Look-Ahead Platooning through Guided Dynamic Programming618851/FULLTEXT01.pdf · GEORGE JITHIN BABU...

Look-Ahead Platooning through GuidedDynamic Programming

GEORGE JITHIN BABU

Master’s Degree ProjectStockholm, Sweden September 2012

XR-EE-RT 2012:035

Abstract

It has already been shown that look-ahead control can result in fuel sav-ings up to 3% and platooning can save around 7%. The aim of this thesis isto combine these two strategies. Various strategies that can be used for thispurpose are analysed. Fuel and time optimal state utilises the momentum orthe stored energy of the truck and at the same time keeps the distance be-tween the trucks as small as possible. This thesis presents a cooperative formof decentralised predictive controller to achieve this. Dynamic programmingstrategy, which is used to solve it, has a very high computational complexitydue to the number of states and its possible values. To avoid this, an itera-tive dynamic programming algorithm which operates only on a small region ofsearch space was developed. The search space is made flexible, which improvesthe runtime and performance of the algorithm. This resulted in a controllerthat decided whether platooning or look-ahead control or partly both shouldtake the leading role in controlling the trucks for the best performance. Thefuel and time optimal velocity profiles thus obtained could save 3.9% of fuel fora two platoon system on a real road simulation.

Acknowledgements

The master’s thesis on look-ahead platooning was done at the Pre-developmentof Intelligent Transportation Systems department (REPI), at Scania CV ABin Södertälje, Sweden, between March 2012 and September 2012. The thesiswas supervised by the Automatic control department, at Royal Institute ofTechnology(KTH), in Stockholm, Sweden.

I would like to use this opportunity to thank my supervisors Assad Alamand Kuo-Yun Liang for giving me the opportunity to do this project. Theirsupport and guidance during the whole project was a great help, especially toidentify various practical aspects of the problem. I would like to acknowledgeHenrik Pettersson at Scania for his outstanding help, support, and knowledge. Ialso want to express my gratitude towards my examiner Karl Henrik Johanssonat KTH. Along with thanks to everyone at the Pre-development department,at Scania for welcoming me and making every day enjoyable.

Contents

Contents i

Introduction 1

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Truck Model 72.1 Power Train Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.2 Mass Flow Model . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Aerodynamic Drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3 Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Control Strategy Analysis 133.1 Velocity and Road Profiles . . . . . . . . . . . . . . . . . . . . . . . . 133.2 Simple Look-Ahead Platooning Strategies . . . . . . . . . . . . . . . 16

3.2.1 Strategy 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2.2 Strategy 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2.3 Strategy 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4 Selection of Controller . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 Look-Ahead Control 214.1 Selection of Optimiser . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2 Dynamic Programming . . . . . . . . . . . . . . . . . . . . . . . . . 234.3 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.4 Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.5 Search Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.6 Algorithm Architecture . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.6.1 Dynamic Programming 1 (DP1) . . . . . . . . . . . . . . . . 27

i

ii CONTENTS

4.6.2 Dynamic Programming 2 (DP2) . . . . . . . . . . . . . . . . 304.6.3 Coordinator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.7 Extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5 Simulation Results 395.1 Uphill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.1.1 Case 1: Heavier Follower Vehicle . . . . . . . . . . . . . . . . 405.1.2 Case 2: Heavier Lead Vehicle . . . . . . . . . . . . . . . . . . 42

5.2 Downhill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.2.1 Case 1: Heavier Follower Vehicle . . . . . . . . . . . . . . . . 465.2.2 Case 2: Heavier Lead Vehicle . . . . . . . . . . . . . . . . . . 48

5.3 Combination of Uphill and Downhill . . . . . . . . . . . . . . . . . . 505.3.1 Case 1: Heavier Follower Vehicle . . . . . . . . . . . . . . . . 505.3.2 Case 2: Heavier Lead Vehicle . . . . . . . . . . . . . . . . . . 54

5.4 Extended Platoon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.5 Real Road . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6 Conclusion 63

Bibliography 65

Chapter 1

Introduction

The first truck rolled out in 1896, which had a 4 hp engine with two forward andreverse gears. Since then a succession of technological revolutions combined to cre-ate the modern trucks as we see today. Now trucks have become a necessity in thelogistic chain and all products we use are transported by trucks at some point oftime. Based on a study done by the Swedish Association of Road Haulage Com-panies in 2009, each year 406 million tonnes of goods are transported using trucksin Sweden, which accounts for 81% of the total freight transport [1]. They have aunique role to play in today’s transportation system which enable proper function-ing of the economy at the same time assuring the quality of life we enjoy, whichmakes it essential for the growth of society.

Today the fuel is widely available everywhere but the prices have become in-creasingly taxing on vehicle owners. The increase in the fuel price affects the heavyfleet providers with increased operational costs, which eventually affects everyoneas transportation costs carry over to the goods and services. Based on the pre-diction of European Commission-Directorate General for Mobility and Transport,there will be a 20% increase in the fuel price and 43% increase in freight transportusing trucks by 2030 [18]. This clearly shows an increase in the cost and numberof trucks on the roads. An increase in the traffic naturally increases the emissionsof the green house gases, which can have devastating effects in the long run. Toensure the quality of the living environment various governmental agencies aroundthe world have set limits for carbon emissions. Directorate-General for Energy (Eu-ropean Commission) expects to reduce the green house gas emissions by 20% andalso save 20% of energy[2]. The numbers point to the fact that energy efficient tech-nology is a necessity for the survival in the future market scenario and to ensure abetter future.

The technological advancement both in hardware and software had been enor-mous in the past decade, which enables us to create a solution for fuel efficiency intrucks without driver intervention.

1

2 CHAPTER 1. INTRODUCTION

Figure 1.1: Representations and notations of a three truck platoon. V1, V2 and V3are the velocities , d12 and d23 are the relative distances between the trucks.

1.1 Background

Scania CV AB has estimated that the contribution of fuel consumption is 30% ofthe operational costs for a heavy duty vehicle [3]. Apart from the cost increase,fuel consumption also results in increased emission. Since fuel cost is a big part ofthe total cost even a fuel saving as small as 1% can result in significant savings,which in turn will increase the profit margins of the transport companies. Drivingat a lower speed reduce the fuel consumption, which will increase the travel time.Thus the aim of reducing the fuel consumption, while maintaining the travel time,is challenging.

One of the automation and energy efficient services that is under study now isplatooning as illustrated in Figure 1.1. Platooning allows several trucks to travelat a small intermediate distance. The main advantage of this is to reduce thefuel consumption due to aerodynamic drag reduction caused by the truck ahead.According to the results published by Alam [3], the fuel consumption can be reducedby up to 7% by maintaining a distance equivalent to 1 sec at 70 km/h between twoidentical trucks. A similar effect can be observed in bicycle racing or skating, wherethe contestants move in formation to use the reduction in air drag and therebyreducing the effort.

The power to mass ratio of heavy trucks are often such that even a moderateslope can have a significant effect on the fuel consumption, if the speed is to bemaintained. When driving in uphill and downhill, gravitational force is the majorforce when compared to frictional force and aerodynamic force. Depending on themass and slope, significantly higher power is required to maintain a constant velocityor acceleration during uphill compared to a flat road. The trucks will accelerateduring downhill without any fuel injection and will decelerate during steep uphills.The weight of the truck can be such that it cannot maintain its velocity duringthe uphill even with maximum power. Thus just by utilising the momentum or thestored energy in the truck there is a potential fuel saving with the knowledge of theterrain ahead. The control technique which uses the above concept is look-aheadcontrol. The results published by Hellström and Ivarsson [10] and [11], showed afuel saving of 3% on a 120 km stretch without affecting the trip time much by usinglook-ahead control.

The studies done by Hellström, Ivarsson and Alam [10], [11] and [3] had al-ready shown that platooning and look-ahead control are capable of providing fuelefficiency. In platooning, the trucks in a platoon act as a single cooperative system

1.2. PROBLEM FORMULATION 3

Figure 1.2: Trucks moving in a platoon over an uphill and downhill. Truck 4 and 5should maintain minimum distance between the heavy duty vehicles for maximumfuel efficiency. Truck 3 should let the gravity reduce the speed to a minimumacceptable level and truck 1 and 2 accelerate to the maximum speed using gravity.In order to reduce the fuel consumption, the distance between the trucks should bekept as small as possible.

and all the trucks follows the lead or the reference truck, at the same time main-taining a safe distance between them. In general all the trucks in a platoon willhave the same cruise control speed. On the other hand, in look-ahead control thespeed of the truck varies depending on the terrain ahead but tries to maintain aspeed close to cruise control speed. The aim of this thesis is study the combinationof platooning and look-ahead control, and to formulate a control algorithm whichcan do it efficiently. A simple scenario for the look-ahead platooning is illustratedin Figure 1.2.

The reduction in air drag coefficient with respect to the distance between thetrucks is illustrated in Figure 1.3. It is necessary to design a strategy, which can usethe gravitational force as much as possible at the same time reducing the distancebetween the trucks. The aim of this thesis is to formulate a look-ahead platooningstrategy and evaluate its performance.

There are several challenges that are involved in this problem, the most im-portant one is the non-linearity of the system. A hybrid optimization has to beused to find the optimal strategy as gear can be changed only in discrete steps, i.e.optimizing a combination of discrete and continuous system.

1.2 Problem Formulation

The aim of this thesis is to derive a time and fuel efficient strategy for a platoonwith the knowledge of the terrain ahead. The strategy should also make sure thatthe trucks always maintains a safe distance between each other. The initial phase isto develop a strategy for a two vehicle platoon and is extended further to 3 vehicles.The vehicle platoon is described as shown in Figure 1.1

The following assumptions are made to simplify the algorithm

1. Speed control of the trucks are capable of maintaining a speed very close tothe reference speed, difference is as low as 0.2 km/h.

4 CHAPTER 1. INTRODUCTION

Figure 1.3: Reduction in drag coefficient Cd depending on the distance. [3]

2. Gear changes are made efficiently by the adaptive cruise control.

3. Linear engine fuel mapping near the operating region around 80 km/h.

4. The adaptive cruise controller is designed only to maintain a set speed andthe set distance between the trucks.

5. A relative distance of 5m between the trucks is considered a safe distance.

To determine the optimal velocity for the whole platoon, the problem can beexpressed as an optimal control problem and then the solution can be found. Itis in essence an extension of the look-ahead control for single vehicle to multiplevehicles. The resulting algorithm should generate the optimal control law for thevelocity of the truck with respect to both fuel and time. The aim of the optimisationis to reduce the total fuel consumption of the platoon for the whole trip. At thesame time, the total trip time should not be more than the one which travels atthe cruise control set speed. In addition to the time and fuel criterion, the platoonshould maintain a safe distance between the two trucks. On top of this, an efforthad to be made to make the algorithm as close as possible to real time in thedevelopment PC.

Inputs to the look-ahead platooning system are cruising speed, mass, gear, posi-tion of the truck and relative distance between the trucks, which are obtained fromsensors and the engine management unit. Apart from these, slope of the road aheadis also an input to the algorithm. Based on the position evaluated by the truck, the

1.3. RELATED WORK 5

slope is collected from a database. Each vehicle in a platoon communicates withother vehicles and exchanges information regarding their velocities, positions andother relevant information.

1.3 Related WorkOne of the earlier works on look-ahead control was done by Schwarzkopf and Leipnik[19]. Several studies were done on optimal fuel strategies using the information ofthe road ahead e.g. Fröberg [8], Hellström[11], Chang and Morlok [7]; based onan affine relation between the fuelling and engine torque. All the studies pointsto the fact that, fuel savings can be achieved by controlling the vehicles dependingon the terrain ahead. These studies suggest various strategies like maintaining thespeed if the slope is very small, enter the downhill with the minimum speed etc.The studies done by Huang and Bevly [13] proposed a solution to the look-aheadcontroller using a non-linear optimiser. A detailed study of look-ahead controllerwas done by Hellström and Ivarsson in [10] and [11]. A controller design usingdynamic programming was proposed by them. The implementation of the lookahead controller in this thesis is based on [10] and [11].

