Design of a Multi-layer Lane-Level Map for Vehicle Route Planning

With the development of intelligent transportation system, there occurs further demand for high precision localization and route planning, and simultaneously the traditional road-level map fails to meet with this requirement, by which this paper is motivated. In this paper, t he three-layer lane-level map architecture for vehicle path guidance is established, and the mathematical models of road-level layer, intermediate layer and lane-level layer are designed considering efficiency and precision. The geometric model of the lane-level layer of the map is characterized by Cubic Hermite Spline for continuity. A method of generating the lane geometry with fixed and variable control points is proposed, which can effectively ensure the accuracy with limited num ber of control points. In experimental part, a multi-layer map of an intersection is built to validate the map model, and an example of a local map was generated with the lane-level geometry.


Introduction
Dig ital maps play an important role in current vehicle applications, e.g. vehicle localization and route planning. With more attention on intelligent transportation system, advanced driving assistance system and even driverless vehicle, the improvements in accuracy and richness are required in dig ital map technology [1]. When it is available to determine the vehicles' position precisely in lane level, there are a lot of p robable benefits we may obtain, i.e. the transportation officials and researchers may determine distinctions in traffic conditions for different lanes on a freeway via probe vehicles [2].
Most of existing digital maps are based on road level data, which may illustrate basic informat ion and provide useful applications for users but ignore some precise details that are essential for vehicles' high precision localization and path guidance. The improvements of accurate localization sensors such as RTK GPS and other on-board sensors such as IMU and LiDA R made the enhanced maps become possible. On the purpose of increasing utility of digital maps in advanced vehicle applications, creating the lane-level map is becoming a prevailing interest among researchers worldwide [3]. Co mpared with the traditional road level map, the lane level map is enhanced with massive data, wh ich are capable of improving the accuracy from about 10 meter to decimetre level or even centimetre level and illustrating more precise geo metry in line with the real situations.
The map model is supposed to be created for routing planning before geometrical representation because vehicle navigation is established on a network consisting of vertices (e.g., intersections) and edges (e.g., roads, lanes). Thus, the map model is supposed to be an abstract representation of the map database [4]. In terms of map model, there are a nu mber of map standards containing specific exp lanations on the map model which we can refer to. In tradit ional road level map, GDF, KiW i, Navteq are mainstream dig ital map standards which have been employed widespread for decades [5], however, these road-level model are not directly applicable to lane level. RNDF is the road network definit ion file designed for DA RPA urban challenge, in which the basic structure segment-lane-waypoint are included to provide basic informat ion to driverless vehicles [6]. Nowadays, OpenDRIVE and NDS are well-known map standard providers, but their comp licated map model and inaccessibility to public (NDS) cause difficult ies for practical uses. Besides the standards above, Qing Zhu et al. [7]  Another significant issue about lane-level maps is the geometrical representation of the lanes. Expanding fro m traditional maps, some lane illustrations in enhanced maps continue using the polyline [9]. Du Jie et al. [2] emp loy the piecewise polyline to appro ximate the centreline in a lane. Betaille et al. [3] in their lane-level enhanced map apply the clothoids for the description of the road lanes in a digital map. Circular arc spline is also applied in the map geometrical model [10]. Co mpared to

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there methods mentioned, Cubic Hermite Sp line CHS may possess some advantages, because it can generate various lines, such as, straight lines, arcs, and even clothoids [11], therefore the whole map would share one type of line to accurately generate the geometrical shapes of different lanes. And there have been several studies employing the CHS to describe the shape of lanes , however, the method mentioned in [4] applies CHS to the whole lanes and even virtual lanes in the intersections without distinguishing the control points with different functions.
This paper is organized as belo w. Firstly, in section 2, the mu lti-layer lane-level map model is proposed, which includes three layer and other significant details. Then a method of geo metrical representation is established by applying the CHS. Finally, the experimental validations are performed in section 4.

Multi-layer lane-level map model
In terms of convenience of geographical illustration and efficiency of further applications like route planning, we propose a mult i-layer lane-level map model, which contains three layers: road level layer, intermed iate layer, and lane level layer.
Road-level layer in this map model reserves most of traditional mathematical exp ressions for current existing map model, containing roads and intersections, which is intended for making use of ripe routing algorithms based on road level maps. The intermed iate layer acts as a bridge between the upper layer and the lo wer one, in which relationship between some sets is stored for routing planning and other applications. And the third layer is designed to express the lane-level details, not only the lane sets on a road and more detailed intersections, but also geometrical elements such as highprecision points on the centre line of a lane, lane lines and so on. An example is Figure 1

Road-level layer
According to intuition that a road network is supposed to include roads and intersections, thus, a road-level layer is expressed as follow, where, a W is the whole road-level network, a C is the set of road-level intersections, and a R is the set of roads. The road-level intersection is defined as, (2) where, c P is the set of road-level nodes entering this intersection, and c E is the set of road-level nodes leaving this intersection. a T , road-level traffic matrix, indicat ing if there is a topological connection between two nodes, defined as, where, the element , . (4) where, r P is the set of road-level nodes entering this road, and r E is the set of road-level nodes leaving this road. a Q includes the road class r k and road length r l .

