Energy Optimal Real-Time Navigation System: Application to a HybridElectrical Vehicle

T. Jurik, A. Cela, R. Hamouche, A. Reama, R. Natowicz, S.I Niculescu, Ch. Villedieu, D. Pachetau

Abstract— Real time traffic information systems likeSYTADIN[11] help in route to destination planning and trafficstate prediction. Energy-optimal routing for electric vehiclescreates novel algorithmic challenges where the computationcomplexity is the main issue. This complexity is induced bythe possible negative values of edge energy as well as thevariability of route and vehicle variables which render thestandard algorithms unsuitable (inapplicable). In this paperwe present an Energy Optimal Real Time Navigation System(EORTNS), implemented on Samsung Galaxy Tab, capable ofcalculating the route to destination based on a informationflow obtained from SYTADIN. As an application example wepropose a real time energy management for a Hybrid ElectricalVehicle (HEV) composed of batteries and Super-Capacitors(SC). The EORTNS is not only capable of energy optimal routeto destination calculation with respect to traffic state but alsooperates the On-Board power splitting between batteries andSuper-Capacitors. Based on calculated 3D energy optimal routeto destination and average speeds for each road segment as wellas the vehicle model the state of charge (SOC) of batteries andSuper-Capacitors for each receding horizon are predicted andmodified in real time.

I. INTRODUCTION

The convergence of communication and sensing on mul-timedia platforms such as smart devices (Smart-phones,iPad, . . . ) provides the engineering community with un-precedented monitoring capabilities. They include a videocamera, numerous sensors (accelerometers, light sensors,GPS, microphone), wireless communication outlets (GSM,GPRS, WiFi, Bluetooth, infrared), computational power andmemory. Due to their portability, computation, and com-munication capabilities, smart devices are transforming ourcars into moving sensors capable of communicating theirposition and operating real time decision. The concomitantadvent of mobile Internet and smart devices calls for a newgeneration of ITS based on collaborative information anddecision making [2][12]. It makes it possible to address andresolve in real time the optimal vehicle navigation problemwhere travel-time costs and traffic network state vary withtime.The HEV and in general the electrical vehicles have the ca-pability to regenerate the braking/deceleration energy whichincrease their range. Moreover, HEV increase substantially

T. Jurik, A. Cela, R. Hamouche, A. Reama, R. Natowicz are with UPE,ESIEE Paris: t.jurik@esiee.fr, a.cela@esiee.fr,r.hamouche@esiee.fr, a.reama@esiee.fr,r.natowicz@esiee.fr.

S.I Niculescu is with Laboratoire des Signaux et Systemes,CNRS/Supelec: silviu.niculescu@lss.supelec.fr.

Ch. Villedieu and D. Pachetau are with AKKA Tech-nologies: Christophe.VILLEDIEU@akka.eu,D.PACHETEAU@akka.eu.

the efficiency of on-board energy sources [14] by optimallysplitting the demanded power between them. The optimalpower splitting can be operated in real time based oncalculated origin to destination (O-D) 3D routes which maybe time optimal, distance optimal or energy optimal ones.Whereas the time and distance metric give positive routesegment costs the energy optimal metric can give negativeones. If for time optimal and distance optimal route calcu-lation the routing algorithms like Dijkstra and its variants,with time complexity O(n2), give generally good results forreal time application [7], [4], [14] it is not the case forenergy optimal metric. The reasons are different. First, asaforementioned, the energy cost of route segment can benegative due to the the 3D route profile (downhill moving)and brake regeneration. This fact discard Dijkstra algorithmand its variants. Secondly, because of traffic state and vehicleparameter variation, the energy cost calculation may beoperated only in run-time and exclude the preprocessingtechniques as Johnson [7] like algorithms based on globalgraph analysis in order to eliminate the negative energy costs.Thirdly, the recuperation of the kinetic and potential energy,even for HEV, depends on the route choice as well as on thecharacteristics of the power sources such as their capacitiesand power efficiency and limits [10], [8], [9]. This impliesthe fact that the route energy cost is not necessarily equal tothe sum of all segments costs composing this path.The aim of this paper is to propose an energy optimalreal time navigation system (EORTNS) based on the realtime traffic information system implemented on a SmartDevice under Android OS and organized in two level. In thefirst level the energy optimal route is calculated based onreal-time traffic information and HEV characteristics. In thesecond level, the energy optimal route is used by the RealTime Energy Management Algorithm (RT EMA)[14] whichcalculate the power splitting ratio for the HEV composed ofbatteries and Super-Capacitors (SC). The traffic area consid-ered for tests and simulation is Paris region which representsa directed graph with 207275 vertices and 467423 edges.Due to the graph dimension, Hardware/Software constraintsas well as real-time traffic state update we propose a Dijkstralike algorithm based on potential function method [7], [10],[8],[9].As aforementioned, we use the real time traffic informationsources SYTADIN[11] as an input to EORTNS but the routeoptimization metric used in this study is different withrespect to that used in [14]. Based on [10], [8], [9] wepropose a route segment cost rescaling which preserve routeoptimality. A Dijkstra like algorithm is proposed which meet

