map line interface for autonomous driving · modern cars are equipped with a multitude of sensors...

9
WHITE PAPER www.visteon.com Map Line Interface for Autonomous Driving

Upload: duongque

Post on 07-Jul-2019

216 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Map Line Interface for Autonomous Driving · Modern cars are equipped with a multitude of sensors to perceive their environment. ... what an interface for lane geometry needs to look

WHITE PAPERwww.visteon.com

Map Line Interface for Autonomous Driving

Page 2: Map Line Interface for Autonomous Driving · Modern cars are equipped with a multitude of sensors to perceive their environment. ... what an interface for lane geometry needs to look

Map Line Interface for Autonomous Driving

Nikola Karamanov†, Desislav Andreev† Martin Pfeifle*, Hendrik Bock*, Mathias Otto*, Matthias Schulze*

Abstract— Delivering an accurate representation of the laneahead of an autonomously driving vehicle is one of thekey functionalities of a good ADAS perception system. Thisstatement holds especially for driving on a highway. Functionssuch as lane keeping assistance rely on a proper representationof the lanes from the perception subsystem. To achieve sucha proper representation, information from various sensorssuch as cameras, LiDARs, radars, HD maps are taken intoconsideration. Up to now HD map information has been mainlyused for longitudinal control, e.g. in cases when there arespeed limits or curves ahead. Using map information for lateralcontrol is more difficult, as the quality of the informationderived from the map heavily depends on the precision ofthe positional and heading information of the ego vehicle.Uncertainty in the ego vehicle position and pose directly resultsin uncertainty in the line information retrieved from the digitalmap. We examine the influence of an uncertain Gaussian egoposition and pose for the resulting map line information whichis not necessarily Gaussian. In order to transport the map lineinformation to other subsystems such as the lane fusion module,we need to approximate the map line distribution by a suitabledata structure which is both accurate and compact. We discussand evaluate suitable approximations of the resulting map linedistributions such as mean values of map lines only, mean valuescombined with standard deviation values and mean valuescombined with the full covariance matrices. We show that theusage of mean values and covariance matrices approximatethe true distributions rather accurately, and therefore are bothfrom an accuracy point of view and from a bandwidth pointof view the way to represent map lines in interfaces.

Index Terms— interfaces, uncertainty, lane fusion, lane de-tection, lanes in HD maps

I. INTRODUCTION

Modern cars are equipped with a multitude of sensorsto perceive their environment. Sensors such as cameras,LiDARs or radars can be used to detect objects around thecars and also to detect lanes. The detection and tracking ofroad boundaries is an important task for driver assistancesystems as many functions such as lane departure warning,lane keeping assistance, lane change warning systems, etc.depend on a correct representation of the lanes.

In order to achieve such a correct representation of lanesinformation from various sources is fused together, e.g.information from front facing perspective cameras, side-facing fisheye cameras, LiDARs, radars, digital maps incombination with an GNSS/IMU system, or even from thetrajectories of leading vehicles.

As many of these subsystems will be provided by differentvendors, it is crucial for a system integrator, e.g. the OEMitself or the Tier1, to define clear and meaningful interfaces

† {nkaraman, dandree2}@visteon.com, Visteon (Sofia)* {martin.pfeifle, hbock, motto, matthias.schulze}@visteon.com, Visteon

(Karlsruhe)

which allow the individual testing of submodules as well astheir easy substitution.

Fig. 1. Communication between a Positioning/Map ECU and ADAS ECU.IMU includes gyroscopes, odometers, accelometers and magnetometers. Thelocalization module is supplied with a corrected absolute position from themap matching module and estimated changes in motion from the ego motionmodules. Localization supplies the map matching module with absoluteposition and serves to calibrate the ego motion modules. Localization andmap matching use technologies such as Kalman filters. The data providerfor the ADAS ECU supplies the map line representation using the map lineinterface. The ADAS ECU builds an environmental model that suppliessensor data, including camera and radar output, to the landmark extractionand visual odometry modules.