Control of vehicles moving as a platoon was earlier studied by Levine and Athans[15]. Their studies concentrated on a centralised controller design. There werevarious studies later for vehicle platooning, focussing on different aspect of it e.g.improvement in traffic flow due to platooning by Varaiya [20]. Several strategies likecentralised controller by Liang [16], decentralised and game theoretical approach byAlam [4] and [5], were proposed for maintaining a safe platoon. A distributed modelpredictive control was proposed by Kuwata and How in [14], which concentrates onfleet level objectives. This proposed a different way of representing the objectivesof the trucks in the platoon. This thesis required the contributions from both thelook-ahead and platooning projects.

1.4 Thesis OutlineThe model that is used for the design of the look-ahead platooning strategy isformulated in Chapter 2. Along with the formulation, the adaptations that wererequired for the algorithms are also explained in detail. Based on the model a pre-study is done to access the scope of the problem and is explained in Chapter 3. Inthis chapter various strategies are discussed and a requirement for the algorithmis formulated, which will act as guidelines for further development. A dynamicprogramming algorithm and a control strategy is developed in Chapter 4. Thischapter also explains about various strategies that are implemented to make thealgorithm faster and effective. The simulation and comparison of all the strategiesare done in Chapter 5, and Chapter 6 concludes this thesis.

Chapter 2

Truck Model

To predict the behaviour of the truck it is required to have a model of the truck.This chapter explains the system models that are used for the development of thecontrol algorithm.

2.1 Power Train Model

The basic power train model is explained in detailed in [3], and is briefly explainedbelow.

2.1.1 Engine

A diesel engine is modelled in such a way to represent the look-ahead problem. Sincethe influence of combustion process and engine dynamics is less when compared tothe vehicle dynamics, the simplified engine model is formulated as shown in (2.1),

Te(ωe, uf )− Tc = Jeωe (2.1)

where Te is the torque generated due to the combustion after considering the enginefriction, Tc is the torque available at the clutch, Je is the moment of inertia of theengine,uf is the engine fuelling and ωe is the angular momentum at the clutch plate.

For vehicle speeds between 75 km/h and 85 km/h the engine torque Te is mod-elled as shown in (2.2). The parameters in (2.2) was derived in [12] and these valueswere used directly in the algorithm.

Te(ωe, uf ) = a1ωe + b1uf + c1 (2.2)

where uf is the engine fuelling which is bounded by

0 < uf < umax (2.3)

where the upper limit umax is modelled by

7

8 CHAPTER 2. TRUCK MODEL

umax = a2ω2e + b2ωe + c2 (2.4)

The torque generated by the engine is then transmitted through the clutch,transmission, drive shaft, differential and finally to the wheels. The gear shifts andthe corresponding changes in torque and speed are assumed to be instantaneous.All the losses in the drive train are lumped in to the efficiency of transmission andfinal drive ηt and ηf respectively. similarly the moment of inertia of the drive trainin lumped in to moment of inertia of the wheel Jw. The torque transmitted to thewheel Tw and the torque balance is given by

Tw = Tcitifηtηf = Jwωw + rFb + Tf (2.5)ωe = itifωw (2.6)

where it and if are the gear ratios of the transmission and the final drive, ωw is theangular velocity of the wheels, ωe is the angular velocity of the crank shaft, Fb isthe braking force, Tf is the net tractive torque on the truck and r is the radius ofthe wheel.

Longitudinal Forces on the Truck

The free body diagram of a moving truck is shown in Figure 2.1. Based on this,using force balance motion model of the truck can be derived as

mv = Ff − Fr(α)− Fg(α)− Fd(v, d) (2.7)

where m is the mass of the truck, α is the road angle, v is the velocity and d isthe relative distance between the trucks. The models of the longitudinal forcesFg, Ff , Fr and Fd are explained in Table 2.1.

The vehicle velocity is

v = rωw (2.8)

Table 2.1: Longitudinal Forces.

Force ModelFg(α),Force due to gravity mg sinαFr(α), Rolling friction mgcr cosα

Fd(v, d), Aerodynamic drag 12cd(d)Aaρav

2

Ff , Tractive force Tf

r

2.1. POWER TRAIN MODEL 9

Figure 2.1: Longitudinal forces acting on a moving truck [3].

From (2.1), (2.6) and (2.7)

mv = Ff −mgcr cosα−mg sinα− 12cd(d)Aaρav

2 (2.9)

(m+i2t i

2fηtηfJw

r2 + Je

r2 )v = itifηtηfTe(ωe, uf )

r− Fb (2.10)

− (mgcr cosα+mg sinα+ 12cd(d)Aaρav

2)

⇒ mtv = KeTe(ωe, uf )− Fb +Kr cosα+Kg sinα+Kdcd(d)v2

(2.11)

where

mt = m+i2t i

2fηtηfJw

r2 + Je

r2 , Ke = itifηtηf

r(2.12)

Kr = mgcr, Kg = mg, Kd = 12Aaρa

mt is called the total inertial mass

The look-ahead horizon is defined in terms of distance S ahead of the truck. Themodels that were formulated above were with respect to time. In order to have asimpler algorithm it is required to convert these equations with respect to distance.We have that for any function f(x), the following holds

df

dt= df

ds

ds

dt= df

dsv (2.13)

Fuel mass (2.14) and the truck model (2.11) can be modified accordingly. Forsolving the differential equations Euler’s backward method was used.


Figure 2.2: Reduction in aerodynamic drag coefficient(cd) depending on the relativedistance [3] .

2.1.2 Mass Flow Model

The mass flow is determined by the fuelling uf and the engine speed ωe. The fuelflow in g/s is

mf = ncyl

2πnrωeuf (2.14)

where ncyl is number of cylinders and nr is number of crankshaft revolutionsper cycle.

When the truck is in neutral gear the fuel flow is equal to idle fuel flow, whichis a constant.

2.2 Aerodynamic DragAny moving vehicle experiences an aerodynamic drag. The main aim of the pla-tooning is to achieve fuel savings due to the reduction in aerodynamic drag. Thismakes it necessary to model its reduction as a function of the distance between thetrucks. From Table 2.1 the aerodynamic force is given as

Fd = 12cd(d)Aaρav

2 (2.15)

The drag coefficient cd(d) given by

cd(d) = Cd(1− fi(d)100 ) (2.16)

2.3. SIMULATION MODEL 11

Figure 2.3: Simplified representation of the model that was used for simulation.

Where Cd is the drag coefficient for a truck without platooning. The change incd(d) with respect to the spacing between the trucks is as shown in Figure 2.2. Thefunction fi(d) is an approximation of the curves in Figure 2.2, where i representsthe position of the truck in the platoon. f1(d) corresponds to the truck in front,f2(d) is the second truck and f3(d) is the last truck. The same linear function usedin [16] is used here and is as shown in (2.17).

f1(d) = −0.9379d+ 12.8966 0 < d < 15f2(d) = −0.4502d+ 43.0046 0 < d < 80 (2.17)f3(d) = −0.4735d+ 51.5027 0 < d < 80

otherwisefi(d) = 0

2.3 Simulation ModelThe model that was derived above was used for developing the control strategy. Forsimulation a more detailed model was used. It was provided by Scania CV AB. Asimplified block diagram of this model is shown in Figure 2.3. The model has acruise controller that is used to maintain the speed of the truck at the set speed.The torque controller determines the amount of torque that is required for thespeed determined by the cruise controller. The torque is then limited and filtereddepending on the engine characteristics and limitations. The torque controller alsodetermines the amount of braking torque required to maintain the speed. Thecombustion process is modelled by diesel engine model, which calculates the actual


torque generated and the corresponding engine speed. These calculations are basedon the actual engine data. The torque thus generated is transmitted to the wheelsthrough a series of gears, which is modelled using transmission model. The truckmodel simulates the behaviour of the truck. The input of the truck model is the sumof brake torque, transmitted engine torque and torque due to losses. The vehiclevelocity is the output of the truck motion model and is the feedback signal to thecruise controller.

Chapter 3

Control Strategy Analysis

The fuel and time optimal profile for a single vehicle based on the road slope isalready presented in the work of Hellström and Ivarsson in [10] and [11]. Thestudies done by Alam and Liang in [4] and [16] had shown that there is a potentialfuel saving and a controller was designed for a platoon. The purpose of this chapteris to analyse the effects of using the optimal fuel and time velocity profiles for eachvehicle in a platoon. Apart from this, an analysis of various strategies that can beused is done here.

The system under study here is a two truck platoon under suitable road condi-tions. The parameters of the trucks and the road profiles are selected such that thereis a considerable difference between the fuel and time profiles of the trucks, makingplatooning almost impossible or less effective for the chosen vehicle configurationsand road conditions. To simplify the analysis, an initial study was performed us-ing a single point mass representation for the trucks. Such an approximation doesnot model the actual dynamics of the system, but it gives a fairly good idea aboutacceleration, deceleration and energy consumption. Apart from this, the losses likefriction, aerodynamic drag and gravity are dependent on the mass, which make thisapproximation good enough. Once the initial analysis was done, the profiles weretested on a simplified truck model. Further development was based on these results.In addition to the simplified truck model, the trucks are considered as point objects,which are separated by relative distance only. Thus the look-ahead horizon of bothtrucks will be approximately same, provided the relative distance is small.

3.1 Velocity and Road Profiles

Selection of suitable road profiles and the corresponding velocity profiles is crucialfor a good analysis. In the studies done by Hellström, Ivarsson and Holma [10],[11] and [12], the fuel and time optimal velocities profiles for different road profileswere studied in detail. The speed profiles thus determined not only depends onthe slope but also on the vehicle masses, losses and other truck parameters. Hencethe optimum velocity profile will be different for different vehicles unless they are

13

14 CHAPTER 3. CONTROL STRATEGY ANALYSIS

identical with same losses. When the trucks are moving as a platoon even identi-cal trucks will have different aerodynamic losses, which results in slightly differentoptimal velocity profiles. The steady state values (speed on a level road) of theseprofiles are determined by the truck limitation, legislation or the adaptive cruisecontrol. This makes the fuel and time optimal steady state speed for each truck ina platoon dependent only on the engine limitation, if the cruise control set speed issame for all. Thus for a platoon of trucks which differs only in their masses, eachtruck will have the same steady value for velocity profile. For example, if the cruisecontrol set speed is 80 km/h, then the optimal velocity for the trucks on a flat roadis 80 km/h. The difference in the profiles will appear only when there is a transitionbetween different slopes or optimum steady velocities, as different trucks will havedifferent optimum transition between the velocities.

In Figure 3.1, each truck follows a different velocity profile due to the differencein their masses, until it reaches a steady state. Assume that the maximum allowablevelocity change is from 75 km/h to 85 km/h. Then, for trucks with masses 35, 30and 25 tonnes the final steady velocities are the same. It can be observed that incase of a 20 tonnes truck the final velocity is 83 km/h because, the weight of thetruck is not enough to accelerate more (minimum allowable acceleration is .06m/s2

due to dynamic programming limitation). Assume 35 tonnes, 30 tonnes, 25 tonnesand 20 tonnes trucks are moving in a platoon, where each truck tries to maintainits optimum profile as shown in Figure 3.1. Then it can be observed that, duringdownhill a 35 tonnes truck always had a higher velocity when compared to theother trucks. This behaviour can either increase the relative distance, or the trucksbecome very close to each other and collide towards the end of the slope, dependingon the position of the heavier truck. This makes it necessary to find another velocityprofile, which is fuel and time optimal for the whole platoon.