Proceedings of the 16th International IEEE Annual Conference onIntelligent Transportation Systems (ITSC 2013), The Hague, TheNetherlands, October 6-9, 2013

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the EORTNS real time specification [14].This paper is organized as follows. Problem formulation ofenergy optimal real time navigation problem as well as themethod of segment cost rescaling based on Johnson methodrevisited in the context of electrical vehicle is given in sectiontwo. In section three we give the general software archi-tecture of EORTNS. In section four an application exampleas well EORTNS algorithm tests and implementation arepresented. Experimental results obtained from the applicationof EORTNS and their analysis are also given. Section five isconsecrated to conclusions and future works.

II. PROBLEM FORMULATION

In this section the energy optimal real time O-D routes cal-culation will be given. The road network graph is composedof vertices representing road junctions or intersection pointsand edges representing the road segment connecting them.The edges cost represents the real time energy necessary totransport the HEV along the road segment calculated at thequery time. So the road network may be given by a directedgraph G = (V,E) where V represent the set of graph vertexor the intersection points of cardinality n and E representsthe set of graph edges of cardinality m. We assume also thatfor each vertex the elevation function z(vi) : V =⇒ R+

0 isgiven. We also suppose that we know the road segment lengthl(vi,v j) : (V ×V ) =⇒ R+ and the real time road segmentspeed s(vi,v j) : (V×V )=⇒R+

0 . The road segments velocitiesare given by SYTADIN and are time varying with respect tothe traffic state.The optimal route or path P from origin point O to des-tination point D is given by an ordered sequence of ver-tices (v0,v1,v2, . . . ,vk,vN), where v0 and vN correspond toorigin point O and destination point D respectively. Eachsub-sequence of two consecutive elements of this orderedsequence is a road segment or an edge of the directed graphG. Note by Pk the sub-path from origin to the point or vertexvk. Note also by P the set of feasible routes from origin todestination point. It is clear that a given route to destinationis feasible if all its sub-paths are feasible.The graph edges cost represents the energy needed to movethe vehicle from the initial road segment point to its finalone. This energy depends on the vehicle characteristics,velocity, chosen route and its 3D profile. This mean that theirvalue have to be calculated only on line and preprocessingtechnics can not be applied. For the clarity of presentationwe will give in the sequel quite briefly the main componentscomposing the vehicle power and energy demand. Theircharacteristics will help us to reduce the optimal energy routecalculation algorithm complexity which is mainly related tothe negative values of some edges costs or road segmentenergy due to vehicle downhill movement.

A. Longitudinal model

The vehicular model of longitudinal dynamics is con-structed based on the theory of vehicle multi-body dynamics[3].

1) Wind resistance: The wind resistance is caused gen-erally by two facts: the viscous friction of the surroundingair on the vehicle surface and the losses by the pressuredifference between the front and the rear of the vehicle,generated by a separation of the air flow. The resistance forceis given by:

Fw(v) =12·ρ ·A f ·Cd · v2 (1)

where v is the vehicle speed, ρ is the density of the ambientair, A f is the frontal area and Cd is the Reynolds coefficient.