Especially for map related topics the encapsulation ofinformation derived from the map is crucial as the mapsubmodule might vary from region to region due to the factthat there are different map providers for different regions.Some OEMs even plan to put the map and positioning relatedsubmodule to an own ECU which then communicates themap content to the ADAS ECU via clear interfaces on topof Ethernet (cf. orange arrow in Figure 1). We investigatewhat an interface for lane geometry needs to look like toenable the exchange of information between a positioningECU/submodule and an ADAS ECU/submodule.

Fig. 2. Representation of the right lane w.r.t. ego vehicle movement.

Many approaches in literature use for representation oflane boundaries or lane center lines a three dimensional

Page 3: Map Line Interface for Autonomous Driving · Modern cars are equipped with a multitude of sensors to perceive their environment. ... what an interface for lane geometry needs to look

clothoid road model [1] [2] [3], due to its high relevanceand flexibility in road analysis owing to it being the favorableand common engineering solution to road and railway design[16] [17]. A common local approximation to the clothoid isbased on the 3rd-order Taylor series. Figure 2 depicts thisrepresentation. Obviously, each lane boundary and the lanecenter line can be represented by such a four dimensionalvector in which the first two dimensions yoff and β describethe translation and rotation to move the car coordinate systemto the coordinate system described by the lane line andthe other two dimensions c0 and c1 describe the lane lineinherent curvature and its rate of change respectively. Thisrepresentation can be used by planning and execution tomove the car close to the centerline of the lane.

Fig. 3. Drive based on a precise map and precise positioning system.

Test vehicles are often equipped with a high precisionand very expensive IMU/GNSS system [9] which allowslocalization errors within a few centimeters. Based on sucha precise localization module and a similar accurate map, itis possible to derive the above described four parameters forthe centerline of the ego lane from the map without errorand use it directly for autonomous driving (cf. Figure 3).

Obviously in series cars it is not feasible to integratehigh cost GNSS/IMU systems. Sophisticated positioningalgorithms use interoceptive and exteroceptive ego-motioninformation as well as additional information coming fromvisual odometry or from the HD localization objects toachieve a fairly accurate position (cf. Figure 4).

Clearly, the better the positional information, the moreaccurate the lines are which are retrieved from the HDmap. The first question we tackle in this paper is how the4D distribution of the line representation for autonomousdriving looks like given an uncertain position and headingfor the ego vehicle and a piece-wise linear line or setof markers from the digital map. The line from the mapprovides us with a function which transforms the positionand heading distribution from 3D space to a 4D distributionin the line representation space used for autonomous driving,called drivable line space. The second question is how theresulting distribution of the lines for autonomous drivingcan be expressed by a data representation which is accurate,compact, and usable by subsequent modules.

A goal of this paper is to evaluate the following three datastructures that may represent the distribution for map linesresulting from positional uncertainty:• The four dimensional mean vector (yoff , β, c0, c1) only.• The vector along with its standard deviation values.• The vector along with the corresponding covariance

matrix.The remainder of this paper is organized as follows. In

Section II, we have a brief look at the related work in this

Fig. 4. Localization module for autonomous driving vehicles. IMU includesgyroscopes, odometers, accelometers and magnetometers. Via DriveCoreTM

Runtime (see [6]), the map matching module receives input from the V2X,digital map, detection and tracking modules. DriveCoreTM Runtime alsosupplies the ego motion estimation modules with IMU (for interoceptive)and tracking (for exteroceptive) module outputs. The GNSS localizationmodule is supplied with a corrected absolute position from the map matchingmodule and estimated changes in motion from the ego motion modules.GNSS localization supplies the map matching module with absolute positionand serves to calibrate the ego motion modules. GNSS localization and mapmatching use technologies such as Kalman filters.

area. In Section III, we will describe the computation ofthe resulting map lines out of uncertain information in amore formal way. In Section IV, we will present a detailedevaluation on the advantages and disadvantages of eachrepresentation. In Section V, we will summarize the resultand indicate some future activities.