A combination of 30 or 35 tonnes and 20 tonnes truck has the considerable dif-ference in the velocity profiles in the above range of masses. Figure 3.2 shows therelative distance between the trucks when a 30 tonnes truck is the lead vehicle and20 tonnes is the follower vehicle. It can be seen that the distance between them isincreased from 5m to 25m, which in turn increases the aerodynamic losses drasti-cally. In the other case where 20 tonnes is in front of a 30 tonnes truck there will bea collision. Due to this difference in the individual velocity profiles 30 tonnes truckand 20 tonnes truck is selected for further study in this thesis. The same results canbe shown for uphill also.

Simple road profiles like uphill, downhill, uphill followed by downhill and down-hill followed by uphill are used. To have reasonable impact on both 30 tonnes and20 tonnes trucks without creating much system limitation, a slope of ±3% is usedfor the study. Aerodynamic losses were also considered while determining a suit-able slope, since it should not lose its significance in the uphill or downhill whencompared to gravitational force.

3.1. VELOCITY AND ROAD PROFILES 15

Figure 3.1: Fuel and time optimal velocities for different masses of trucks with thesame slope ignoring the position and air drag reduction in a platoon.

Figure 3.2: Relative distance between 20 tonnes and 30 tonnes truck with the alti-tude as shown in Figure 3.1.


3.2 Simple Look-Ahead Platooning Strategies

Three strategies are analysed in this section. Based on the results from this analysisa suitable strategy for control was decided. One is that both the trucks follow thesame velocity profile, in most cases the velocity profile of the heaviest vehicle orthe vehicle with least powerful engine. The second strategy is to allow both thetrucks to continue with their individual optimal velocities. Another strategy wasto completely ignore the optimal velocity profiles and create a profile using a PIcontroller.

All the cases are tested with the approximated vehicle model as described aboveand then to confirm the findings they were verified in a more accurate truck model.The actual truck behaviour was much different from these two models but it gavea fairly good idea which was enough during this stage.

3.2.1 Strategy 1

Consider a two truck scenario. One of the trucks in the platoon is selected as thereference truck. Both trucks in the platoon will move with the fuel and time optimalvelocity of the reference truck. Thus the trucks are driven with a common velocity,which is considered as the platoon velocity. The reference truck is the one withlowest speed limitation. The speed limitation occur due to the weight or due toa relatively less powerful engine. In any case the weakest truck will be consideredas the reference truck. For the study, same engine was chosen for both the trucks,hence the weakest truck is the heaviest one.

In this strategy the velocity profile will be the optimal for the heaviest or thereference truck and the lighter one will follow, which assures that the platooning iseffective and safe as the distance between them is maintained. The optimal velocityfor a platoon of 20 and 30 tonnes truck in an uphill and downhill are shown in Figure3.3. A small kink that can be observed in the optimal velocity of a 30 tonnes truckalong a downhill is due to the discretisation of the model.

The fuel and time optimal velocity profile is the one which requires the leastamount of braking and fuel. In case of downhill, the common velocity is higher thanthe optimal velocity for the lighter truck along the downhill. This means that lightervehicle must spend a little amount of fuel to attain this acceleration. Along thedownhill it is optimal to use the gravitational force to accelerate and maintain thespeed of the truck. In this situation fuel saving due to platooning is not significant.The advantage of platooning during a downhill is that gravitational force can resultin slightly higher velocity and acceleration as the losses are reduced. In other wordsthe platoon velocity profile is optimal only for the heavy vehicle, i.e.optimal fuel,time and brake.

In case of uphill, even though the velocities are different, the platoon velocityprofile for the lighter will result only in slightly higher fuel consumption when com-pared to the optimal case. There is some saving as the distance between the them

3.2. SIMPLE LOOK-AHEAD PLATOONING STRATEGIES 17

Figure 3.3: Common velocity profile for a platoon of 20 tonnes and 30 tonnes truck,compared with the fuel and time optimal velocity of the 20 tonnes trucks in an uphilland downhill.

is kept small. This points to the fact that there is a possibility of another velocityprofile which is time and fuel optimal for the whole platoon.

This strategy performed well and could result in fuel and time savings whencompared to adaptive cruise control strategy. The main disadvantage of this methodis that it does not consider the second vehicle, the optimal profile is generated basedon the weakest truck. The velocity profile will be the optimal only for one truckand might not be for the others. Apart from this, the second truck might not beable to follow the velocity profile accurately due to its engine limitation.

3.2.2 Strategy 2

In this strategy, each vehicle in the platoon moves with its fuel and time optimalvelocity. In order to make sure that the trucks do not collide and distance betweenthem is small on a level road, an attempt to design a controller for relative distancewas done. Unlike the previous strategy it requires different profiles depending onthe position of the vehicle in the platoon. The implementation of this strategy us-ing a proportional integral(PI) controller was not very effective. The controller hadan oscillatory behaviour. The calibration of the PI parameters was difficult as therelative distance changed very fast. This main disadvantage of this controller wasthat there was no information for the controller regarding the preferred variationof the relative distance. Without this information, the PI controller had the samecontrolling effect depending on the calibration, irrespective of the slope. The strat-egy works in case of similar trucks in which case the velocity profiles are similar. Asimilar strategy is used in the next chapter, where the problem is expressed as an


optimal control problem and solution is found, hence this analysis was not done indepth.

3.2.3 Strategy 3

In this strategy, a profile was generated such that, the trucks were decelerated usinggravitational force during uphill till it reached the minimum velocity. Similarly,the trucks were accelerated during downhill without using any fuel till it reachedthe maximum velocity. These behaviour has the least fuel consumption. Also inthis strategy, the previously determined optimal velocity profiles were not used. Aproportional integrating(PI) controller was used to control the speed of the vehicle.Along with this velocity controller, another proportional integral derivative(PID)controller was added to control the relative distance. The relative distance controllerwas necessary to make sure that the trucks always keeps a safe distance betweenthem. In short the controller can be described as

• When slope is zero the cruise set speed and the relative distance were main-tained at the set values

• When the truck enters a downhill and before the exit of an uphill, the fuelwas cut-off, so that vehicle moves under gravitational force (either accelerateor decelerate) until it reaches the maximum or minimum velocity.

• Whenever the relative distance crosses acceptable limits, a correction fromthe PID controller was added to the velocity controller and the distance wasmaintained.

• To make sure that the travelling time was least affected, the velocity wasmaintained at the set value for the first half of the slope during an uphill.The truck decelerated only towards the end of the slope.

• Controller was not intelligent, it operated based on the value of current ve-locities, slope and relative distance.

The velocity for such a controller is shown in Figure 3.4. It can be observedthat there is an intermittent braking and acceleration.

3.3 DiscussionAll the above analysis were done on the assumption that the trucks were pointobjects, i.e. the look-ahead horizon is the same for both vehicles. In practice thetrucks are separated by a distance, truck length plus relative distance. Hence boththe trucks have slightly different slopes, as the slope changes are gradual this ap-proximation is good if the relative distance is small. For the analysis, the controllersgenerated the truck velocity for each time step and outputs were represented with

3.4. SELECTION OF CONTROLLER 19

Figure 3.4: Velocities and the corresponding relative distance of a 30 tonnes truckfollowing a 20 tonnes truck in a 2% uphill followed by a 2% downhill.

respect to time. In other words, time was chosen as the reference. This controller isgood only if both the trucks are moving with the same velocity. If the trucks moveswith a different velocity, the time taken by the trucks to travel the same distancewill be different. This can influence the performance of the controller.

One observation from the calibration was that relative distance responded fastercompared to the velocity of the trucks. Thus there was a fast and a slow controllercontrolling the same system. This resulted in oscillations, when the same PIDparameters were used for different cases. The performance was better when thevelocity profiles were similar. The analysis points to the fact that there was energysavings when the relative distance was kept small. This suggest that an intelligentcontroller with preview information should be more fuel efficient than a simple PIDcontroller.

3.4 Selection of Controller

As an optimal velocity has to be determined based on the slope of the road ahead,a predictive control strategy is required. The controller can either be a centralisedcontroller or a decentralised one. A centralised controller has all the informationregarding the trucks in the platoon. The space-time complexity of such a controllerincreases exponentially as the number of trucks in a platoon increases. The advan-tage of this method is that, as it has all the state information of the trucks, sucha controller can provide an optimal solution, which has the best performance theplatoon can achieve. However, the increase in the space and time complexity makesit impossible to use this in case of a larger platoon. Another disadvantage is that


if a centralised controller is designed for a two truck platoon, adding a third truckwill require a recomputation of the controllers.

Decentralised controller design on the other hand, has one controller for eachtruck. Each controller will have information regarding the state of the correspondingtruck, and has only limited knowledge about the other trucks. In short, a controllerthat is unaware of the limitations, capabilities and dynamics of the other trucks.Hence, in case of a decentralised strategy, each controller uses this limited knowledgeof the other trucks to generate its optimal strategy. This is a major drawback forthis strategy. The advantage is that, it is easy to add additional trucks to a platoon,and can be applied to a larger platoon also.

In case of a platoon it is more meaningful to design a decentralised controller,which enables addition or removal of trucks from the platoon. The controllerscommunicate with each other regarding their relative distance and velocity. Thevelocity profile determined for a truck gives a good indication about its capabilities,limitations and dynamics, which are significant for the given condition. Hence, adecentralised controller will be designed, which cooperates with the other controllersto design an optimal strategy.

Chapter 4

Look-Ahead Control

In this chapter a predictive control strategy resulting in fuel and time optimal ve-locity profile is developed. The idea behind the controller is to use the informationthat is available about the truck and the terrain to predict the behaviour of thesystem for a specific distance ahead. The concept is shown in Figure 4.1. Theprediction can result in many behaviours with varying performance like high fuelsaving and decreased trip time, low fuel savings and decreased trip time, no sav-ings in trip time or fuel etc. The predictive controller that has to be derived willselect one behaviour which maximises the fuel saving and minimises the trip time.In simple terms, predictive controller searches all possible combinations of inputsand selects the one which maximises the profit, which also implies that with thesize and dimensions of the search space the time and code complexity will also in-creases drastically. The look-ahead platooning problem is represented as an optimalcontrol problem and is solved using standard methods. This chapter explains theformulation of an optimisation algorithm from the basic concepts.

Figure 4.1: An overview of look-ahead platooning. The controller will decide thevelocity and gear at B, which can have the minimum fuel while maintaining thetravelling time for the look-ahead horizon.

21

22 CHAPTER 4. LOOK-AHEAD CONTROL

4.1 Selection of Optimiser

There are several methods in which the optimal control problem can be solved.It is very important to select the most suitable one as each method has it ownadvantage and disadvantage. One method is to linearise the system model andthe performance measures are incorporated in a quadratic cost function. For thisproblem an analytical solution can be found using Pontryagin’s principle. Thismethod offers a fast way of computing the optimal control solution. In case ofconstrained input and states the solution has to be determined numerically. Thecomputational complexity increases linearly with the dimension of the states, whichis an advantage of this method. The disadvantage is that it can lead to multiplesolutions in some cases, one among the solutions is optimal. This method can onlybe applied to deterministic systems.

Another method is to use dynamic programming introduced by Bellman, whichis basically searching the entire search space for an optimal solution. It also of-fers much more flexibility when compared to the previous method and can be usedto optimise without linearising the system. This method always finds the optimalsolution if it exists, but the major drawback is that the computational complex-ity increases exponentially with the states. This makes it impractical for higherdimensional problem.