2) Tire rolling resistance: The tire rolling resistance canbe expressed as

Fr(v, p, ...) = µr(v, p, ...) ·M ·g · cos(θ), v > 0 (2)

where M is the vehicle mass, g the acceleration due togravity, term θ is road slope and µr is the rolling frictioncoefficient.

3) Gravitational force: The uphill and downhill move-ment of a vehicle is partially influenced by gravitational forceas given by relation (3. Depending on the value of road slope,θ , it can accelerate or decelerate the vehicle movement.

Fc(θ) = M ·g · sin(θ) (3)

4) Acceleration resistance: The acceleration resistancedue to the inertia of the vehicle and of all rotating partsinside the vehicle causes frictions (d’Alembert) forces. Therotating parts are here represented by

Fa(v) = M(1+δeqm) ·dvdt

(4)

where δeqm is the vehicle equivalent moment inertia repre-senting the rotating parts such as wheels and power-traininertia.According to an analysis of the summation of performingforces acting on the vehicle body in the longitudinal direc-tion, the power balance for the controlled vehicle is governedby:

PD(t) = fPD(v, v,M,θ) = (Fw +Fr +Fc +Fav) (5)

=ρ

2·A f ·Cdv3 +M ·g · v · (µr · cosθ + sinθ)+

+M · (1+δeqm) · vv

5) Position-based power calculation: As an important pa-rameter in equation (5), the road slope may change frequentlyat the actual road environment, especially in the mountainterrain, and has a major impact on the energy consumption.Road slope and vehicle speed are relevant with respect tooptimal routing problem if they are dependent on positionrather than time. Therefore, the time-based equation (5) isnot suitable for optimal route to destination calculation anda power expression depended on position, s, is preferable.Using the transformation:

v =dsdt

dvds

=dtds· dv

dt=

1v· dv

dt,v 6= 0

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the equation (5) can be transferred into a position-based form

PD(s) =ρ

2A fCd · v3 +M ·g ·µr · v · cosθ +M ·g · v · sinθ +

+M · (1+δeqm) · v2 · dvds

(6)

From the equation (6) and under the assumption that thevelocity and the slope is constant on each road segment(1)we may give the energy needed to move the vehicle fromthe beginning to the end of the road segment (vi,vi+1) as:

ED(i) =ρ

2 ·A f ·Cd · v2i · li +M ·g ·µr · li · cosθi +M ·g · li · sinθi

(7)In the equation (7) the only term which may have negative

value is the third one which corresponds to potential energy.If its absolute value is also superior to the sum of two otherterms then the edge energy cost is negative. Lest us note byER the energy corresponding to wind and rolling resistanceand by EP the potential energy. So we can define them by:

ER(i) =ρ

2 ·A f ·Cd · v2i · li +M ·g ·µr · li · cosθi

EP(i) = M ·g · li · sinθi(8)

The energy optimization criteria for the energy optimalroute planning may be given by the following expression:

J(r j) =i=N

∑i=0

ER(i)+EP(i) (9)

where r j = (v j0,v

j1,v

j2, . . . ,v

jN) is the jth possible route

( j ∈ N+) from origin O, to destination D.

B. Road segment energy cost modification

The optimal route to destination is necessarily a feasibleone and it optimize the criteria (9). It means that batteryand Super-Capacitors have sufficient energy to movethe vehicle through each road segment and in the sametime sufficient available capacity to stock the downhillrecuperation energy. It is clear that each sub-path of theoptimal one has to be feasible and its concatenation witheach road segments originating from its last vertex remainfeasible. The question we may ask is how to decide, inrun time, which sub-sequence is feasible and which isnot one and which modification in the energy model ofroad segment edges we have to operate. Intuitively, if theremaining energy is not sufficient to move the vehicle to thenext vertex of the road segment its cost has to be infinity.Naturally, we have also to transform all the road segmentscost in order to obtain only positive values. These necessaryroad segments energy cost model modifications have tobe consistent with the optimal energy problem and reducesubstantively its complexity.