II. RELATED WORK

As mentioned, many approaches in literature use for therepresentation of lane boundaries or lane center lines a threedimensional clothoid road model [1] [2] [3]. Regardless ifthis structure is created by fusing information from varioussensors or by using a Kalman filter to stabilize the informa-tion coming from one sensor, the information is in both casesnaturally accompanied by a covariance matrix expressing theuncertainty of this structure (cf. Figure 12:a).

The key question, we tackle in this paper is whetherthere exists a representation of the drivable line along withuncertainty information coming directly from the map. Toour knowledge there is nothing like this available neither inindustry nor in research.

In industry, there exists an initiative called ADASIS [10],ADAS Interface Specification, which transmits the map

Page 4: Map Line Interface for Autonomous Driving · Modern cars are equipped with a multitude of sensors to perceive their environment. ... what an interface for lane geometry needs to look

information in front of the vehicle via CAN (ADASIS v2)or via Ethernet (ADASIS v3). In both cases, representationsof the map line geometry are sent out via interfaces. Themap lines are sent out in WGS84 coordinates as stored inthe database. In addition, the position of the ego vehicleis sent out with some accuracy values. The problem howto get correct drivable line representations out of uncertainposition and map lines is not tackled. The reason is thatmap content is so far used mainly for longitudinal controland not for lateral control. The map line representation asintroduced in [1] [2] [3], on the other hand, is mainly used forlateral control. There are many activities dealing with maprelative positioning, e.g. [10]. An overview of localizationand mapping can be found in [11]. All of these approachesdo not examine the distribution of the drivable lines whichfollow out of an uncertain ego vehicle position and heading.As no paper is dealing with this question, there is also nopaper dealing with the question of how well a Gaussian canapproximate the distribution of the drivable lines.

III. COMPUTATION OF MAP LINES BASED ON UNCERTAINPOSITIONAL INFORMATION

In general there is uncertainty in the positional+heading(hereafter referred to as “ego”) information and possibleuncertainty in the map information. Here we deal with thecase where the map information is considered accurate orby reduction of the model we take the best estimate. Theproblem then becomes to compute the distribution of the lineparameters as a function of the ego distribution and the mapinformation. Let (ex, ey) represent the x and y coordinatesof the ego position and eh represent the heading (angle) interms of the map coordinate system.

We concentrate on the case where the information aboutthe ego distribution is given to us via the 3-dimensional meanµ and a 3x3 covariance matrix Σ. For computational andsampling purposes we may approximate the true distributionover (ex, ey, eh) using a Gaussian with mean µ and covari-ance Σ.1

A. The Curve Function

Let x be the distance along the x axis (forward direction)of the car coordinate system. Then we define the line as

l(x):= yoff + tan(β)x+c02x2 +

c16x3 (1)

Suppose we are given points from a map2 and we knowsomehow that they correspond to the same curve3 {(si, ti)}iin the map coordinate system. We convert these points totheir equivalent in the car coordinate system {(ui, vi)}i,where (ui, vi) = coordinate transform(ex, ey, eh, si, ti).Then we fit a polynomial to a subset of these points: v =

1This is the Gaussian that best matches the true distribution (if it is well-behaved) in terms of Kullback–Leibler distance. Proof by expanding thedefinition and differentiating.

2HD Map information comes in this form.3The procedure for choosing the points and grouping them is outside the

focus of this paper.

p0 +p1u+p2u2 +p3u

3 via a method such as least-squares4,i.e. (p0, p1, p2, p3) = arg min{pk}3k=0

∑i(vi −

∑k pku

ki )2.

Finally, we set yoff := p0 , β := tan−1(p1) , c0 := 2p2, c1 := 6p3. This gives us a way to convert map info intolines in the car coordinate system all based on the vector(ex, ey, eh).

