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A two-stage strategy is used to describe the human drivers’ path preview process, which involves simultaneous previews of a near- and far-point on the roadway. The human driver previews path coordinates in the near visual field to minimize the lateral position error between the vehicle trajectory and the desired roadway. The preview of a distant location, on the other hand, is used to control the relative orientation error between the

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direction of motion of the vehicle and the far preview point on the roadway. The two- stage preview strategy is formulated to identify locations of the near and far preview points, in three sequential steps involving: (i) identifications of the near and far visual fields; (ii) locating the near preview point with respect to driver’s position; and (iii) locating the point of tangency and far preview point with respect to driver’s position. These are described below considering the path geometry.

The majority of the reported studies have defined path coordinates with respect to the vehicle cg, assuming that the driver is located at or near the vehicle cg. This, however, may lead to substantial errors, particularly for articulated vehicles. The coordinates of the driver’s seat (point D in Figure 4.4) can be determined from the lateral (WD) and

longitudinal (LD) position of the seat with respect to the tractor cg:

(4.8)

where is the tractor heading angle, and (Xg, Yg) and (XD, YD) are, respectively, the

coordinates of the vehicle cg and the driver’s seat in the global axis system (OXY). Referring to Figure 4.4(a), the driver's overall visual field is described as a circular sector centered at the driver’s seat position. The overall visual field is defined by the field angle Φ and its radius, which is determined through minimization of a performance index, as described in the following sections. In the two-stage preview strategy, it is hypothesized that the driver determines the coordinates of the roadway at two target points within the overall visual field in consideration of the road curvature. These include a near preview point and a far preview point. The overall visual field is thus represented by near and far visual fields, indicated by radii LN and LF, respectively, in Figure 4.4(a).

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Through measurements, it has been shown that the visual field angle of human drivers is in the order of 120˚, while the temporal field of vision describing the left/right rotation of the driver’s head is approximately 35˚ [157].

A methodology is developed for locating the near and far preview points considering straight-line and curved roadways. For a straight-line road segment, the driver aims to maintain a central lane position, while compensating for the environmental disturbances. In this situation, the near and far preview points are located at the intersection of the boundaries of the near and far visual fields with the centerline of the road, respectively, as shown in Figure 4.4(a). The near and far preview distances are thus obtained equal to the visual field radii, DPN=LN and DPF=LF, respectively. Assuming constant driving

speed within the preview interval, the preview distance is generally expressed in terms of preview time TP, where TP =Dp/vx and Dp is the preview distance.

X Y Ф LN LF Pc(x) D Wr N F

Far visual field Near visual field

O _X Y Ye T F Ф . LN LF P A N D Pc(x) Pi(x) Ψe O

Figure 4.4: Estimation of the near and far preview points on: (a) a straight-line roadway; and (b) a curved path

During curve negotiation, the driver aims at near and far preview points within the overall visual field so as to minimize the lateral position and orientation errors of the vehicle, while maintaining a central lane position. The near preview point ‘N’, located at

(a) para mete rs (b) para met ers

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the near visual field boundary, is described by a function Pc(x), such that DPN = LN. The

driver’s preview process to locate the near preview point on the centerline of the road Pc(x) as a function of driver’s seat coordinate (XD,YD) and the near preview distance LN,

can be mathematically expressed as:

( ) { (√( ) ( ( ) ) )|

} _(4.9)

where (XN, Pc(XN)) are coordinates of the near preview point on the centerline of the

desired path. In the above equation, ( ), may be described a function or by a look-up table.

For a given forward speed, the near preview distance is assumed to be a constant for both the straight-line and the curved paths, while the far preview distance varies substantially with the path curvature. The driver locates the far preview point by projecting a tangent line to the inside edge of the previewed path (line DF), as shown in Figure 4.4(b). The coordinates of the tangent point T on the inside edge of a curved roadway ( ), can be related to the driver’s seat coordinate (XD,YD) in the following

manner:

( ) {( ( ) ( ))|

} _(4.10)

where ( , ( )) are coordinates of the tangent point T, and ( ) describes the inside edge of the roadway, which is parallel to ( ) but shifted laterally by 1.85 m for a standard lane width of the high-speed divided highways [159].