1The flow speed given by SYTADIN is constant. In order to betterapproximate the road slope we generate intermediary discretization pointbetween two road segment vertices

From (7) and (8), the road segment energy cost may begiven by:

ED(i) = ER(i)+EP(i) (10)

In case of a perfect recuperation of potential energy (down-hill movement) we can completely ignore this energy com-ponent in expression (10). The vehicle transfer potentialenergy does not depends on the calculated routes but on theorigin and destination points altitudes. This fact permits us toeliminate the possibles negatives values of the road segmentcost induced by downhill movement. If there is no perfectrecuperation of descending energy or the corresponding co-efficient we have to modify the energy cost of the given roadsegment as given in (11). This transformation is consistentwith energy optimal routing problem [8], [10], [9].

EmD (i) =

{ER(i)+(α−1) ·EP(i) if EP(i)≤ 0ER(i) if EP(i)> 0 (11)

where α is the downhill energy recuperation coefficient(0 < α < 1).

C. Minimum energy routes problem formulation

Let us defined the sub-sequence r ji = (v j

0,vj1,v

j2, . . . ,v

ji−1)

of order i of the route to destination sequence r j =(v j

0,vj1,v

j2, . . . ,v

jN). The optimal cost of the sub-sequence

r ji+1 = (v j

0,vj1,v

j2, . . . ,v

ji−1,v

ji ) is given by:

J(r ji+1) =

k=i

∑k=0

EmD (k) (12)

If we note by Cinit the initial state of charge of battery(SOCb), minimizing J(r j

i+1) is the same as maximizing(Cinit − J(r j

i+1)). Let us note by:

∆i =C(r j

i )+EmD (vi−1,vi) (13)

where C(r ji ) is given by (see [10]):

C(r ji ) =

0 if i = 1∆i if i > 0, 0≤ ∆i ≤Cinit∞ if i > 0, ∆i >Cinit

(14)

If the second situation of (14) doesn’t induce anymodification of the road segment energy cost Em

D (i) givenin (11), the third one raise its value to infinity becausethere is no more energy to move the vehicle to vi+1. If thiscondition is never verified then ∆i, C(r j

i ) and J(r ji ) have

identical energy value.

So we can give the formulation of the Energy opti-mal routing problem as[10]: Given an energy graph G =(V,E,ED) and origin and destination points O,D ∈ V , theinitial state of charge of battery Cinit and the maximumcapacity Cmax ∈ R+,Cinit ≤Cmax, the energy optimal routingproblem is to find a path P j in G from O to D with minimalcost C(r j

N−1) given by (14) under the road segment energycost given by (11).

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III. SOFTWARE ARCHITECTURE SOLUTION

Figure 1 and figure 2 show the main component andapplication structure of the EORTNS software architecture.The core of the system is composed of three main modules:Navigation module, Energy Optimization module, GraphicUser Interface module and Real Time Energy ManagementAlgorithm (RT EMA)[14] module. The Graphic User Inter-face module handles the interaction with user, draws thefound route on the map and displays calculation progress andresults of the optimization. The Navigation module operateswith the map database from which the traffic area directedgraph is retrieved. The static nodes and route segment infor-mation are enhanced with the traffic real time informationlike velocities and time duration for each road segment.Moreover, information such as speed and 3D elevationprofile are calculated for each discretization points of eachcalculated route to destination segments. This informationis necessary to obtain the route to destination power profilein order to operate real time power splitting ratio betweenbattery and SC from the RT EMA module as given in figure 2.

Fig. 1. Architecture of the Energy Optimal Real Time Navigation System.

A. 3D Maps and routing data-base

The geographic data is exported from the OpenStreetMap(OSM) [12] server, which provides free data distributed underthe Creative Commons CC BY-SA 2.0 license.

1) Routing map export: The OSM map is exported into abinary file with a simple structure which consist of severaltables with records. Each record has fixed byte length sowe can easily seek in the file with only knowing the id tofind the right record. During the export, we store only therelevant information for road routing and the rest is ignoredand we store the map in a format that is suitable to describea directed graph. Three tables are created: nodes, edges andgeometry. Table with nodes contains only the junctions nodesor nodes where some characteristic of the road change (e.g.road class, speed,. . . ) and new edge should follow. In theedge table we store the information that is needed to calculatethe cost to travel this path. Finally, in the geometry table westore intermediary nodes that describe the shape of the road.

