转向感被优化。对人的认知的了解在设计初期可能协助发展一种良好的感觉。为了进一步了解哪些因素促成对转向系统的感觉，三个心理实验己经进行。在第一个实验中，它研究了描述感觉(即触觉性质)的方向盘的参照系，表明测试者把注意力集中在施加于车轮上稳态的力，而非稳态扭矩。测试者把注意力集中车轮转动角度而非手中方向盘的位移。在第二次实验中，在稳态方向盘力与稳态方向盘角度状态下，检测到的闽值变化量被确定在15%左右.分别用震级估算和震级产生对稳态方向盘力与稳态方向盘角度下转向感变化速度进行确定。据发现，据史蒂文斯的定律，在强度为1.39上，随着力的增加，稳态方向盘力的感觉增加。而在强度为0.93上，方向盘转角的感觉随着方向盘转角的增大而增大。转向系统将被讨论 关键词:转向感觉，本体感觉，触觉反馈 1引言

开车是一项复杂的工作，牵涉到许多的司机和车辆的互动。二者组成的系统的良好运行取决于车辆能理解驾驶者的意图，以及如何区别这些意图和司机能很好感知车辆的反馈。在一辆车上，转向系统是最重要的控制系统之一，让司机来控制汽车方向。转向系统，不仅让司机控制车，而且也提供给司机了车辆的反馈，通过反馈，给予触觉感官路一轮胎系统的影响。

来自脚下的路一轮胎系统的力(以及相关的进路轮角度，车轮速度和道路附着力)作用在方向盘，而司机通过车轮与它们(转向系统运动损失及受到各种援助方式转向系统，如液力和电磁的协助)互动，建立转向系统内部性能和环境的模型。 方向盘转矩和方向盘角度关系来一直被视为一个有用的方法描述转向感觉。各种度量的关系，是用来界定转向感觉。实验发现，改变方向盘力和方向盘角度的关系，都无法改变的驾驶经验。山司机所感知的方向盘的触觉的刺激的有关知识，被视为是可能有助于转向系统的设计. 认知刚度和观感粘度似乎来自力的位置和速度。心理生理学研究表明，肌梭的受体，皮肤的感受器，与联合受体提供了神经输入，用于感知运动和的肢体的作用力.

神经物理学提供技术来描述主体如何感受刺激。典型的措施包括差阐(需要检测的改的最小变化刺激)和神经物理学函数(刺激程度的变化和对这些变化的感知之间的关系)。不过，第一步，利用神经物理学方法对转向感进行量化是要确定方向盘触觉反馈哪些方面是司机能感知的。

转向力矩和转向角度描述转向系统的稳态特性，而它们之问的关系己经定义为转向感觉.似乎有必要检查实验者衡量什么，。也没有说明是否转向系统的性能用一个旋转参照系(即扭矩和角度)或传动的参照系(即力和位移)来描述。

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木文描述了三个实验，旨在研究司机如何感知方向盘的稳态性能。第一个试验研究转动或传动参照系对于主观者是否更直观。据推测，如果要求匹配不同大小方向盘，旋转或移动的参照系也能更加一致与它们匹配。第二实验确定观感方向盘力量和角度的差别闽，如果假定韦伯的法律将适用双方的刺激。第三实验研究了方向盘物理特性的神经物理学等级观念，它确定了方向盘力和方向盘观感之问关系，以及方向盘角度和方向盘角度观感的关系。据推测史蒂文斯的定律提供了充分的模型描述神经物理学等级观念。 2仪器

一个平台被建立来模拟驾驶一个型号2002年美洲虎S型轿车的位置如图1该框架为主观者提供了一个脚跟点和支撑汽车座椅和转向柱总成。美洲虎S型的方向盘的截面被用来作为的实验方向盘，这种方向盘由快速成型聚合物和优质皮革做成，以形成良好的对握。