To complete the analysis consider a possible alternativeposition and heading of the car (e′x, e

′y, e′h). Through the

described procedure, this would give rise to a different linefor the same map points: (y′off , β

′, c′0, c′1).

This polynomial refitting gives us the recipe for mappingego + map to line parameters. As mentioned previously weseek to use this mapping in order to understand the resultingdistribution over the lines.

1) Invariance of least-squares: We also considered poly-nomial fitting via total least squares (see [18]) whose ob-jective function is invariant to the coordinate system usedsince it relies on the orthogonal distances between thepolynomial and the data points. This method would be morecomputationally expensive and in general is not guaranteedto converge to an acceptable solution. We do not expect thatthe total least-squares solution be better for obtaining lineparameters from map points. Nor is it known a priori thatany coordinate system invariant fitting would produce a moreaccurate curve than least squares when we know the expectedheading.

However, when we are already given a line (such as oneobtained from least-squares fitting of map points) that linewill have an implicit coordinate system by definition. If wethen want to calculate its parameters relative to an alternativecoordinate system we simply take many points (4 can beenough) along this line and apply an invariant method suchas the total least-squares objective. This makes sure that thenewly fitted curve is not influenced by a coordinate-variantdistance measure. Luckily, regardless of this we can still usesimple least-squares fitting since we know that its solutionwill be achieved with all distances 0 (we can obtain a perfectfit) and thus will not be affected by the distance measure usedsince all distance measures must yield the same 0 distances.

B. Monte Carlo Curve Sampling

One way to understand the resulting distribution over theline parameters is to sample from it. This means samplinglines in the car coordinate system. To do this we first generaten samples from the ego distribution {(exi, eyi, ehi)

T }ni=1 ∼Gaussian(µ,Σ). For each of the coordinate system sampleswe refit the polynomial to obtain the needed line samples{zi = (yoff i, βi, c0i, c1i)

T }ni=1. The line samples then giveus the information needed to analyze the distribution overpossible lines.

4The LASSO method may be preferable, but this consideration is irrele-vant for this discussion.

Page 5: Map Line Interface for Autonomous Driving · Modern cars are equipped with a multitude of sensors to perceive their environment. ... what an interface for lane geometry needs to look

Emc=1

n

7∑i=1

zi ≈ E[(yoff , β, c0, c1)T ] (2)

Cmc=1

n

7∑i=1

(zi − Emc)(zi − Emc)T

≈ Cov[(yoff , β, c0, c1)T ] (3)

where E and Cov are the statistical expectation and co-variance operators respectively and Emc and Cmc are theirapproximators.

C. Sigma Points Method

The sigma-points method is a basic and quick way toget special “sample” points from an input distribution. Thepoints are mapped through a possibly non-linear function,as is the case with our polynomial refitting. The mappedpoints are then used to approximate the true distributionthat would result from applying the non-linear mapping. Aseparate set of weights is used to compute the estimatedmean and covariance matrix of the mapped distribution.The sigma points method tries to preserve the structure ofthe resulting distribution so that the variance and higher-order moments match the true distribution. There are afew alternative formulations which try to preserve differentproperties of the true distribution. We use the 7-point versionwith n = 3, κ ≥ 0, α ∈ (0, 1], β = 2 parameters usually usedin the unscented Kalman filter (UKF) described in [13], [14],[15]. The points defined in this version are as follows:

λ= α2(n+ k)− n (4)w0

m= λ/(n+ λ) (5)w0

c= w0m + (1− α2 + β) (6)

wim= wi

c = 1/(2n+ 2λ) ∀i > 0 (7)(x0, y0, h0)T = µ (8)

(xi, yi, hi)T = µ+

√(n+ λ)Σ

1/2i i = 1, 2, 3 (9)