Fig. 2. Energy Optimal Real Time Navigation System application flow-chart.

They are not necessary for the routing but are used for theenergy optimization algorithm and for drawing of the roadin the GUI.

The resulting routing database for the Ile-de-France regionhas 36 MB.

2) Exported 3D map: In order to add the third dimen-sion to the exported OSM map we have two possibilities:retrieve the altitudes of a calculated route with an on-lineelevations service request or with a device stored elevationsfile. The first was the initial solution to obtain the altitudeprofile necessary for the power profile used by RT EMAmodule. The second is a more complicated solution sinceit consists of retrieving NASA’s Shuttle Radar TopographyMission (SRTM) generated files, treating them and generatinga permanent data base for the application. The advantagesof the second option are Internet independence and fasterelevations retrieval for given coordinates. A single requestcontains a list of all geo-coordinate elements. For SRTM,the binary files provided by NASA are divided by tiles ofone degree per one degree of latitude and longitude.In our implementation we currently use one five to fivedegree tile that is created by combining the individual onedegree SRTM files. Most of the time we want to know anelevation for a coordinates that are not exactly positioned atone of the known nodes of the elevation grid so to calculatesuch elevation we use a bi-cubic interpolation.

B. Real time traffic information

As a real-time traffic information source, we use SYTADINweb service which provides traffic information for the Parisand Ile-de-France region. First, we have attributed theSYTADIN’s traffic IDs to our OSM nodes in the map databaseby parsing SYTADIN’s MapInfo traffic net geometry file. TheSYTADIN web service provides an updated XML file withtraffic information of each road segment identified by it’sID every few minutes (3 to 5 minutes). This way, we can

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obtain instant segment speed or traffic state (fluid, traffic-jam,closed) for every node in our database.

C. Optimal route planning

As stated above obtaining of the estimated speed profileand the altitude profile along the path are necessary tocalculate the power profile. This process, given in figure 2,consists of several steps that necessarily follow each other.This sequence is described below.• Select origin and destination node in the routing

database.• Select a desired metric.• Find a path that is optimal for the chosen metric by

the routing algorithm. This path is described only byintersection nodes.

• Find a speed profile along this path. This profile is basedonly on the intersection nodes.

• Inject the intermediate nodes into the profile. At this stepwe also have to inject a duplicate speed samples to thespeed profile correctly. The path is now described withthe intersection and intermediate nodes. The distancebetween each two consecutive nodes is variable.

• Re-sample the path and the speed profile in such waythat the distance between each two consecutive coordi-nates is identical to the discretization step. We obtaina new ordered list of coordinates and a list of speedsamples between these nodes.

• For each of the new re-sampled coordinates look up anelevation value and insert it into the elevation profile.

• Pass the speed and elevation profile to the energyoptimization algorithm.

IV. APPLICATION EXAMPLE

A demonstration application was developed including allthe aforementioned modules. For the computation device weuse the Samsung Galaxy Tab 10.1 tablet, which embedsNVIDIA Tegra 2 dual-core 1GHz processor, 1GB RAM, 16GB of internal storage and also offers a 10.1 inch touch-screen, wi-fi, GPS and 3G connection.

A. Implementation, simulation and analysis

The prototype HEV vehicle to carry out the simulationis the DaimlerChrysler[3] car. The power sources are com-posed of 2×66 series connection SCs[15] and a branch of 14series connection 90Ah[15]. The parameters of the prototypevehicle are listed in table I.

In figure 3 the routes calculated for the three metrics usedare given. The route characteristics in term of, length, timeduration and the state of charge (SOCb) of battery at thetarget point are given in table II. It is interesting to calculatethe energy gain ratio obtained from energy metric algorithmwith respect to the distance metric one. We can easily observethat for this application test, the energy gain ratio is about10% which is far from negligible.Naturally the value of energy recuperation coefficient, α ,plays an important role on the energy efficiency as wellas on the altitude profile of the calculated route. Its value

TABLE IELECTRICAL VEHICLE PARAMETERS

Parameters ValueM (nominal mass) 1680.0 kgM (total mass) 2095 kgrt (Tire radius) 290 mmCd (reynolds coefficient) 0.32 kg/m3