测试者位置山座位，方向盘足跟点的位置决定。对弯头角度进行监测和调整，使它保持在1100左右，以确保所有测试者不要离方向盘太近或太远。转向柱总成包括光学增量编码器以便测量角度(结果0.0440)，应变片扭矩传感器测量扭矩(0. 01N准确性)，轴承以便使车轮转动自由(等距控制)，夹锁以便锁定位置(等渗控制)。 3实验 做三个实验，是为了研究司机对于方向盘稳态的性能的反应，以及确定司机的参照系，确定为力和角度感知的闽值变化量，确定力和角度的感知的增长率。人体实验、安全与伦理委员会研究所和南安普敦大学的声学与振动研究通过这次实验。 3. 1司机的参照系

参照系提供方法来描述空间中的实体的位置和运动.有两个主要分类为参照系，在空间知觉:外部中心(外部的人的框架)，而自我中心(框架集中于人)。对于某些任务，选择的参照系可能仅仅是出于方便。在人类空问认知和导航的参照系，决定着人的观感。方向盘的位置和运动的触觉的感知，是受车轮限制，车轮只能围绕转向柱转动。

在工程方面，利用方向盘扭矩和方向盘的角度，也可很方便地描述了一个方向盘在转动参照系运动。不过，当感觉转向系统时，司机可使用不同的参照系;他们可能会感觉方向盘力而非方向盘的扭矩，感觉方向盘位移而非方向盘角。另外，司机可既不使用外界参考系也不使用自我中心的参照系，反而可能会使用一些由kappers建议中间参照系[10],

这项实验的目的是检验驾驶者是否能感知方向盘力或力矩，以及是否他们能意识的角度或位移。这些特性的关系是 T=rF (1)

X=rB (2)

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为了研究哪个变量是被司机直觉所感知，找出旋转和移动的参照系的关系是十分必要的。这项工作可以通过改变方向盘的半径来完成。假设这种情况，当被问及他所感知的一个参考系，在等距(方向盘不转动)改变方向盘半径条件下，测试者要么感知手上的作用力要么感知施加于方向盘的扭力。也有这样一种假设，当使用变半径的等渗方向盘(即车轮转动，不能抵抗运动)测试者要么感知手中方向盘的位置或方向盘转过的角度. 3.1.1方法

采用调整的方法，从参考方向盘到测试方向盘，测试者都能感知。在抓好参考方向盘后，受试者需要完成达到预期刺激程度的按顺时针方向转动方向盘的动作。用一台11项固定的指标的电脑监视器米显示视觉反馈情况。电脑显示器指示指导测试者小角度，中角度，或大角度转动方向盘，去寻找参考方向盘的感觉经验。受试者需要在6秒的范围完成相关操作，并且在随后的4s内保持力或转角。受试者需要在6秒内移动他们的手来完成给定的试验内容。建立参考空间和把握方向感的总时间为20秒。

测试者分成两组，一组参加等距方向盘项目，一组参加等渗方向盘项目。在每组中有四个参数状态需要测试:5N, 15N, 1. 5N., 3N.用等距方向盘), 30 , 9、10毫米、30毫米(用等渗方向盘)。这些力和距离与方向盘臂的力和距离有关。

这项实验中，12名男性，年龄在18至26岁，应用主观实验设计方法，所有测试者参加了在所有的条件下的测试。整体的测试结果更加均衡合理。第一组的六个参与者用等距方向盘:至于第二组的六个参与者使用等渗方向盘

对于每一个参数状态，共有18个试验进行:9个实验收集下列对象的状态数据:3个参考方向盘的组合和3个不同直径试验方向盘(小型，中型和大型)。包括，重复上述相同尺寸方向盘的九个状态实验。

受试者需要保持力或转矩的时间的长短能最大限度地防止疲劳。通常，测试者历时10秒，以达到预期的力量或方向盘角度。测试者的双手被掩盖，使他们并未获得自己的位置或运动的视觉反馈。 3.1.2结果

实验中的一个典型测试者的等距控制的结果在图2以力的方式表现，在图3中以扭矩图形式表现。实验中的一个典型测试者的等渗控制的结果在图4以角度的方式表现，在图5中以位移形式表现。

物理量的参考条件和试验条件之问的相关系数在表1每个测试者位置处给出。对于等距控制，相关系数通过在方向盘臂处的力矩和力获得。对于等渗控制，相关系数通过在方向盘臂处的位移和角度获得。据推断，相关系数越大的变量(力或转矩，角度或位移)是越容易表现在数据中。对于12个测试者，等距控制中通过力取得的相关