The system equation of the look-ahead platooning problem can be representedas shown below.

xi+1 = f(xi, ui, slope) (4.1)

where ui denote inputs and xi represents the states of the system and i represents thediscreet time steps. The optimal control algorithm should find the fuel and timeoptimal velocity for the type road ahead such that the constraints are satisfied.The type of road is represented using the slope, which can be considered as aconstrained input that can take only one particular value for a segment of road. Asthe values can be obtained in real time through GPS, modelling the slope variationis not meaningful. One method is to consider slope as a noise in the system anddetermine an analytical solution. To ensure a realistic prediction, the noise in suchcases are usually white making its modelling easier. But in this case the slopedoes not show the properties of a noise. The behaviour of the slope clearly denotesthat a white noise approximation is not reasonable. This means the system is nolonger deterministic without slope as the input and an analytical solution cannotbe determined unless a way is found to incorporate slope also in to the system.When dynamic programming is used to solve the optimal control problem suchconstraints can be avoided. Thus dynamic programming was chosen instead ofPontryagin’s maximum principle.

4.2. DYNAMIC PROGRAMMING 23

Figure 4.2: Dynamic Programming.

4.2 Dynamic Programming

Dynamic programming is an approach of solving complex problems by splitting itin to sub-problems, which are simpler and is explained in the work of Bellman [6].A simple representation of dynamic programming is as shown in Figure 4.2. Here,the whole problem is broken down into a sequence of decision steps over time. Eachblock in Figure 4.2 represents a state and the arrows represent the transition of thestates along various stages or steps over time. Every such transition is associatedwith a cost and the decision is taken based on this cost till it reaches the finalstage. Dynamic programming is a structured way to find a sequence of states toreach the final state with minimum cost. The cost function is used to evaluate theperformance of the solution and is a function of states and inputs. The cost functionis shown in (4.2) where x represents the state vector, u represents the input vectorand N is the number of stages.

J =N−1∑i=0

f(xi, ui) (4.2)

4.3 Constraints

The objective is to minimise the total fuel consumption of the platoon and the totaltrip time for the road profile ahead. The velocity should be within the limits shown


belowvmin < v < vmax (4.3)

where vmax is set by the engine limitation or legislation and vmin is set by theallowable deviation from the set speed. The brakes are assumed to be powerfulenough and no limitations are considered. Apart from the speed limitation; thetorque, engine speed and fuel are also limited by the maximum or minimum valuesspecified by the engine characteristics. Possible gear shifts are also limited alongwith the velocity. The gear should be such that the engine speed should be withinthe limits set by the engine specifications. In addition to the system limitations, anadditional constraint is added to the acceleration to ensure driver comfort.

A deviation ± 5 km/h from the set speed is allowed, i.e. if the set speed is 80km/h the maximum and minimum speed are respectively 85 and 75 km/h.

4.4 CriterionThe main objective of the optimisation is to minimise the fuel and reduce or maintainthe trip time. In addition to this, there were others objectives like driver comfortand safety. The cost function was formulated to represent these objectives as shownin (4.4), where the look-ahead horizon is divided into N steps each of length l.

J =N−1∑k=0

ζ(mk, tk, dk, gk, δvk) (4.4)

ζ in (4.4) is called the transition cost and is given by

ζ =[1 α β γ ε

]mk

tkdk

gk

δvk

(4.5)

In (4.5) α, β, γ and ε are constants andmk, tk, dk, gk and δvk are fuel mass, time,relative distance, gear and change in velocity respectively for kth stage. The con-stants represents the trade off made between the fuel savings, trip time and drivercomfort for optimal behaviour. When compared to the other objectives no compro-mises were made for the safety and engine limitations.

The fuel consumption(mk), time(tk) and change in velocity(δv) for a step of sizel are given by (4.6) where mf is the fuel flow in g/sec and v is the velocity of thetruck.

mk =l∫

0

1vmfds, tk =

l∫0

1vds

δv = |vk − vk−1| (4.6)

4.5. SEARCH SPACE 25

Table 4.1: Range and resolution of the variables.

Variable Quantisation level Range Number of discrete valuesVelocity 0.2 km/h 75 - 85 km/h 51

Relative distance 0.4m 3 - 80m 193Gear 1 10 - 12 3

4.5 Search Space

The search space is an imaginary space where the solution to the optimal controlproblem lies and whose dimensions are the states and control signals. In dynamicprogramming approach, the continuous state and control variables are discretised,i.e. the whole search space can be considered as a finite multidimensional grid. Thegranularity of the grid determines the accuracy and complexity of the algorithm.As the grid becomes finer, the complexity increases and at the same time the ap-proximation is more closer to the actual problem. Thus a suitable grid size hasto be chosen, which reduces the complexity as much as possible at the same timeapproximating the problem effectively.

For look-ahead platooning there are 2 states and 2 control signals, velocityand relative distance are the states and gear and fuel flow are the control signals.This means the search space is a 4 dimensional grid space. Dynamic programmingsearches in this 4 dimensional space for a solution for the problem. In standardapproach of the dynamic programming the outputs are the control signals, i.e. fuelflow and gear. Unlike the standard approach, in this case the output of the algo-rithm consists of a state and a control signal, which are gear and the velocity. Thefuel flow, which is the other control signal can be derived from these two. The fuelflow is proportional to the engine torque and engine speed. This selection of outputprevents the interaction of look-ahead controller with the controllers inside the en-gine management unit and adaptive cruise controller. The engine management unitand the adaptive cruise controller will have controllers, which governs the torqueand fuel flow so that engine is operating efficiently and effectively. Hence it is not agood strategy to use torque or the fuel flow as the control signal. Even though thealgorithm evaluated both the velocity and gear profiles, only the velocity profile isgiven to the adaptive cruise controller, the optimal gear is maintained automaticallyby the adaptive cruise control. The gear profile determined by the algorithm is usedto calculate the fuel consumption, which is required for the evaluation purpose.

To analyse the complexity of the program, a study was required regarding thesize of the search space. Quantisation level and range of values were determinedbased on previous studies on look-ahead control, platooning, constraints and ex-periments . Fuel flow was calculated from velocity, relative distance and the gear,which will be explained later in this chapter. The number of discrete levels can becalculated from the range and quantisation levels, these are shown in Table 4.1.

As the fuel can be calculated from velocity, relative distance and gear; dimensioncorresponding to fuel is ignored in the search space. Thus the initial search space is


Figure 4.3: Architecture of the algorithm. For simplicity the coordinator is repre-sented as two blocks, based on its function.

reduced to a 3 dimensional space. Table 4.1 shows that the size of this 3 dimensionalgrid space is 51 x 193 x 3. This means that the algorithm has to search 29529combinations of states in each step. There are 100 such steps each of length 20mfor each look-ahead horizon (the look-ahead horizon is 2 km with step length of20m). This makes the time complexity of the algorithm very high.

One method to reduce this computational complexity is to use an approximationof the cost function by using neural networks. At any stage, the cost of transitiondepends on the road slope at that stage. This makes it difficult to design such anetwork, which could perform the dynamic programming with reduced computa-tional complexity. The resulting algorithm could still have high complexity. Hencethe standard implementation of the dynamic programming was chosen. In order tohave a practical solution, the standard dynamic programming algorithm had to bemodified to make it faster.

4.6 Algorithm Architecture

For look-ahead platooning, a look-ahead distance of 2 km is selected and each step isof length 20m . Based on the slope of this 2 km road ahead, the algorithm calculatesthe fuel and time optimal velocity and the gear profile. As explained in the previoussection the standard dynamic program algorithm can be very expensive when runtime is considered. Hence an algorithm was developed which could perform dynamicprogramming much faster than the conventional one. This algorithm uses only apart of the search space to search for a solution and relies on the repeated run ofthe controller to converge to the optimal solution. The convex cost function makes

4.6. ALGORITHM ARCHITECTURE 27

sure that the algorithm converges to the optimal solution.The architecture of the algorithm is as shown in Figure 4.3. The algorithm

has two different dynamic programming algorithms, DP1 and DP2, with slightlydifferent cost functions. The first one to be executed is DP1. It generates a fuel andtime optimal velocity profile without considering the other truck. In other wordsDP1 is look-ahead control. As the dynamic programming ignores the presence ofthe other truck, the velocity profile generated for each truck need not satisfy thenecessary safety requirements. To incorporate safety requirements, a coordinator isadded to generate feasible solutions as input to DP2. The coordinator makes surethat the trucks have a safe distance between them, when moving in a platoon, inother words feasible solution. DP2 generates the final fuel and time optimal velocityprofile for the whole platoon. Depending on the variation of the output velocities,the search space is limited by the search space limiter block.

4.6.1 Dynamic Programming 1 (DP1)

DP1 is a look-ahead controller, which determines the fuel and time optimal veloc-ity profile for a single truck irrespective of the other vehicles in the platoon. Theobtained velocity profile might not be even feasible when the second truck is con-sidered. This velocity profile acts as the base on which the algorithm starts. Thealgorithm is similar to the work done on look-ahead control by Hellström [11] andIvarsson [10]. DP1 has velocity as state with gear and fuel flow as control signals.The only difference in the cost function when compared to (4.4) is that it does nothave the term for relative distance. The cost function used in DP1 is shown in (4.7)

J =N−1∑k=0

ζ(mk, tk, gk, δvk) (4.7)

ζ in (4.7) is a function is given by (4.8)

ζ =[1 α γ ε

] mk

tkgk

δvk

(4.8)

Search Space

Consider that the look-ahead horizon is divided in to N stages each of length l.At any point of time the status of the truck under consideration is its velocity vand gear g. The search space of any stage k comprises of all possible velocities Vk

and gears Gk bounded by the constraints explained in the previous section. It isdenoted by the set Sk. Sk can be represented as shown in (4.9), where ωmin andωmax are the engine speed limits.


Figure 4.4: Limited velocity search space.

Sk = {(v, g)|v ∈ Vk, g ∈ Gk}, where (4.9)Vk = {v|vmin < v < vmax}Gk = {g|ωmax < ω(v, g) < ωmin}

The time complexity of the algorithm depends on the total number of grids inthe search space. The lower the number, the faster the algorithm will be, but thisaffects the accuracy of the results. If the search space can be reduced without losingthe optimal solution, this will make the algorithm faster and more closer to realtime. An algorithm was developed for this purpose, which runs before the dynamicprogramming. The current velocity of the truck is used to limit the set of possibleinitial states. To avoid terminal effects, the final velocities are also limited. Theterminal velocity is limited to 80 km/h (set speed) whenever the engine is powerfulenough to maintain it. With the initial and terminal velocities limited using themodel, the search space is traversed forward and backward at the same time. Thisremoves the velocities which are not feasible, thereby downsizing the search space.In most cases where the engine is not limiting the possible velocities, the searchspace looks as shown in Figure 4.4.

Terminal Cost

A terminal cost was introduced in order to avoid terminal effects of the dynamicprogramming algorithm completely. This was necessary to avoid the terminal effectsat the same time downsizing the search space. Terminal effect is the tendency of


the algorithm to choose the lowest possible velocity for the last horizon, whichhas the least fuel consumption. The terminal cost is a reflection of the futurefuel consumption of the truck. In short terminal cost represents an approximateamount of fuel that is required to accelerate the truck to the set speed from thecurrent speed. Thus, all the velocities less than the set velocity has an additionalcost. This additional cost make the velocities below set velocity less attractive forthe dynamic programming, when compared to the velocities above the set velocity.

Algorithm

At any stage k, the fuel flow that is required for a transition from (v, g) ∈ Sk to(v, g) ∈ Sk+1 is determined. The fuel flow thus determined is used instead of usingpredefined discrete fuelling levels. The resolution of the fuelling level depends on theresolution of the velocity. The equations and more details are available in the workof Fröberg and Nielsen [9]. The advantage of this approach is that, the discretisationof the fuel flow is not required. If a feasible fuel flow cannot be determined for thetransition, then the transition is either impossible or it requires a valid brakingsignal. In the former case, the cost is set to infinity and in the later one, fuel flowis set to zero. The benefit of this method over the standard one is that the controlsignal need not be discretised, hence no interpolation also. The quantisation level ofthe fuel flow is indirectly dependent on the granularity of the velocity search space.