(xi, yi, hi)T = µ−

√(n+ λ)Σ

1/2i−n i = 4, 5, 6 (10)

where Σ1/2i is the i’th column of the matrix square root of

Σ.For each of these sigma points {(xi, yi, hi)T }7i=1 we

apply our refitting procedure to obtain 7 line parameters{zi = (yoff i, βi, c0i, c1i)

T }7i=1. These line parameters arethen used in the following way to estimate the mean andcovariance of the true line distribution:

Esp=

7∑i=1

wimzi ≈ E[(yoff , β, c0, c1)T ] (11)

Csp=

7∑i=1

wic(zi − Esp)(zi − Esp)T

≈ Cov[(yoff , β, c0, c1)T ] (12)

where E and Cov are the statistical expectation and co-variance operators respectively and Esp and Csp are theirapproximators.

IV. EXPERIMENTAL EVALUATION

In this section, we will present various examples depictingthe true distribution of the map lines for a Gaussian egomotion position and a given map line. We will show anddiscuss in detail the limitations of using an approximationto this true distribution while analyzing what information isbest to convey over our interface.

We will explore two scenarios: one that is similar to ahighway situation and one akin to a street turn situation.Before discussing the results we will explain the commonstructure of the experimental figures included here.

A. Figure Explanation

Figures 5, 7, 8, 9, 10, 11 all share the same structure. Theyare comprised of 4 subplots. Each of the subplots depicts theline fitted based on the mean position and heading dotted inblack. In each, the positional distribution is shown in thecenter of the subplot using an ellipse which contains 99% ofthe probability mass. The heading distribution is shown inthe center with a white arrow indicating the mean heading(in all cases direct forward) and black arrows between whichlies 99% of the probability mass for the heading. A closerview of this is given in figure 6.

a) The top-left subplot: shows the Monte Carlo sam-ples. The sample can be seen both as red arrows whoseposition and orientation signify (ex, ey, eh) and as whitedotted lines which indicate its corresponding (refitted) line(yoff , β, c0, c1).

b) The middle-left subplot: shows the sigma points. Thepoints can be seen both as red arrows whose position and ori-entation signify (ex, ey, eh) and as white dotted lines whichindicate its corresponding (refitted) line (yoff , β, c0, c1).

c) The top-right subplot: shows line samples arisingfrom the Gaussian distribution computed from Monte Carloas blue dotted lines (see section III-B). The mean of theGaussian distribution is shown as a white dotted line (closeto the black one). The samples should be compared to thetop-left subplot to evaluate the Gaussian approximation.

d) The middle-right subplot: shows line samples aris-ing from the Gaussian distribution computed from sigmapoints as red dotted lines (see section III-C). The mean of theGaussian distribution is shown as a white dotted line (closeto the black one). The samples should be compared to thetop-left subplot to evaluate the Gaussian approximation.

e) The bottom-left subplot: shows the correlation ma-trix for the 4-dimensional Gaussian over (yoff , β, c0, c1)obtained via the sigma points method. The values are shownboth in text and also signified by the size and color ofthe square (red for positive and blue for negative). Thisis included so we can gauge how the different parametersinteract with each other and whether they are correlatedenough to warrant including covariance information in theinterface.

Page 6: Map Line Interface for Autonomous Driving · Modern cars are equipped with a multitude of sensors to perceive their environment. ... what an interface for lane geometry needs to look

f) The bottom-right subplot: shows the individual (di-agonals) and pairwise (off-diagonals) marginal distributionsof the 4-dimensional Gaussian over lines. From top to bottomand left to right the grid is split as in the correlationmatrix: yoff , then β, then c0, then c1. So, for example,the square of the second row and third column depicts themarginal distribution of β with c0. The true distribution isrepresented by its samples (white dots). The Monte Carlo andsigma points output Gaussians are represented by ellipseswhose center is the mean and whose area contains 99%of the probability mass of the distribution. These subplotshelp to determine how well the distributions match the truedistribution in line parameter space. The diagonal entries aresimply each parameter plotted against itself which may helpassess if the individual marginals appear Gaussian.