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系数明显高于通过扭矩获得相关系数(p<0.01 wilcoxon配对标记的等级检验)。对于等渗控制，通过角度获得的相关系数明显高于通过位移获得的相关系数(p<0.01)> 3.1.3讨论

最适合的数据的线的梯度小于11个测试者单元的整体。实验数据的梯度大于1.0的单一测试者只用了角度的数据。其结果己经才从正在表现第一参数中产生(即命令生效)。另外，它可以显示物理变量并不反映被测试者调整的参数。无论参数与450线匹配的偏差多大，斯尔曼相关系数在没有做关于参数和匹配的确切值的假设情况下对参数和匹配进行分级。

结果显示，在理想化等距和等渗控制中，比方向盘扭矩感来，司机有更好的方向盘力的感觉。和方向盘角度感相比，司机有更好的方向盘位移感。看来，受试者用其肌肉上的力及手臂关节点的角度来定位方向盘

为了判断扭矩，测试者将需要估计力与乎与方向盘的中心的距离。为了判断方向盘臂位移，测试者需要估计关节节点的角度与手脚的长短。估计扭矩和距离比估计力量和角度需要更多的信息和更大的工作。因此，扭矩和距离不准砍的、不被喜欢和不自然，这就不足为奇。 3.2差别阂

一个差别阂是最小的变化和刺激，能够引起人感觉器官的注意[111.差别闽可说是绝对单位，差别闲是描述测试的变量的物理单位，或者是相对而言，差别闭是用韦伯分数描述的一个量。韦伯提出的绝对差别L7是一种线性的刺激强度，因此，可以用一个固定百分比或分数描述刺激的强度。这体现在韦伯的法律中，C是一个常数，称为韦伯分数，常以百分比表示。

感知力的阐值的形式为多种多样。琼斯[12」报道乎肘屈肌所产生的力的差别闽为韦伯分数0.07(了%)。墓于一项实验laming[13]报道了举起重物的差别阂是韦伯分数0.059(5.9%)。这项实验中希纳把重量从300克增加到3000克。奥伯[15]测量了限制重量为50至550差别闺，韦伯分数为0.043(4.3%). gaydos [16]报道了手指跨度的宽度为了70至100毫米触觉闭值为0.021(2.1%).琼斯报导肘运动的闽值为8%。ftinker[18]研究了手指运动闺值的规律为正弦规律。差别阂的范围从10%到18%, 本实验研究稳态方向盘力的差别闲(用等距方向盘)和稳态方向盘角度的差别1A7(用等渗方向盘)。 3.2. 1方法

差别闽值是用两种替代被迫选择程序测定，即上下转化反应方法【19],受试者需要根据刺激程度在方向盘上完成预定的力或角度。完成动作所需的水平由一台11项固定的指标的电脑监视器所显示。分别介绍了参考刺激和试验刺激的顺序和随机秩序，受检者报告这两个刺激的感觉哪个更大。UDTR的方法是一个三升一降规则(即三个正

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确的反应使刺激更加接近参考刺激，而一个不正确的反应增加，导致增加参考和测试刺激的不同)。三升一降规则意味着得到的差别I"7值有79.4%正确反应水平 三个参考程度被用来在每一组:(等距方向盘的5.25N. 10.50N. 21N)和(等渗方向盘4、8.、160)。为了确定每个参数的差别闭，测试者做了一系列判断，而判决的总数取决于其反应。测试终止后进行三升一降规则逆方向的测试。差别阂的平均值为最后两个上和最后的两个下的逆转值测定口

这项实验中，12名男性年龄18至28岁，参加了内部主观实验设计。相关状态出现的次序通过测试者进行平衡。六个测试者由等距控制，六个测试者由等渗控制. 3.2.2结果

差别闲值位数绝对值和相对值见表2。对于力和角度，随着参考幅度增加(P<0. 01弗里德曼测验)，绝对差闽值明显增加。

力和角度差别阂值位数的绝对值和相对值列于图6和图7.随着参考力的增加，差别阂值位数相对值均呈下降(从16.5%到11. 5%).随着参考角度的增加，差别闽值位数相对值均呈下降(从17.0%到11.5%)。不过，总体而言，相对的差别闺值没有超过三个力参照和三个角度参考((P>0.4弗里德曼测验)。 3，2.3讨论