Let ζ(i,p)→(j,q)k denotes the transition cost when the truck velocity and gear

is changed from (vi, gp) to (vj , gq). Jk(vi, gp) is the cost function of kth stagecorresponding to vi and gp . Then algorithm is as shown below.

1. The cost function of the N th stage is JN = J∗N , where J∗N is the terminal cost.

2. k = N - 1.

3. Calculate

Jk(vi, gp) = min(vj ,gq)∈Sk+1

(ζ(i,p)→(j,q)k + Jk+1(vj , gq)), where (vi, gp) ∈ Sk

4. k = k-1 and continue step 3 till k = 0.

5. J0 is the optimal cost. The optimal velocity profile was derived using a forwardpass on the search space using the results of step 3 and 4 starting from theinitial state.

Calibration

The output of the algorithm depends on the calibration of the parameters in the costfunction. The calibration in other words is to make the necessary trade off betweenfuel consumption, time and driver comfort. It is not possible to have the lowest


trip time and fuel consumption at the same time, which makes it very important tohave the right values for the parameters. The time parameter α has to be set suchthat the optimal velocity is equal to the set velocity (80 km/h) when the look-aheadhorizon has a zero slope. The parameter γ is to discourage gear changes as muchas possible and ε is to smoothen the velocity profile.

4.6.2 Dynamic Programming 2 (DP2)

DP2 is responsible for look-ahead platooning. The main difference when comparedto DP1 is that DP2 also considers the relative distance between the trucks. Hence ithas velocity and relative distance as state and gear and fuel flow as control signals.Along with the optimal velocity and gear profile, DP2 also generates an optimalrelative distance profile which is used internally. The cost function is as shown in(4.4).

Search Space

Consider that the look-ahead horizon is divided in to N stages each of length l. Atany point of time the status of the truck under consideration is its velocity v, gearg and relative distance d. When compared to the search space of DP1 the onlydifference is that DP2 has an additional dimension for relative distance between thetrucks. Thus the search space is a 3 dimensional space consisting of velocity, gearand relative distance. The search space can be represented as in (4.10), where dmin

and dmax are the minimum and maximum acceptable relative distance.

Sk = {(v, g, d)|v ∈ Vk,g ∈ Gk d ∈ Dk} where, (4.10)Vk = {v|vmin < v < vmax}, Dk = {d|dmin < d < dmax}, and

Gk = {g|ωmax < ω(v, g) < ωmin}

The increase in the time complexity with the increase in dimension of the searchspace was drastic. This is one of the main drawbacks of dynamic programming.The same search space downsizing explained for DP1, was also used in DP2. DP2took a long time to search the entire search space for an optimal solution. In orderfor the algorithm to execute in reasonable time, further downsizing of the searchspace had to be performed. The search space was further reduced by removing thevelocities and relative distances, which are less likely to be optimal.

The search space for the current step was determined based on the referencevelocity and relative distance profile. The reference velocity and relative distanceprofiles were the optimal profiles for the previous time step, which was generatedeither by DP1 or DP2 determined by the coordinator. The new search space isdefined as a small region above and below this reference velocity and distance. Inmost of the cases the fuel and time optimal profiles were within this region. In caseswhere the optimal profiles were not within this range, the algorithm converged to


Figure 4.5: Downsizing of velocity search space.

Figure 4.6: Downsizing of relative distance search space.

the optimal solution during the subsequent runs as the cost function is convex. Theconcept behind this method is taken from differential dynamic programming [17].Downsizing of the velocity and relative distance space are shown in Figure 4.5 and4.6 respectively.

Thus the algorithm had to search only a small portion of the actual search space,which drastically improves the time complexity. To make the downsizing algorithmmore effective; the entire horizon was divided into 4 overlapping segments, based


Figure 4.7: Splitting and further downsizing of velocity search space.

on the observations made on the variation of the profiles between subsequent runs.Depending on the variance and the maximum variation of the velocity and relativedistance between subsequent runs, the width of the region also varies among thesegments. This is illustrated in the Figure 4.7.

Relative Distance Disretisation

It was explained in the previous sections that the accuracy of the algorithm dependson the granularity of the search space, in other words the quantisation level. FromTable 4.1 it can be seen that the quantisation level chosen for relative distanceis 0.4m. The quantisation level chosen should be such that the discrete modelcaptures the actual dynamics of the system. The discrete model with grid size0.4m completely fails to capture slow changes in the distance, and such slow changeshappens very frequently during the simulation. One solution to this problem is toreduce the grid size to model even the slow changes, but this increases the timecomplexity drastically. Thus another solution had to be found for improving theperformance of the discrete model without reducing the quantisation levels.

In the standard case, a discrete state is denoted using a single value; this singlevalue is the discrete level corresponding to that state. The accuracy of the model wasimproved, without affecting the time complexity, by using a different representationof discrete states. In this case, each discrete state was represented using a pairof values. One of which is the discrete level corresponding to the state and theother one is the deviation of this discrete level from the actual state. Both thevalues were used for the calculation. Thus the loss in accuracy due discretisationwas compensated up to an acceptable limit due to presence of the error component


Figure 4.8: Accuracy of the relative distance model.

along with the value. Even though the discrete states are stored as pair of values,for the purpose of simplicity only discrete levels are plotted. The error is used onlyfor internal calculations. The result is shown in the Figure 4.8, it can be observedthat the predicted values of the relative distance and the actual values are very closefor both slow and fast changes.

The quantisation level of 0.4m for the relative distance along with the modifiedrepresentation made sure that the effective quantisation level is much smaller than0.4m without increasing the time complexity.

Algorithm

The approach followed in DP1 was a backward approach where the algorithm startsfrom the last horizon. In general for a look-ahead horizon, the uncertainty of allthe states grows towards the last horizon, i.e. there is more certainty for the valuestowards the first horizon. The search space has to make sure that the uncertaintyis not bigger than the search space itself. In case of DP2 the uncertainty of therelative distance was higher than the modified search space itself for some stagesin some cases. To deal with this uncertainty a forward approach was adopted forDP2, where the algorithm starts from the first horizon. In order to improve theperformance a reference follower was also added to the cost function, which will beactive only when the truck enters a level road.

During the execution of DP2, it was observed that many states for relative dis-tance in the downsized search space was impractical. To improve the performancefurther, the relative distance search space of each stage was limited further depend-ing on the results of the previous stage. This resulted in considerable reduction in


the distance search space. Along with this, for the cases in which the width of thesearch space was found too small, additional values for the states were added. Thusmaking the search space flexible and improving the overall performance.

At any stage k, let the status of the system be represented by xik which comprises

of velocity, gear and relative distance (v, g, d). Let ζi→jk denote the transition cost

when the truck velocity, gear and relative distance is changed from (v, g, d) in stagek to (v, g, d) in stage k + 1. Jk(xi

k) is the cost function of kth stage correspondingto xi

k. Then algorithm is as shown below.

1. The cost function of the 1st stage is J1 = 1.

2. k = 2

3. Calculate

Jk(xi) = minxj∈Sk−1

(ζj→ik + Jk−1(xj)), where xi ∈ Sk

4. k = k+1 and continue step 3 till k = N.

5. The cost function of the N th stage is JN + J∗N , where J∗N is the terminal cost.

6. min(JN ) is the optimal cost. The optimal velocity profile was derived using abackward pass on the search space using the results of step 3 and 4 startingfrom the optimal final state to initial stage.

The optimal velocity profile will be determined iteratively. The velocity profilethus determined will be optimal in the reduced search space on which the dynamicprogramming is done. The cost function is designed to be convex with only oneminima, which is at the optimal velocity. The set velocity is the optimal velocity ona level road. Once the relative distance is added to the cost function, this propertychanges slightly. This is because unlike the previous case, now the cost function alsodepends on the velocity of the other truck in a two truck platoon. The resultingcost function tries to keep the relative distance equal to 5m, which is considered asa safe distance between trucks in a platoon. Along with the relative distance, thecost function also tries to maintain the optimal or set speed, depending on the slope.The resulting total cost function will still be convex, but the minimum cost need notbe for the set or the optimal speed, it always depends on the velocity profile of thesecond truck. The reason is that each controller assumes that the other controllerhad already performed its best. Hence, it tries to match its profile with the profileof the other controller in terms of relative distance. In other words the convexityof the cost function also depends on the other truck. But new minimum will bevery close to the optimal velocity. This is explained with an example for a platoontravelling over a level road.


When the velocity profile of the second truck is the set speed, then the totalfunction is convex and the minimum cost corresponds to the set velocity. Butif the second truck have a velocity profile close to the set speed, then the costfunction has the minimum cost, when the velocity of both the trucks are equal.The reason is that, if the velocity of the truck had to be changed, then there isa corresponding change in the relative distance also, which is not preferred. Thereference follower tries to make the cost minimum at the set speed on a flat road,by reducing the dependency with the other truck. In case of slopes, this is handledby the coordinator.

Calibration

The disadvantage of determining the search space using the previous optimal pro-files is that, it can lead to reduced performance, the algorithm might breakdowncompletely or it might have an oscillatory behaviour. In order to avoid this, thewidth (width is the distance between the minimum and maximum values for eachstep) of the search space had to be high enough. As the width increases the timecomplexity increases and algorithm becomes more accurate and, as the width de-creases the performance and time complexity also reduces.

The values of the parameters were similar to the ones used in DP1. Parameterfor relative distance has to be calibrated here. Since there is a decrease in the fuelconsumption, there is a tendency to reduce the relative distance to a minimum. So ifthe relative distance is left unattended the trucks will eventually collide, as this is themost fuel optimal strategy but unsafe. To prevent this, a reference relative distancewas chosen. The weights were calibrated such that the cost function of the relativedistance look like the letter ’V’ as shown in the Figure 4.9. The lower tip of the’V’ represents the reference distance and the cost increases as the distance increasesfrom the reference distance. In order that fuel and time have more importance theweights assigned to distance was very small in the range 0.001 - 0.05. Even thoughthe value of the weight is small it had significant impact. A discounted weight wasused for the acceleration and the relative distance, i.e. a higher weight was used forthe last horizon and the magnitude of the weight reduced towards the first horizon.

4.6.3 Coordinator

Coordinator acts as a supervisor for the dynamic programming algorithms. Theinput to the coordinator is the output of DP1 and DP2. The coordinator at theoutput of DP1 checks the feasibility of the velocity profiles when applied to a pla-toon. The velocity profiles from DP1 were used for DP2, if the trucks could maintaina safe distance between them when moving in a platoon. If the profiles are not fea-sible, the coordinator will decide on a velocity profile. This profile ensures a safedistance between the trucks moving in a platoon. This is done by determining thefuel and time cost of all the combinations of DP1 profiles and then choose a pair


Figure 4.9: Cost function for relative distance. The blue dot indicates the cost whenthe relative distance is 4m.

with least cost. The profiles selected by the coordinator ensures a safe distance andthe velocity profile could be followed by the truck.

As each DP2 algorithm considers the profile of the other truck as the bestprofile, it completely ignores the fact that the other truck’s velocity profile mightnot be optimal or it can change. Hence DP2 algorithm tries to match its velocityprofile according to the other truck’s profile. This makes the relative distance verydominant in the cost function even though its weight is very low. The main role ofthe coordinator is to reduce this behaviour of DP2 and make it more independentof the other truck’s profile. Thus, ensuring that the profiles are not deviating fromthe optimal ones.

