Proposed Road Geometry Model

A new way of defining accurately the road geometry and traffic data in four dimensions is proposed in this study to support theSEDAS. Topological road data are expressed as a series of connected data points of interest (segments) in four dimensions. The digital map database provides carefully measured data points which represent the centre line position

Slop e, θ (s ) Position, s Segment i si−1 si ais2+ bis + ci Hi (s − si− 1 ) Hi (s − si )

Figure 3.17: Proposed road slope model at segment i

of the road. In this study, the road slopes, road curvatures, and traffic speed limit zones data are modelled as continuous and differentiable functions of the vehicle’s position. These functions represent the data points of interest in each segment of the road. The hyperfunction concept as a kind of generalised functions is used to interconnect the estimated segments of the road to each other at the boundaries. These models use the vehicle’s position to provide the upcoming road geometries and traffic information to the system controller.

3.4.1.1 Road Slopes Model

The road slope data allows the vehicle to be informed of static road slope conditions, and take efficient actions based on that information. This is an effectiveEco-drivingstrategy that takes advantage of the gravity to improve the travel time and energy consumption efficiency. The road altitude Ralt information from the digital road map (in meters) is

used to calculate the gradient angle θ(sh) at location sh as follows (M. A S Kamal et al.,

2011):

θ(sh) = tan−1(

Ralt(sh+ ∆sh) − Ralt(sh− ∆sh)

2∆sh

) (3.8)

where ∆sh is a relatively small value (in meters). The interval determination of data

points of interest can lead to a tradeoff challenge between the accuracy level and size of data points. In this study, the road slope profile is proposed to be the sum of quadratic functions of the position representing each road segments slope data. The modelling concept is shown in Figure3.17. Based on the stated context, the road slope profile can be defined as: fslope(θ(s)) := Nsgm X i=1 Hi(s − si−1)(ais2+ bis + ci)Hi(s − si), (3.9)

where Nsgm is the number of road segments, the Hi(s − si−1) and Hi(s − si) are the

the approximate Heaviside’s functions at the boundary position values, si−1 and si, as follows: Hi(s − si−1) = 1 2(1 + tanh(ki+(s − si−1))), (3.10) Hi(s − si) = 1 2(1 − tanh(ki−(s − si))) (3.11) where a large ki±corresponds to a more sharp transition at the boundary positions. The

ki±and coefficient of the quadratic functions are estimated by the curve-fit process from

the data points, which provides a smooth transition from one road segment to another. The vehicle position based function (3.9) is a continuous and differentiable function that represents the data points of interest in each segment of the road. In this approach, the tradeoff challenge between the high and low-fidelity models forSEDASis avoided. The proposed model can now be efficiently integrated into theBEV dynamics (2.1) to form a unified system model.

3.4.1.2 Road Curves Model

A horizontal curve provides the directional transition on the horizontal plane, between two straight sections of the roadway running in different directions. Horizontal curves are expressed as circular curves with constant radii, or successive curves with different radii (for more details see Fwa (2006)). The road curves alignments can also be modelled in a similar concept with the proposed road slope model. The horizontal road curves may be parabolic or circular, which can be classified as simple, compound, reverse, and deviation curves. A simple road curve has the same radii (in meters) around a single arc of the circle (Rcrv). Since the road curve is defined as R−1crv, similar to the geometry of

the Euler spiral, the simple circular curve is used to express the total absolute curvature alignment in this study, which is defined as:

fcurve(δ(s)) := Ncrv X i=1 Hi(s − sent)     1 Rcrvi(s)     Hi(s − sext), (3.12)

where Ncrvis the number of roadway curves, and Rcrviis the radii of a circle valid for the

curve’s constant radii with two position points, sent and sext, at the respective entrance

and exit position of the curve i independent of the bend direction. The Rcrvi for a

straight road segment can be considered as a large numerical number. It is noteworthy, the related ki± in the approximate hyperfunctions (3.10) can determine the transition

between the straightforward segment of the roadway, known as tangents and the circular curve.

Figure 3.18: Centre de Formation pour Conducteurs S.A., Colmar-Berg, Luxembourg (Schroeder,2016)

3.4.1.3 Road Traffic Speed Limit Zones Model

The road sign information that have influence on the cruising velocity play an important role in theEco-drivingstrategy. In this study, the traffic speed limit zones as one of the most effective item is considered to be modelled similarly to the previous road geometry methodology as follows:

flmt(s) := Nlmt

X

i=1

Hi(s − sstr)(vlmt− vmax)Hi(s − send) + vmax, (3.13)

where Nlmtis the number of speed limit zones along the roadway, and vlmtis the specified

speed limit value at positions starts from sstr upto the end of the zone position send.

The vmax is the maximum speed value of the vehicle. Note that, the associated ki± in

the approximate hyperfunctions can regulate the transition policy between the speed free and limit zones. The proposed model for the road curves and traffic speed limit zones can now be efficiently utilised in theSEDASconcept.