统计分析意味着力量和角度的相对差别阂是独立的，而应用韦伯的法则可对这个状况进行研究。在检测变化力时，不同程度的参考刺激的平均相对差别阂为15%。当检测变化的角度时，不同程度的参考刺激的平均相对差别阂为14%口这意味着探测变化力和角度的准确性没有根木区别。表明力量和角度提供同样反馈变动。

对于力的感知，15%相对差别闺值达到正确的性能水平的79.4%。但直接比较上述研究报告的力的感知是不可能的，因为正确反应水平是不表现在这些研究中。对于角度的感知，在本研究14%与肢体运动的差别阎值的10^18%(按71%的正确率)相比，据rinker的调查。与肢体运动的差别闭值的8%(71%正确率)， 3.3感知的增长率

刺激感的增长率采用史蒂文斯的法则确定.w表示感觉的程度，中是刺激的强度，K是一个由具体情况决定的常量, N是描述了刺激感的增长速度的指数，并决定感官(例如力的感知或感知响度)。

以前的研究报告了在各种实验条件下〔21-24]感觉力和体重的增长速度指数在。.8和2.。之间。史蒂文斯和斯顿研究了手指跨度的触觉感觉[25」利用跨度为2.3-63.7毫米来估算指数次方为1.33的震级。

指数n的值可要么由震级估计决定要么由规模生产决定。震级估计需要测试者作一个感觉的知觉程度的数值预测，而规模生产需要测试者调整刺激产生等于给数值感应程度。这些方法有系统性偏差。这被史蒂文斯[20」叫做回归效应[11]偏差都归因

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于一种测试者限制刺激超过他们所控制的范围的趋势:所以在震级估计中他们限制他们所报告的数值的范围，在模生产中他们限制了各种所产生的刺激口偏差造成的规模生产产生了坡度(即高值n)而不是震级的估计

第三实验均雇用震级估算及生产规模研究稳态方向盘力与稳态方向盘角度的知觉程度。 3. 3. 1方法

对程度的估计，测试者首先在顺时针方向操作方向盘中应用参考力(或角度)。对于等距方向盘，参考力是10.5N，对于等渗方向盘，参考角度是9度。在中等参考下产生了一个n点的规模的反馈。受试者被告诉参考范围相当于100以内。测试者应用于11个不同的测力(或角度)，用力或角度直到指针摆在中间标志的11点尺度处。被指定的力或角度相当于50%, 60%, 70%, 80%, 90%,100%, 120%, 140%, 160%, 180%, 200%的参考力或角度。对于力，这些刺激介于5. 25N-21N，而对角度而言，他们介于4. 5度至18度。在出示一份检验刺激测试者被要求根据参考的比例提出报告来表现试验力(或角度)来。出现试验刺激的顺序是随机。为程度产生，测试者首先在顺时针方向上操纵方向盘应用参考力(或角度)。对于等距方向盘，参考力是10. 5N。对于等渗方向盘参考角度是9度在中等参考下产生了一个11点的规模的反馈。受试者被告诉参考范围相当于100以内。指针移动，显示的数字被代替(50, 60, 70, 80, 90, 100, 120, 140, 160,180或200)0测试者被要求产生给定的数目并与参考成正比一个力(或角度).出现试验刺激的顺序是随机

这项实验中，12名男性年龄18至28岁，参加了内部主观实验设计。测试者分成两组按顺序进行力，角度和程度估计，震级和生产实验。相关状态出现的次序通过测试者进行平衡。

该指数表明感知的增长速度，是山史蒂文斯的定律决定的。随着对数轴上的刺激，该指数是斜率n由下列公式所决定。

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3.3.2结果

感知的增长速度的指数通过最小二乘法回归中位数得到。对从12个测试者的每次试验程度和实际试验程度及被假设的变量决定的震级实验中的数据进行最小二乘法回归「26]。计算的指数分别为1.14力震级的估计)，1. 70力程度产生)，0.91(角度震级估算)和0.96(角度规模产生). 中位的数据，最适合于所有的测试者的线列于图8、9, 10和11。力的估计，力的产生，角度估算，角度的产生分别在图12中比较。