It compares the fuel and time cost of the DP2 velocity profile with the output ofDP1 (with all the combinations of DP1 profiles). If one combination of DP1 profilecan keep a safe distance and has a minimum cost, then it is selected over the DP2profile as the next reference profile. As the coordinator increases the overhead of thealgorithm, the execution was executed once in every 250-500m. The switching logicensures that there is no jump in the velocity profile given to the cruise controllerof the truck. In short, the coordinator can be considered as an evaluating functionwhich measures the performance of the velocity profiles, and resets DP2 if necessary.A simple block diagram is as shown in the Figure 4.10

The coordinator indirectly affects the terminal velocity profiles by making itmore smooth. The evaluating function of the coordinator does not have brake asa parameter, hence the resulting velocity might result in more braking than thatis expected from the dynamic programming algorithm. The coordinator can alsobe considered as a logic that mixes the output of DP1 and DP2 to obtain good

4.7. EXTENSION 37

Figure 4.10: Coordinator architecture.

performance. The switching logic, which decides when to switch between DP1 andDP2, is crucial for the effectiveness of the algorithm. The coordinator also preventsthe algorithms from getting stuck due to second truck as explained in the previoussection by reseting the reference profile.

4.7 ExtensionThe algorithm was extended for a platoon consisting of 3 trucks. The architectureis same as shown in Figure 4.3. There is one more DP1 and DP2 blocks and thecoordinator now handles all the six dynamic programming algorithms. The costfunction also slightly differs in case of extended platooning. The middle vehiclehas an additional factor. The cost function is as shown in (4.11), where d(2)

k is therelative distance between the middle vehicle and the vehicle behind and dk is therelative distance to the vehicle in front.

ζ =[1 α β γ ε ψ

]

mk

tkdk

gk

δvk

d(2)k

(4.11)

Cost function remains the same as in (4.5) for the first and last vehicle.

Chapter 5

Simulation Results

This chapter contains all the simulations that were performed using the controllerstrategy explained in the previous chapter. A comparison is also presented to evalu-ate the performance. The control strategy was tested under various load conditionsand different combinations of trucks in a platoon. Apart from this, the tests werealso performed under various road conditions (uphill and downhill). An overviewof the test strategies are shown below.

Load conditions:

1. Tests are performed on trucks with weight 30 tonnes and 20 tonnes only.

2. Truck length under test was 11m.

3. All the combination of the trucks in a two vehicle platoon is considered. Thecombination being, 30 and 20 tonnes, 20 and 30 tonnes etc.

Road conditions:

1. The slope conditions under consideration were uphill, downhill, uphill followedby downhill, downhill followed by uphill.

2. The uphill was always with 3% slope and downhill was always with -3% slope.

3. Slopes of lengths 500m and 1000m were tested.

The following control strategies were used for comparison:

1. Look-ahead platooning as mentioned in the previous chapter.

2. Adaptive cruise control strategy in which the truck tries to maintain the setspeed and relative distance.

A summary of the test strategies are shown in Table 5.1.

39

40 CHAPTER 5. SIMULATION RESULTS

Table 5.1: Test strategies.

Road conditions Load conditions Total slope lengthTwo truck platoon (20 and 30 tonnes trucks)

Uphill Heavier follower truck 500m and 1000mHeavier lead truck 500m and 1000m

Downhill Heavier follower truck 500m and 1000mHeavier lead truck 500m and 1000m

Uphill followed by downhill Heavier follower truck 1000m and 2000mHeavier lead truck 1000m and 2000m

Downhill followed by uphill Heavier follower truck 1000m and 2000mHeavier lead truck 1000m and 2000m

Real road Heavier follower truck 100 kmHeavier lead truck 100 km

Three truck platoon (20, 20 and 30 tonnes trucks)Uphill Heavier lead truck 1000m

Downhill Heavier in the middle 1000m

5.1 Uphill

The simulations are done on a 2.6 km stretch of road with a single uphill of length1000m and 500m. The magnitude of the weights for relative distances greater thanfive was kept low, i.e. slope of the curve for relative distance greater than five inFigure 4.9 was low. This emphasised the deviations in the relative distance. In anuphill, a 30 tonnes truck was not able to maintain a constant speed of 80 km/h. Thiscaused the adaptive cruise control strategy of the heavier truck to maintain a lowervelocity along the slope. At the same time, the lighter vehicle could maintain itsset speed. This also resulted in considerably different individual optimal velocities.The fuel and time optimal behaviour of the lighter truck was to cruise at the setspeed.

5.1.1 Case 1: Heavier Follower Vehicle

Table 5.2: Comparison of adaptive cruise control and look-ahead platooning strate-gies for a platoon with 30 tonnes and 20 tonnes truck.

Fuel(%) Time(%)hhhhhhhhhhhhhhhhhConfiguration

Slope length 1000m 500m 1000m 500m

Downhill Heavy follower truck 18.8 13.8 1.1 0Heavy lead truck 20.7 14.4 0.6 0

Uphill Heavy follower truck 4.8 3.5 0 -0.1Heavy lead truck 0.1 0 1.7 0.6

5.1. UPHILL 41

In this case a 30 tonnes truck was the follower and a 20 tonnes truck was thelead vehicle. The output of look-ahead platooning strategy with slope length 1000mis shown in Figure 5.1(a), and with slope length 500m is shown in Figure 5.1(b).In both the figures, the top plot represents the velocity of each truck, the middleplot represents the relative distance and the bottom one represents the altitudeprofile. Before the uphill both the trucks started to accelerate, the lighter leadtruck accelerated first until it reached a steady speed. Since the lighter one hadhigher speed the relative distance began to increase till it reached the steady speed.After a few meters the heavier follower truck also started to accelerate. Unlike thelighter truck, the heavier one continued to accelerate till it reached the maximumvelocity. As the lighter truck had a lower speed towards the end of the level road,the relative distance started to decrease. When the heavier truck entered the uphill,it started to decelerate and the relative distance continued to decrease. Once thevelocities of both the trucks were the same, they started to decelerate with thesame velocity. Towards the end of the uphill the heavier truck decelerated untilthe minimum velocity 75 km/h, while the lighter truck maintained a velocity higherthan 75 km/h. This increased the relative distance. After the uphill the heaviertruck accelerated, but the lighter truck maintained its velocity for some distance tomake sure that the relative distance was reduced to five meters at the end.

In this case, the individual optimal velocities led to a collision, if followed by theplatoon. The velocity of the lighter truck was modified to ensure a safe platoon.As the heavier truck was limited by its engine power, its profile remained verysimilar when compared to its optimal profile (30 tonnes truck on a 3% uphill).The adaptive cruise control strategy is shown in Figure 5.2. A comparison betweenadaptive cruise control strategy and look-ahead platooning is shown in Table 5.2.

It was observed that, during both the end and beginning of the uphill, thetrucks tend to increase the relative distance momentarily and then decrease. If theindividual optimal velocities were applied to the trucks in the platoon, the relativedistance decreases in the beginning. This would result in a collision of the trucks,during the first half of the slope. To prevent this collision, optimal look-aheadplatooning strategy increased the relative distance towards the end of the planeroad. This distance was later reduced during the uphill, when the lighter truckmaintained its velocity. The same can be observed at the end of the slope, where therelative distance was allowed to increase during the uphill and was decreased lateron the level road. Note that during uphill fuel was consumed while decelerating,to increase the average travel time. Hence, the relative distance was kept small toreduce the fuel consumption. For shorter and longer stretches of slopes the responsewas similar.


(a) An uphill of length 1000 m.

(b) An uphill of length 500 m.

Figure 5.1: Look-ahead platooning velocity, relative distance profile and correspond-ing altitude for an uphill with a heavier truck as the follower and lighter truck asthe lead truck.

5.1.2 Case 2: Heavier Lead Vehicle

In this case a 30 tonnes truck was the lead vehicle, driving in front of a 20 tonnestruck. The adaptive cruise control strategy is shown in Figure 5.3. The output oflook-ahead platooning strategy with slope length 1000m is shown in Figure 5.4(a)and, the results with a slope length 500 is shown in Figure 5.4(b). The plot setupis same as in Figure 5.1(a). The top plot is the velocity, the middle one is the

5.1. UPHILL 43

Figure 5.2: Adaptive cruise controller strategy for an uphill of length 500m with aheavier as the follower vehicle.

relative distance and the bottom plot is the altitude under which the simulationwas performed.

Unlike the case in which the heavier truck was the follower vehicle, the velocityand relative distance profiles for the longer and shorter slopes are much different.If the individual optimal velocities were applied to the trucks in the platoon, therelative distance increased during the first half of the slope and then decreased.This resulted in a safe platoon and the relative distance was maintained at 5m atthe end of the slope for both longer and shorter slope length. This had a significantimpact on the response and was clearly observed in case of a shorter slope length,where the relative distance did not increase much due to optimal behaviour. Itwas observed that the velocity of the lighter truck was very close to 80 km/h, whilethe heavier truck decelerated during the downhill and accelerated both before andafter the slope. The relative distance increased during the first half of the slope anddecreased during the second half.

In case of a longer stretch the optimal behaviour increased the relative distancemuch, which in turn increased the fuel consumption. Note that fuel was consumedduring the uphill also, which was required to maintain the travel time. To reducethe increase in the relative distance both trucks accelerated before the slope but thelighter one accelerated with a higher acceleration rate. This reduced the relativedistance at the beginning. The heavier truck accelerated to the maximum velocity,while lighter to a velocity lower than the maximum and maintained it, reducing therelative distance. As the lighter truck decelerate faster in an uphill, it deceleratedfaster and maintained the relative distance at 5m. Towards the end of the downhillthe lighter decelerated faster again and then it maintained a velocity higher thanthe minimum velocity, while the heavier decelerated till 75 km/h. This behaviour


Figure 5.3: Adaptive cruise control strategy for a uphill of length 500m with heaviertruck as the lead vehicle, driving ahead of a lighter truck.

increased and then decreased the relative distance.This results shows that the look-ahead platoon controller tried to maintain a

balance between the look-ahead control and platooning. In case of a shorter stretchthe look-ahead controller gained the upper hand. This was mainly because of tworeasons, one was that the increase in the relative distance was not much, the secondone was that the optimal behaviour does not have any effect on the platoon in thelong run i.e. the relative distance was 5m at the end of the slope. In case of alonger stretch the individual optimal profiles resulted in a higher relative distance.In order to reduce this the lighter truck followed the heavier for some distance, thencontinue to follow its optimal behaviour to maintain its velocity. The lighter truckcan decelerate faster when compared to a heavier truck in an uphill without usingbrakes. This was used to make sure that the relative distance was 5m, wheneverthere was a possibility of increase in relative distance during uphill.

As the adaptive cruise control strategy has a lower speed than the set speed, thefuel savings for the look-ahead platooning was not significant. Even though therewas no fuel savings, the total trip time was reduced. The fuel and time optimalvelocity profile was in between the individual optimal profiles.

5.2. DOWNHILL 45

(a) An uphill of length 1000 m.

(b) An uphill of length 500 m.

Figure 5.4: Look-ahead platooning velocity, relative distance profile and correspond-ing altitude for a platoon with heavier truck as the lead vehicle, and lighter follower.

5.2 Downhill

The simulations are done on a 2.6 km stretch of road with a single downhill of length1000m and 500m. The percentage of fuel savings was considerably high (21%) asthe simulation was done on very small stretches (2.6 km) of road.



In this case a 30 tonnes truck was the follower vehicle and 20 tonnes truck was thelead vehicle. The output of look-ahead platooning strategy with slope length 1000mis shown in Figure 5.5(a), and with slope length 500 is shown in Figure 5.5(b). Theadaptive cruise control strategy is same for both heavier follower and heavier leadconfigurations and is shown in Figure 5.6. A comparison between the adaptivecruise control strategy and look-ahead platooning is shown in Table 5.2.