Fig. 5. Results for a “highway line” with simple distribution over the egoinformation (see figure 6 for a closer view of the ego distribution). Referto section IV-A for more details.

B. Analysis

Here we analyze the results in our experimental figures(5-11).

We assessed the true distribution over lines by simplylooking at the empirical distribution arising from applying

Fig. 6. Closer view of the center of figures 5 (top row) and 7 (bottomrow). left: The sigma points (indicated by red arrows) obtained from theGaussian distribution over position (black ellipse) and heading (black/whitearrows). The white arrow shows the mean heading and the mean position isthe center of the ellipse. The black arrows show an interval for the headingbased on 3 standard deviations (in this case 3x5 degrees). right: Monte Carlosamples obtained from the same distribution. Refer to section IV-A for moredetails.

curve refitting to the Monte Carlo samples (white in the top-left subplots and bottom-right subplots of figures 5, 7, 8,10, 11). We assess the 4-dimensional Gaussian distributionsover lines which are obtained from Monte Carlo and sigmapoints individually by looking at their samples on the map(top-right and middle-right subplots) as well as their marginaldistributions (bottom-right subplots). Our visual comparisonwill involve these true distribution samples vs. the resultingGaussian distribution samples.

1) The Gaussian approximation: Our first observationis on our highway scenario; that if the uncertainty in theheading is reasonable then the Gaussian distributions arisingfrom both methods seem to fit the true distribution fairlywell. In figures 5, 7 the output Gaussian samples (redand blue) encompass the samples from the true distribution(white). This means we do not expect many false-negativeswhen using the information provided over the interface ratherthan the true distribution. Figure 7 shows that changes inthe positional distribution do not affect the accuracy of theinterface.

In figure 10, however, we see that there exists a classof lines for which all correlations are large (positive ornegative). This is our street turn scenario. The marginals arealready looking non-Gaussian even for smaller uncertainty inthe heading. We also see some indication that false-positivesarise, especially for the sigma points method.

2) Significance of the heading distribution: Figures 5, 7,10 depict a scenario where the standard deviation of the

Page 7: Map Line Interface for Autonomous Driving · Modern cars are equipped with a multitude of sensors to perceive their environment. ... what an interface for lane geometry needs to look

Fig. 7. Results for “highway line” with correlation in positional uncertainty(see figure 6 for a closer view of the ego distribution). Refer to section IV-Afor more details.

heading is 5 degrees. 5

However, as we see in figure 8 and 11, changes in theheading distribution do affect the accuracy of the interface.6

In the bottom-left subplots of figures 8 and 11 notice thatincreasing the heading uncertainty leads to increases in thecorrelations between parameters.

The same figures show that increasing the heading uncer-tainty may create enough false-positives to require additionalinformation for decision making. Some of the marginaldistributions, especially between the curvature and its rateof change have become dramatically non-Gaussian; we areassigning more and more probability mass to parameterconfiguration that do not occur (hence the false-positives).

In figure 11 the results are similar to that of figure8, however the use of the Gaussian approximation ratherthan the true distribution is clearly detrimental for decision

5This is already a larger value than commonly encountered in our practicalexperience and we chose this larger value to be able to evaluate and confirmour methods to even this range.

6The level depicted in those figures may not ever be experienced inpractical situations, but it gives us a good idea what levels are tolerablefor the interface.

Fig. 8. Results for “highway line” with increased uncertainty in the heading(double the standard deviation to 10 degrees). Refer to section IV-A for moredetails.

making in our street turn scenario because too many false-positives will occur.

3) Significance of the covariances: Notice that in figures5, 7, 8, 10, 11 the correlation matrix shows high correlationbetween most of the parameters indicating that the covariancematrix contains important information.

Passing only the variances forces the user to effectively usea spherical Gaussian to model all marginals. In the bottom-right subplot of figure 9 we notice that a few of the marginalsare very poorly represented. Figure 9 also shows that becauseof this the reduction causes too many false-negatives, i.e. wewill fail to detect the true line location in many instances.