物理程度及认知程度之问的斯尔曼的秩相关系数r分别为。.89(力震级估计)和0.65(力的规模产生)，0.89(角震级估计)和0.87(角规模产生)。刺激和估计或指定

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程度之f7的相关显着性(P<0.01, N=132)具有较高的关联性。 3.3.3讨论

随着震级的估计，随着力量和角度的增加，力和角度的所有位数估计的排序增加，中部(100和120)的力量估计除外。这个偏差是随机的上升.为了评估这种偏差对中位数据的指数的影响，指数回归到全部测试者的所有数据点。由此得出的一个指数为1.14,这同从中位数据确定的指数是一样的。同样地，对于规模产生，所需的数值而增加的中间力和角度也一样，除两个最低位力。当受试者被要求产生一个与幅度70相应的力量时，最低位的力被产生。对于明显震级60和50，中位力略高(虽不显着)。这种偏离预期的秩序是随机的，这意味着力的产生的指数(1. 70)比无最低的二个力时要高。回归所有来自所有测试者的关于力生产的数据(代替位数判断)算出的指数1.38.

回归效果表现在力量和角度的数据上。估计没有偏见的力量和角度的明显感觉的增长率，当作幅度估计和规模生产的增长率的几何平均值.在这项研究中，转向盘力的估算和生产斜率的平均值是1.39，而方向盘角度的值为0.93.

方向盘力感的增长率所在，在先前报道的范围内【22]a增长率为1.39意味着力感的增长快于力的增长.例如，增加了一倍力量将引起感知的162%增加。方向盘角度有平均增长率为0.93;这样角度感的增长速度比角度的增长慢。例如，增加了一倍的角度会引起只提高了91%角度感 4一般性讨论

虽然希望优化转向感，但是很少有系统的研究。这些研究包括司机的感觉，他们感知的差别。和随着转动方向盘的力和角度变化，感觉怎样变化.第一次实验给了适当的术语转向感，配合随后的两个研究。当考虑了施加在司机上的负载时，第一项研究的结果表明了车辆的转向系统的触觉特能应顾及方向盘的半径。方向盘半径的变化衡量力感和力感的改变口

第二实验确定了被测试到的方向盘力量和角度的差异。相差15%的力和相差14%的角度将引起79. 4%时间差。差别闽运用信号检测理描述。差别闽的值通过正确的反馈变化。ROC曲线(接受操作特性)曲线描述了所有反馈的差别闭值。该实验提供了ROC曲线的一点;最好能测量其它的点，并建构一个ROC曲线。差别阂与概率检测差异之P的关系可以看出。 测定差t01值的环境可能影响闽值测定。在木研究中，测试者与力的实验相联系，在角度试中使方向盘回正。它们代表个别刺激而不是力或角度的增量变化就像发生在驾驶过程中。虽然试验有限制，结果可能是在各个领域有用的。举例来说，它们提供差异的见识是可以接受的，从转向系统不对称到重复转向可接受差异。

第三次实验的结果表明，无论是方向盘力感部队还是方向盘角度感都不是线性。

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了解如何看待司机感知方向盘力和方向盘的角度的反馈需要承认无论是力或角度的感知并不是线性关系。

研究报告说，方向盘力和方向盘角度的感知如何依靠力和角度。对于汽车转向系统中的方向盘作用力和方向盘角度一起变化的情况，应用研究的结果可能有局限存在。力或角度的感知可能被角度或力的变量改变.此外，听觉、视觉或其他身体感官刺激表现车辆上，但这些不被包括在本实验室中，这些可能影响方向盘力和角度的感知。 5结论

方向盘力是更有效的转向感的描述而非方向盘扭矩。方向盘的角度更有效的转向感的描述而非双手放在方向盘的平移位移的。在连续的判断结果中方向盘力感的差别闽的中位数被发现为15%，方向盘角度感的差别闲的中位数为14%。方向盘力感的增长率。所以转向力感增加的速度比力增加的速度快。相比之下，方向盘角度感增长率遵守指数为0.93的幂函数。所以方向盘角度感增加速度要比方向盘角度增加速度慢。

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