A f (windward area) 2.31 m2

µr (rolling resistance coefficient) 0.0088ρ (air density) 1.25 kg/m3

δ eqm (equivalent moment inertia) 0.195 kg·m2

Power of electric motor (nominal) 45 kWSC bank 2×66 series connection SCsBattery pack 14 series connection batteries

TABLE IISHORTEST, FASTEST AND ENERGY OPTIMAL ROUTE PARAMETERS

Metric Color Path length Duration Arriving battery SOCb

Shortest Red 13.8 km 21 min 94.9 %Fastest Blue m 16.6 km m 15 min 92.2 %Energy optimal Green 14.3 km 23 min 95.4 %

depends on several factors and more specifically on thecharacteristics of the power train architecture as well as onthe road surface condition[16]. In Figure 4, for differentvalues of α , we give the optimal routes calculated usingenergy metric. In figure 5 we give the different values ofα used and the associated color codes corresponding todifferent optimal routes. In the same figure, we give alsothe cumulative elevation gain, energy demand and the lengthof the calculated route. The cumulative elevation gain is anindicator of the route elevation variation. We may observefrom figure 5 that the route elevation variation increases withthe increase of α value.

V. CONCLUSIONS AND PERSPECTIVES

In this paper an energy optimal real time navigation system(EORTNS) is proposed focused mainly on energy optimalroute calculation. It constitute a new release of Optimal RealTime Navigation System (ORTNS)[14] and is based on thereal time traffic information system given by SYTADIN. TheEORTNS offers HEV real time energy optimal navigationwhich consists of optimal and parametrized O-D route calcu-lation as well as optimal power splitting ratio between batteryand SC. It is fully independent and capable of retrieving realtime traffic network information from SYTADIN and operateroute to destination updates.

From the simulation test presented in this paper wecan clearly see that the energy metric helps in on boardenergy optimization and the results obtained are better thanthose obtained based on distance metric or time metric.Another advantage of EORTNS is related to the increasesof battery life operated through the reduction of batterycharging cycles[14]. We observe also the importance of theenergy recuperation coefficient α in route calculation aswell as in on-board energy optimization. This fact givesus a clear direction of research in order to increase the

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Fig. 3. Shortest (red color), Fastest (blue color) and Energy optimal route(green color). The origin point corresponds to the red tag and the destinationpoint corresponds to the violet one. The coefficient of energy recuperationα used is equal to 0.85.

Fig. 4. Energy optimal routes for different values of recuperation coefficientα . The chosen values of α as well as the color code are those given infigure 5. The origin point corresponds to red tag and the destination pointcorresponds to violet one. The route characteristics (duration, length, SOC,. . . ) given in the black band of the Samsung Galaxy Tab screen correspondsto the route calculated with α = 0.1.

energy efficiency of HEV as well as of other types of hybridelectrical vehicles.The future development of EORTNS will be focused onthe integration of other traffic network information sourcesand real time route state estimation in order to enhancethe information provided by SYTADIN and increase theprecision of route velocity profile.

ACKNOWLEDGMENT: This research work is partiallysupported by AKKA Technologies (http://www.akka.eu/),our industrial partner in this project, that we warmly thankfor the support and the confidence which we have granted.

0 5 10 15 20 2520

40

60

80

100

120

140The dependence of elevation profile on recuperation efficiency

Distance [km]

Ele

vation [m

]

α = 1.00, cumulative elevation gain = 255 m, energy demand = 1.271 kWh 100 %, length = 20.82 kmα = 0.90, cumulative elevation gain = 255 m, energy demand = 1.427 kWh 112 %, length = 20.82 kmα = 0.60, cumulative elevation gain = 232 m, energy demand = 1.876 kWh 148 %, length = 21.72 kmα = 0.30, cumulative elevation gain = 216 m, energy demand = 2.295 kWh 181 %, length = 22.52 kmα = 0.10, cumulative elevation gain = 202 m, energy demand = 2.553 kWh 201 %, length = 22.24 km

Fig. 5. The dependence of elevation profile on energy recuperationcoefficient α . The cumulative elevation gain or the route elevation profilevariation as well as the route energy reduction increase with the value ofα .

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