The intersection of the tangent line with Pc(x) within the far preview field is

considered as the far preview point F, as shown in Figure 4.4(b). During curve negotiation, the far preview distance, DPF, is generally less than LF, but approaches LF on

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straight-line segments. The point F may also lie beyond the far visual field for relatively large curve radius. In this case, the far preview point is considered to lie on the boundary of the far visual field, leading to DPF = LF. The temporal field of vision is employed when

the driver fails to identify the preview points on the road surface within the overall visual field of 120˚ due to possibly excessive road curvature or vehicle orientation [157].

The instantaneous lateral position error of the vehicle, Ye, is assessed by the driver

from the predicted tractor path, shown as point P in Figure 4.5, with respect to the near preview point N. The coordinates of point P, (XP, YP), are obtained using the ‘internal

vehicle model’, described in section 4.3.1, considering the near preview interval TPN=LN/vx. This position error is normal to line (DN), and is given by (Figure 4.5):

(√( ) ( ) ) _(4.11) where: ₍ ) ( ) (4.12)

The far preview point is also applied to determine the instantaneous orientation error of the vehicle, Ψe, defined as the angle between the vehicle longitudinal axis passing

through point D (AD) and the far preview distance line (FD), as seen in Figure 4.4(b).

X Y Ye P N D θn O

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4.3.3 Decision Making Process

The decision making process involves the driver's strategy to simultaneously compensate for both the estimated lateral position and orientation errors, which have been described by a first-order lead-lag and a proportional gain function, respectively [72]. The compensation functions corresponding to the lateral position and orientation errors have been widely expressed by the well-known crossover model [29], which implies that the driver undertakes compensations so as to realize a stable and well-damped non- oscillatory vehicle response in the vicinity of the crossover frequency. The crossover model, however, may lead to substantial tracking errors and a directional instability at frequencies distant from the crossover frequency, which are mostly attributed to the lead- lag compensation strategy [9,32]. The decision making process of the human driver, G3(s), as shown in Figure 4.3, may thus be expressed as a function of the position and

orientation errors together with the perception of vehicle states :

( ) (

∑

) (4.13)

where (j=1 to 7) represent proportional compensatory actions of the driver with respect to the estimated lateral deviation and orientation errors of the tractor unit, and the selected perceived motion states of both the tractor and semi-trailer units, (j=3 to 7).

Under medium- and low-speed steering maneuvers, it is hypothesized that driver is able to track the desired path by considering only the lateral position and orientation errors of the vehicle that has been commonly employed in reported studies on two-axle vehicles [7,8,10,12-26]. The driver’s perception of the lateral position and orientation errors alone, =0 (j=3 to 7), is thus used to formulate the ‘baseline driver model’. In the

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case of articulated vehicles, it is suggested that a qualitative perception of additional vehicle states can help the driver to improve the path tracking performance during high speed emergency situations [11]. Considering only the lateral dynamics of the articulated vehicle using the yaw-plane vehicle model, the additional vehicle states in the above formulation are limited to lateral accelerations and yaw rates of the tractor and semi- trailer units ( , , and ) and articulation rate ( ̇). The effect of human driver's perception on the path-tracking performance are further investigated by considering combinations of nine different motion cues of the vehicle in Chapter 6. In Eq. (4.13), is the processing time delay of the human’s central nervous system, which is determined using the regression model formulated on the basis of the simulator-measured data, Eq. (3.2). The compensation gains, K1 to K7, are identified through minimization of a

composite performance index comprising the steering effort, path tracking and directional dynamic measures of the vehicle.

The driver’s compensatory command is subsequently transmitted to the vehicle steering system through the limb motions. The limb and steering motion function, ( ), is a coupled function of the muscles and steering dynamic Gm(s), reference model ( ),

the muscles reflex model ( ) and active muscle stiffness function Km(s) [67]. Each

element of the limb and steering motion function is mathematically expressed in Eqs. (1.11) to (1.13), described in section 1.2.5. The coupled muscles and steering dynamic is characterized considering muscular dynamics of the human hand-arm and the steering system relating the front-wheels steering, , to driver's steering command, , as shown in Figure 4.3, is described in the following manner:

( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

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