The optimal behaviour for a truck in the downhill is to use the gravity as muchas possible to accelerate and maintain the speed without using any fuel or brake.In case of a longer slope, the weight of the truck is such that, both of them canbe accelerated to the maximum speed using gravitational force. To exploit this,both the trucks decelerated before the beginning of the slope. The heavier truckdecelerated first till it reached the minimum speed. After a few meters the lighterone also decelerated, but to a velocity higher than the minimum velocity. Since thelighter truck had a higher velocity, the relative distance increased. Once the trucksentered the slope both of them started to accelerate till they reached the maximumspeed. The heavier truck always accelerate faster compared to a lighter truck, thiscaused the heavier truck to gain more speed compared to the lighter one. Hencethe relative distance started to decrease. Towards the end of the slope, both thetrucks maintained the maximum speed and the relative distance at 5m. After theslope both the trucks decelerated to the set speed at the same rate.

In case of a shorter stretch the behaviour is slightly different. The downhill wasnot long enough to accelerate the lighter truck to the maximum speed without usingfuel. This would result in an additional decrease in the relative distance at the end,if the optimal behaviour is followed. The lighter truck entered the downhill witha slightly higher velocity than the heavier truck. Both of them accelerated at thesame rate during the first half of the slope. The heavier truck was coasting, whilethe lighter truck had to spend a small amount of fuel. During this acceleration thelighter truck had a slightly higher speed, which increased the relative distance. Inthe second half of the slope both the trucks started to coast. The heavier truckcoasted until the maximum speed, while the lighter truck could coast only to aspeed lesser than the maximum. This reduce the relative distance back to 5m.

A heavier truck accelerates faster in a downhill when compared to a lighter one.It was observed that, this fact was used by the control algorithm to derive an optimalcontrol strategy in case of a downhill. Note that both the trucks coasted as much aspossible. In case of a shorter slope length, the acceleration in the initial section wasrequired to avoid a collision at the end of the slope. If the lighter truck coast in thebeginning, it had to accelerate at the end. Thus it was clear from this simulationthat the trucks try to perform its look-ahead behaviour on the slope, as long asthe platoon is safe. In another perspective, it can also be considered that therewas a transition between a controller trying to maintain a platoon and a look-aheadcontroller at the edges of the slope. Due to the different objective of these controllersand decoupled nature of the control algorithm there were velocity fluctuations in

5.2. DOWNHILL 47

(a) A downhill of length 1000 m.

(b) A downhill of length 500 m.

Figure 5.5: Look-ahead platooning velocity, relative distance profile and correspond-ing altitude for a downhill with heavier truck as the follower and a lighter truck asthe lead vehicle.

most of the simulations. The velocity fluctuations were concentrated mainly on theedges of the slope where the transition happens. One more important observationwas that always lighter truck profiles were adjusted more when compared to theheavier truck, to make sure that the platoon was maintained.


Figure 5.6: Adaptive cruise control strategy for a downhill of length 500m withheavier truck as the lead vehicle.


In this case a 20 tonnes truck was the follower vehicle and a 30 tonnes truck was thelead vehicle. The output of look-ahead platooning strategy with slope length 1000mis shown in Figure 5.7(a), and with slope length 500m is shown in Figure 5.7(b).A comparison between adaptive cruise control strategy and look-ahead platooningis shown in Table 5.2. It can be observed that in this case the platooning wasmaintained. A small kink can be observed in case of a longer slope, which is due tothe discretisation of the velocity.

The optimal behaviour had a tendency to increase the relative distance at theend of the slope when heavier truck was the lead vehicle, which increased the fuelconsumption in the level road. Hence, the behaviour look-ahead platooning strategywas different from the previous case, where heavier truck is the follower, drivingbehind a lighter one. The strategy to use the higher acceleration of the heaviertruck resulted in a higher fuel consumption. This was because, the lighter onehad to be accelerated at the end of the slope or during the slope to maintain theplatoon distance, which increased the total fuel consumption. Hence, in this case theoptimal strategy was to maintain a platoon. It can be observed that the trucks tendto keep the relative distance at 5m even though the weights on the relative distancewere very relaxed. Compared to the previous case, this strategy will require morebraking without increasing the fuel consumption. The fuel is close to zero duringthe downhill, the required acceleration is achieved using brakes.

The adaptive cruise control strategy is same in case of heavier lead and heavierfollower configurations and is shown in Figure 5.6. For both the load configurations(heavier truck as lead and heavier truck as follower) the fuel consumption was very

5.2. DOWNHILL 49

(a) A downhill of length 1000 m.

(b) A downhill of length 500 m.

Figure 5.7: Look-ahead platooning velocity, relative distance profile and correspond-ing altitude for a downhill with heavier truck as the lead vehicle. Note that the scaleof the relative distance plot is higher compared to the other plots.

similar, but the fuel consumption when the heavier lead truck was the lead vehiclewas slightly lower.


5.3 Combination of Uphill and DownhillThe simulations were done on a 3.4 km stretch of road with a single uphill followedby a downhill with a total slope length 2000m. The same simulations were repeatedfor a total slope length of 1000m also. All four cases that were explained in sections5.1 and 5.2 were repeated with a stricter weight for relative distances greater thanfive, i.e. slope of the curve for relative distance greater than five in Figure 4.9was high. The fuel consumption and the travelling time were very close and thevelocity profiles were very similar when compared to the case with relaxed weighton relative distance. Based on these results, for the configurations with heaviertruck as the follower vehicle, the weights were such that the relative distance couldincrease during the slopes. In case of heavier truck as the lead vehicle, the variationsof relative distance were more restricted. This just made sure that the profiles aresmooth. It was observed that, in general the results that were obtained were acombination of the profiles that were obtained in the previous simulations.

Table 5.3: Comparison of adaptive cruise control and look-ahead platooning strate-gies for a platoon with 30 tonnes and 20 tonnes truck.

Fuel(%) Time(%)XXXXXXXXXXXPlatoon

Slope 2000m 1000m 2000m 1000m

Downhill and Uphill Heavy follower 13.8 11 -0.2 -0.2Heavy lead 8.8 8.4 1.3 0.3

Uphill and Downhill Heavy follower 10.5 9.5 1.4 0.2Heavy lead 6.6 6.4 2 0.8


In this case a 30 tonnes truck was the follower and 20 tonnes truck was the lead vehi-cle. The output of look-ahead platooning strategy with uphill followed by downhillof total length 2000m is shown in Figure 5.8(a), and with a downhill followed byuphill slope of total length 2000 is shown in Figure 5.8. The corresponding plots fora shorter slope lengths are shown in Figure 5.9(a) and Figure 5.9(b) respectively.The adaptive cruise control strategy for a downhill followed by an uphill is shownin Figure 5.10(a), and with an uphill followed by a downhill is shown in Figure5.10(b). A comparison between the adaptive cruise control strategy and look-aheadplatooning is shown in Table 5.3. The fuel and time optimal strategy was that eachtruck coasts during downhill, and decelerate during uphill if the velocity cannot bemaintained.

The same behaviour as seen in the above cases can be observed in case of com-binations of uphill and downhill also. The look-ahead platooning strategy is acombination of case 1 of downhill and case 1 of uphill. In case of downhill followedby a uphill, at the beginning of the downhill the relative distance was increased,

5.3. COMBINATION OF UPHILL AND DOWNHILL 51

(a) An uphill followed by a downhill with a total slope length of 2000 m.

(b) A downhill followed by an uphill with a total slope length of 2000 m.

Figure 5.8: Look-ahead platooning velocity, relative distance profile and correspond-ing altitude with heavier truck as follower, driving behind a lighter truck.

so that it could be reduced due to the optimal behaviour along the downhill. Atthe end of the uphill, the relative distance which was increased due to the optimalbehaviour along the uphill was reduced on the level road. In case of uphill followedby a downhill the same behaviours can be seen. When the trucks enter the downhillafter uphill the lighter had a higher velocity than the heavier truck. This enabledthe relative distance to increase and then decrease, when the trucks are coasting.

In case of a shorter slope length, the behaviour along the uphill is similar to the




Figure 5.9: Look-ahead platooning velocity, relative distance profile and correspond-ing altitude with heavier truck as follower, driving behind a lighter truck.

case in which the slope is longer. Unlike uphill, during a shorter downhill the slopelength was not enough to accelerate the lighter truck to the maximum speed. Thisresulted in the reduction of the relative distance as the heavier truck accelerated toits maximum speed. In order to compensate this reduction, the relative distancewas increased at the beginning of the slope. Finally the velocity profile was changedsuch that, the relative distance is still 5m at the end. The final fuel and time optimalprofiles of the platoon is in between the individual optimal velocity profiles of eachtruck.


(a) An uphill followed by a downhill of total length 1000 m.

(b) A downhill followed by an uphill of total length 1000 m.

Figure 5.10: Adaptive cruise control strategies with heavier truck as the follower,driving behind a lighter truck.

The trucks cannot follow the output of DP1 as it leads to a collision betweenthe trucks. Hence, a new velocity profile was determined. It was observed thatthe heavier truck tend to preserve its optimal velocity profile, and the lighter oneadjusted its profile to ensure a safe and fuel and time optimal platooning. Thiswas expected as the heavier truck was limited due to its weight especially duringthe uphill. For the optimal behaviour, the trucks had to accelerate or decelerateas much as possible without using brake or fuel. This behaviour was observed as


long as the relative distance was not too high or small. To make sure that therelative distance is within the limits while optimally accelerating or decelerating,the relative distance was adjusted mainly in the region where the slope changes i.e.beginning or end of the slope or at both regions.


(a) An uphill followed by a downhill with a total slope length of 2000 m. Note that the scale ofthe relative distance plot is higher compared to the other plots.


Figure 5.11: Look-ahead platooning velocity, relative distance profile and corre-sponding altitude with lighter truck as follower, driving behind a heavier truck.


(a) An uphill followed by a downhill with a total slope length of 1000 m. Note that the scale ofthe relative distance plot is higher compared to the other plots.


Figure 5.12: Look-ahead platooning velocity, relative distance profile and corre-sponding altitude with lighter truck as follower, driving behind a heavier truck.

In this case a 30 tonnes truck was the follower vehicle and a 20 tonnes truckwas the lead vehicle. The output of look-ahead platooning strategy with uphillfollowed by downhill of total length 2000m is shown in Figure 5.11(a), and withdownhill followed by uphill slope of total length 2000m is shown in Figure 5.11(b).The corresponding plots for a shorter slope lengths are shown in Figure 5.12(a)and Figure 5.12(b) respectively. The adaptive cruise control strategy are shown inFigure 5.13(a) and 5.13(b). A comparison between adaptive cruise control strategy




Figure 5.13: Adaptive cruise control strategies with lighter truck as the follower,driving behind a heavier truck.

and look-ahead platooning is shown Table 5.3.When compared to the case in which the heavier was the follower driving behind

a lighter one, the algorithm is less oscillating and more smooth. The reason for thisbehaviour is that if the heavier truck is the lead, the individual fuel and time optimalvelocity profiles were safe for a platoon to follow in most of the cases (these velocitieswill not lead to a collision). In this case also, the fuel and time optimal velocity forthe platoon is in between the individual optimal velocities. It was observed thatthe velocity profiles followed the same strategies that were observed in the previous

5.4. EXTENDED PLATOON 57

cases. Apart from this, it was noted that fuel consumption was the lowest when theheavier truck was the lead vehicle. This simulation results also supports the factthe platooning is more important in case of level road and look-ahead behaviouris more important in a slope, and the transition between them happens during theedges of the slope.