Intermediate layer
In this layer, a logic connection between upper and lo wer layer is designed. On the purpose of providing higher precision data and conserving the advantages of traditional maps, the intermediate layer serves as a library of corresponding relationship from road level to lane level.
In an intersection c , c P is the set of its road-level incoming nodes. And without losing generality, let us assume this intersection has four road-level inco ming

Micro layer in lane level
Lane-level layer should not only possess more data with higher accuracy which could supplement the deficiency of road-level layer, but also provide informat ion of complete road network for navigation. To achieve this goal, the lane-level layer is defined as,

Node and control point
There are nodes in road-level and lane-level (Notice that nodes in intermed iate layer co me fro m the other two layers.), which on ly exist at the connection knots between intersections and roads(lanes) and are defined as, Particularly, in a co mmon scenario, the nodes at the start/end of a lane share the same positions and tangent direction with the first and the last control points.

Geometrical representation
The detailed geometry in road level is not necessary because the detailed info rmation and precise geometry is presented in lane level and it is easy to obtain the lanelevel geometrical information v ia intermediate layer fro m road level and on the other hand, the road level nodes are easy to locate, simple lines such as straight line could illustrate the connection and topology in road level completely. Thus, according to our mu lti-layer model, the lane-level geometry is discussed as below.

Lane-level geometry
In order to achieve the global conformity and continuity, as we ment ioned before, CHS curve is emp loyed in this part. CHS is a spline in wh ich each segments between two control points is a three order po lyline represented by Hermite form.
Assuming that two given control points are i s , +1  (12), then the CHS generated by these two points is presented as, 3 where,

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It is easy to get the i i Q n u , v , thus at each control point the first order continuity is realized, which may offer convenience for vehicle path planning due to global tangential continuity.

Control Points Choosing
The control points serve as the shape points in the lane level geomet ry, and simultaneously some of them are supposed to be feature points, of which on two sides there are some different attributes, at particular positions, e.g., the control points at the start/end of a lane. Though this kind of control points own the same form with the common control po ints, because these do not change with other variable control points, we call them the fixed control points.

Fixed Control Points
The fixed control points

Variable Control Points
The determination of shape control points occurs in two adjacent fixed control points in a lane. Assume that a series of sampled points representing the centreline of a lane are known, exp ressed as

Experimental Validation
Two experiments are conducted to validate our theoretical model and geomet rical repres entation respectively.
In order to demonstrate the validity of mu lti-layer map model, we co mb ine the aerial photography and ground calibration to establish a local map including a complete intersection wh ich is displayed as Figure 5. The left g raph is the road-level layer with the backg round of an aerial photo, in wh ich the points symbolized by star are road-level nodes. The right one is the lane-level map, and the details on lanes corresponding to the road they belonging to are shown. Besides, the traffic matrix and other informat ion are stored in TAB format wh ich can be  In the other experimental test, our test vehicle is equipped with RTK GPS and IMU system. The RTK GPS is BD982 fro m Trimb le, and IM U is produced in Oxts, the model is RT2502 which can measure the position and orientation accurately. In order to measure the centreline of lanes on a road, the vehicle in our test is required to drive along the centreline as close as possible. Then the vehicle state space is established for applying Kalman Filter to obtain the precise results of locations regarded as the true value of points on centrelines. The nodes and fixed control points are determined by static vehicle with equipment running. When all the fixed lanelevel control points are measured, the stepwise method of variable shape control points is executed to pick up the other control points for lane-level geo metrical representation.
As Figure 6 shows, the geometry representation can illustrate the shape of lanes and even intersections, increasing utility compared to the traditional geometry.

Conclusions and future researches
This paper proposes a mu lti-layer map model for route planning, in wh ich we integrate the traditional road-level map with enhanced lane-level map, we also design an intermediate layer to connect the other two layers. According to advantages of CHS curve in p resenting lane-level geometry, a stepwise approach to generating lanes is discussed and a geometrical system including fixed control points and shape control points is performed. A test to validate the feasibility of the map model and geometrical representation is conducted.
There are some ongoing researches based on this mu lti-layer map model. We have fin ished the route planning algorith m based on this layered map model [12], and due to lane-level layer in this model contains all detailed informat ion for routing, a route planning method directly employing lane-level map is also designed [13]. Then, there is a large-scale map we are building in a South-eastern province, China, wh ich is co mpletely based on this our layered model.