4) Trade-off between Monte Carlo and sigma points:Our two ways of deriving the Gaussian approximation ofthe line parameter distribution seem to yield similar resultsin all cases (figures 5, 7, 8, 10, 11). The sigma pointsmethod suffers more false-positives. Considering that theMonte Carlo is more computationally expensive we mayprefer to use sigma points results whenever the increase infalse-positives is acceptable.

Page 8: Map Line Interface for Autonomous Driving · Modern cars are equipped with a multitude of sensors to perceive their environment. ... what an interface for lane geometry needs to look

Fig. 9. Results for “highway line” when passing only variance values andno covariance values over the interface. Refer to section IV-A for moredetails.

V. CONCLUSION

In this paper, we investigated the impact of uncertainposition and heading information for retrieving drivable lineinformation from a digital map. Basically, the geometry fromthe map provides us a non-linear function (curve refitting)which transforms a 3D Gaussian into a 4D distribution inthe drivable line space. We supplied a way to visualize andstore this complex distribution via sampled curves whichwere passed through the non-linear function. We providedless expensive parametric ways of storing information byapproximating it with a Gaussian distribution. We showedthat there is a large enough class of lines and scenarios(in particular for highways) where this approximation issufficient and even desirable for decision making. Two waysof arriving at this distribution were given, one via MonteCarlo sampling and one via the sigma points method.

With regard to our main question of what to pass overthe interface we have also found some important insights.Passing only the mean of the distribution may be sufficientfor some applications, but in general we are looking toinform about the uncertainty of the distribution as well.The experimental results show that there is significant and

Fig. 10. Results for a “street turn” with simple distribution over the egoinformation. Refer to section IV-A for more details.

valuable information available in the covariance matrix dueto the geometry involved in alternative line recalculation. Anapproach where we pass only the mean and the variances(and not the covariances) would be equivalent to assuming adistribution that has 0 covariance between the parameters. Wehave shown that this can lead to too many false-negatives (seefigure 9). Passing the mean of the distribution (4 values) andthis covariance matrix (4+6 unique values) over the interfacerequires passing 14 values in total, rather than 4 if onlypassing the mean. This will not detrimentally burden theinterface with respect to bandwidth. Therefore we stronglyrecommend to use the mean vector and the correspondingcovariance matrix for representing drivable lines. As men-tioned in section IV-B.4 it may be computationally desirablefor common applications to obtain this representation via thesigma points method.

In addition, the chosen description containing the covari-ance matrix along with the four dimensional mean value(yoff , β, c0, c1) can naturally be processed by the fusionmodule. The mean value can be regarded as measurementupdate whereas the corresponding covariance matrix canbe handled as a kind of dynamic measurement noise. This

Page 9: Map Line Interface for Autonomous Driving · Modern cars are equipped with a multitude of sensors to perceive their environment. ... what an interface for lane geometry needs to look

Fig. 11. Results for “street turn” with increased uncertainty in the heading(double the standard deviation to 10 degrees). Refer to section IV-A formore details.

dynamic measurement noise, often denoted by R in theKalman filter domain, changes for every measurement.

Thus the chosen representation for the interface betweenmap line detection and lane fusion naturally fits to the stan-dard Kalman filter based fusion algorithms (cf. Figure 12:a).As the chosen representation for map lines is identical to theoutput representation of the lane fusion module, the planningmodule could choose either the map representation or theresult of lane fusion (which in principle may use the sameinterface) for their lane keeping activities without changingtheir input interface (cf. Figure 12:b). Finally, the drivableline representation could be used for sanity checks comparingthe fusion result to the map representation of the lines. Sucha setup is especially helpful for ASIL decomposition. Asdistance measure the Earth Mover Distance [8] could beused (cf. Figure 12:c). In our future work, we will showthe benefit of fusing map line representations together withline representations coming from camera, LiDAR or leadingvehicles.

Fig. 12. Architectural examples of how to use the proposed drivableline representation from maps. a) input to lane fusion b) driving directlyaccording to them c) use them for sanity checks in an ASIL decompositionsetup.

REFERENCES

[1] S. Strygulec, D. Mueller, M. Meuter, C. Nunn, S. Ghosh, C. Woehler,“Road Boundary Detection and Tracking Using Monochrome CameraImages”, Delphi Electronics & Safety; TU Dortmund, Image AnalysisGroup

[2] E.D. Dickmanns and B.D. Mysliwetz. “Recursive 3-d road and relativeego-state recognition”. Pattern Analysis and Machine Intelligence, IEEETransactions on Pattern Analysis and Machine Intelligence, 14(2):199- 213, Feb 1992.

[3] A. Eidehall and F. Gustafsson. “Combined road prediction and targettracking in collision avoidance”. In Intelligent Vehicles Symposium,2004 IEEE, pages 619 - 624, June 2004.

[4] Google Inc., “Protocol Buffers”. https://developers.google.com/protocol-buffers/

[5] itemis AG, “Franca User Guide”. Release 0.12.0.1, 2018 https://github.com/franca/

[6] Visteon Corporation, “DriveCoreTM”. https://www.visteon.com/media/newsroom/2018/180109_story1.html

[7] Morgan Quigley, Ken Conley, Brian P. Gerkey, Josh Faust, Tully Foote,Jeremy Leibs, Rob Wheeler and Andrew Y. Ng, ”ROS: an open-sourceRobot Operating System”, ICRA Workshop on Open Source Software,2009.

[8] Elizaveta Levina; Peter Bickel (2001). ”The EarthMover’s Distance isthe Mallows Distance: Some Insights from Statistics”. Proceedings ofICCV 2001. Vancouver, Canada: 251256.

[9] Oxford Technical Solutions Ltd., “RT4000”. http://www.oxts.com/products/rt4000/

[10] Christian Ress, Dirk Balzer, Alexander Bracht, Sinisa Durekovic,Jan Lwenau. “ADASIS PROTOCOL FOR ADVANCED IN-VEHICLEAPPLICATIONS”. 2008

[11] R. Matthaei, G. Bagschik, M. Maurer. “Map-relative localizationin lane-level maps for ADAS and autonomous driving”. IntelligentVehicles Symposium 2014, pages 49-55

[12] S. Kamiljo, Y. Gu, L.Hsu. “Autonomous Vehicle Technologies: Local-ization and Mapping”. October 2015 DOI10.1587/essfr.9.2 131

[13] E. A. Wan and R. Van Der Merwe, ”The unscented Kalman filter fornonlinear estimation,” Proceedings of the IEEE 2000 Adaptive Systemsfor Signal Processing, Communications, and Control Symposium, 2000,pp. 153-158.

[14] S. J. Julier and J. K. Uhlmann. “Unscented filtering and nonlinearestimation”. Proceedings of the IEEE, 2004, pages 401-422

[15] Eric A. Wan and Rudolph van der Merwe. “The Unscented KalmanFilter”. Kalman Filtering and Neural Networks, Wiley-Blackwell, 2002,chapter 7, pages 221 - 280.

[16] M. E. Vazquez-Mendez and G. Casal, The clothoid computa-tion: A simple and efficient numerical algorithm, Journal of Sur-veying Engineering, vol. 142, no. 3, p. 04 016 005, 2016. doi:10.1061/(ASCE)SU.1943-5428.0000177.

[17] E. Bertolazzi and M. Frego, Fast and accurate clothoid fitting, 2012.doi: 10.1002/mma.3114. eprint: arXiv:1209.0910.

[18] T. G. Davis, “Total least-squares spiral curve fitting,” Journal ofSurveying Engineering, vol. 125, no. 4, pp. 159176, 1999. doi:10.1061/(ASCE)0733- 9453(1999)125:4(159).