5.4 Extended PlatoonThe control strategy was extended for a three vehicle platoon. The simulationresults are shown in Figure 5.14 and Figure 5.15. Two cases that was under consid-eration was a single uphill and a downhill of length 1000m. The comparison withadaptive cruise control strategy is shown in Table 5.4.

A platoon with a heavier in between two lighter truck was simulated along adownhill. The results are as shown in Figure 5.14. It was observed that the lighterlead, driving in front of a heavier truck behaviour was similar to case 1 of downhill,where the relative distance increased in the beginning and then decreased. Thelighter last and the heavier middle truck behaviour was similar to the case 2 ofdownhill, where the optimal strategy was to maintain the platoon. The influence ofthe third vehicle can be clearly seen in the magnitude of the relative distance. Therelative distance between the first and the middle truck was not allowed to increasemuch, as it affected the performance of the last one. Similarly, the relative distancebetween the last and the middle truck was influenced by the presence of the firstone.

A platoon with a heavier in front of two lighter truck was simulated along anuphill. The results are as shown in Figure 5.15. It was clear that the results were incompliance with the previous observations. The behaviour of the front and middlevehicle was similar to that of a two vehicle platoon with a heavier lead truck ridinguphill. The lighter third truck follows the middle one and maintains a small relativedistance between them. It is noted that the velocity of the first truck did not reachthe minimum allowable velocity as in the case of a two truck platoon. Thus even ina three truck platoon, each truck tend to follow the strategies that were observed inthe corresponding two truck platoon. But, velocity profiles were slightly differentto ensure the performance of the third truck.

Table 5.4: Comparison of adaptive cruise control and look-ahead platooning strate-gies.

`````````````Configurationsavings Fuel(%) Time(%)

Uphill 30 tonnes in front of two 20 tonnes trucks 0 1.7Downhill 30 tonnes in between two 20 tonnes trucks 18.9 1.1


Figure 5.14: Look-ahead platooning velocity, relative distance profile and corre-sponding altitude for a downhill of length 1000m with heavy in between two alighter trucks.

Figure 5.15: Look-ahead platooning velocity, relative distance profile and corre-sponding altitude for a downhill of length 1000m with heavy in front of two alighter trucks. Note that the scale of the relative distance plot is higher comparedto the other plots.

5.5. REAL ROAD 59

5.5 Real Road

(a) Heavier truck as the follower vehicle.

(b) Heavier truck as the lead vehicle.

Figure 5.16: Real road simulation results for a 20 tonnes and 30 tonnes truck.

The control strategy was simulated on a real road condition. The section underconsideration was a 100 km stretch between Södertälje and Norrköping. Simulationswere done for a two truck platoon with both heavier truck as the follower and asthe lead vehicle configurations. The results of the 100 km stretch of road are asshown in the Figure 5.16(a) and 5.16(b). From the whole profile it was observedthat the deviations in the relative distance from the reference was less in case of


Table 5.5: Comparison of adaptive cruise control and look-ahead platooning strate-gies.

`````````````Configurationsavings Fuel(%) Time(%)

Real road Heavier leading 2.6 0Heavier following 3.9 0.3

heavier leading configuration. This denotes that the heavier leading configurationprefers to retain the platoon more than the heavier follower configuration. In table5.5 the heavier leading configuration has lower fuel savings when compared to theheavier following configuration due to the adaptive cruise control strategy. Notethat the scale of the relative distance plot is higher compared to the other plots.

5.6 Summary

To summarise it was observed in general that, the fuel and time optimal strategy fora truck along the downhill is to accelerate as much as possible using gravitationalforce. Similarly, along an uphill the optimal strategy is to maintain the speed ifpossible. If the speed cannot be maintained, accelerate before entering the uphilland adjust the speed along the uphill such that the average travel time is notreduced. In a platoon each of the trucks tend to follow the above strategies, butwhen these are followed the relative distance either decreases or increases dependingon the platoon. In order to avoid a collision or a large relative distance at the end ofthe slope, the relative distance was adjusted in the regions where the slope changes.For example, this change can happen at the beginning of the downhill, end of the flatroad or at both the places. In general it was observed that if the individual optimalprofile reduces the relative distance, then the relative distance was increased beforeor at the beginning of the slope. If the optimal individual velocity tend to increasethe relative distance, then it was reduced at the end of the slope, in order to havebetter strategy the relative distance was reduced little before the slope. Irrespectiveof the behaviour during the slope, there was a strong tendency for the trucks toreduce the relative distance and maintain the platoon during flat road and whenthe slope is low. A summary of all the simulations performed is presented in Table5.6.

It was observed that the performance of the platoon did not differ much for alarge range of weights for the relative distance. Hence, the best strategy will beto select the weights, which offer a practical solution. Apart from this it was alsoobserved that it is always a good strategy to maintain a strict platoon, provided theengines are identical. This control strategy uses decentralised approach to determinethe optimal solution. It was also observed that there is a dependency between theweights in the cost function and the weight of the truck, when velocity fluctuationsand performance were considered. Calibration affects the regions where the slope

5.6. SUMMARY 61

Table 5.6: Summary of the simulation results.

Two truck platoon (20 and 30 tonnes trucks)Fuel(%) Time(%)

`````````````PlatoonSlope length 1000m 500m 1000m 500m

Downhill Heavy follower 18.8 13.8 1.1 0Heavy lead 20.7 14.4 0.6 0

Uphill Heavy follower 4.8 3.5 0 -0.1Heavy lead 0.1 0 1.7 0.6

`````````````PlatoonSlope length 2000m 1000m 2000m 1000m

Downhill and Uphill Heavy follower 13.8 11 -0.2 -0.2Heavy lead 8.8 8.4 1.3 0.3

Uphill and Downhill Heavy follower 10.5 9.5 1.4 0.2Heavy lead 6.6 6.4 2 0.8

`````````````PlatoonSlope length 100 km 100 km

Real road Heavy lead 2.6 0Heavy follower 3.9 0.3

Three truck platoon (20, 20 and 30 tonnes trucks)`````````````Platoon

Slope length 1000m 1000m

Uphill Heavy lead 0 1.7Downhill Heavy in the middle 18.9 1.1

changes, when compared to other regions like level road, uphill, downhill etc. Forthe simulations presented here a common weight, which gave a good performancewas chosen. It can be observed that some of the results have velocity fluctuationsand some are more smooth. Simulations on a shorter slope gave more flexibility forthe heavier truck to change its velocity profile.

In this approach, a truck does not have any information regarding the othertrucks except the relative distance and the velocity profile. This resulted in velocityfluctuations that can observed commonly in the results, which can be eliminatedusing proper weights. The simulations were also performed for trucks with lengthmore than 15m. It was observed that the fuel saving also depend on the lengthof the truck. This is because if the net distance between the truck was more than20m (including truck length and relative distance), there was a small difference inthe fuel saving.

In general it was observed that, with this calibration fuel consumption was lowerwhen the heavier truck is the lead vehicle. At the same time, the fuel savings is mostwhen the heavier truck is the follower, when compared to adaptive cruise controllerperformance. This difference is due to the adaptive cruise control behaviour. It


is noted that, by changing the calibration parameters it is possible to attain thesame fuel consumption for all the configurations, without changing the trip timemuch. Apart from this it was also observed that, when heavier truck is the leadvehicle, the deviations in the relative distance is low. In other words a heavier leadconfiguration prefers to maintain a small relative distance, when compared to theheavier follower configuration.

Chapter 6

Conclusion

A look-ahead platooning controlling strategy was developed with the aim of re-ducing the total fuel consumption and at the same time maintaining a reasonabletravel time. The controller make use of the information regarding the road ahead.The strategy is an iterative approach using a tailored and truncated dynamic pro-gramming. The implementation was a challenge due to very high computationalcomplexity of the algorithm. The actual algorithm was tailored resulting in an op-timised algorithm that could run with a much reduced computational complexity.Several strategies were implemented to avoid numerical errors and to make the al-gorithm stable and robust enough for different type of terrains, truck length, truckspecifications etc. The final algorithm could yield a smoother velocity profile in lessthan one tenth of the initial time estimate.

The first stage of this thesis was to analyse the effect of road topology on aheterogeneous platoon. The study started with an implementation of a simple PIcontroller that could simulate the optimal behaviour of a truck on an uphill anddownhill. The results showed intermittent braking and acceleration along the slopeeither to keep a safe distance between the trucks or to avoid an increase in therelative distances, denoting the possibility of another solution. The next stagewas to incorporate the look-ahead control strategy, which can save up to 3% fuelwhen a single truck is considered, in to platooning. A controller which incorporatesboth look-ahead control for single and multiple trucks was used for this purpose.The controller was initially implemented for two trucks and was expanded to threetrucks.

The simulation results showed that considerable fuel savings can be achieved fora platoon using the look-ahead strategy. In addition to the savings due to platooningthe real road simulation showed that, look-ahead strategy can achieve 3.9% and2.6% fuel savings for a platoon of 30 and 20 tonnes truck, when heavier truck wasthe follower and heavier truck was lead respectively. The observations made fromthe simulations suggest that even though the trucks are moving in a platoon, theyshould make use of gravitational force to accelerate as long as possible. The controlstrategy enables the trucks to do so without endangering the safety of the platoon

63

64 CHAPTER 6. CONCLUSION

or increasing the aerodynamic losses in the long run. This is achieved by adjustingthe relative distance appropriately, during the beginning or at the end of the slope.The results also showed that the heavy follower platoons had more fuel savings, atthe same time a platoon with heavier truck as the lead vehicle, had the least fuelconsumption. Even though the relative distance was more sometimes; in generalthe strategy tend to keep a relative distance as small as possible, which in turnreduce the aerodynamic losses. The expanded look-ahead platooning also followedthese tendencies.

To conclude, the controller basically decided when the platooning and look-ahead control should take the role in controlling the trucks. On a level road and onsmall slopes the platooning controller leads the platoon, which make sure that theaerodynamic losses are less at the same time keeping the platoon safe. During theuphill and downhill, the look-ahead controller tend to play an active role as muchas possible. The platoon controller’s role is to make sure that the platoon is withinthe safety conditions and the relative distance is not increasing much. The regionswhere the slope changes is where the calibration comes to play, it decides how big therole of look-ahead is and how much deviation is allowed, which is acceptable for theplatoon controller. The results suggest to choose a calibration, which gives the mostpractical profiles, as the performance were close for a large range of calibrations.

Future Work

For the algorithm to work efficiently, the trucks should have more accurate veloc-ity controller, the reason is that even a relatively small relative velocity differencecan lead to an increase or decrease of the relative distance. This problem can besolved upto a limit by using a relative distance controller that can maintain theoptimal relative distance determined by the algorithm. Even though the runtimewas reduced more than one tenth of the actual one, it has to be reduced furtherin order to make it real time. This can be achieved by limiting the search spacefurther. Another suggestion is to design a simpler controller, which can incorporatethe results of an optimal controller. Such a controller had to be designed based onthe results of an optimal controller, so that it does not have to rely on the optimalcontroller every time to calculate the control signal. In short, the controller shouldbe able to generate a control signal, which is close to the optimal control signalwithout using an optimal controller.

For the purpose of analysis a longer horizon (2000m) was used in this thesis,experiments showed that the velocity profiles generated were stable and yieldedsimilar results when a shorter horizon (1500m) was used. In [10] and [11], it wasshown that the performance remains same as the look-ahead horizon was increasedfrom 1500m to 2000m. Apart from this, a higher step size also can be used (30m)by using Runge Kutta method to solve the state space equations. These results arealready shown in [10] and [11]. Along with these, to measure the actual performanceof the controller a sensitivity analysis could be performed.

Bibliography

[1] A week without truck transport: Four regions in Sweden. Swedish associationof road haulage companies, 2009.

[2] EU energy trends to 2030 -update 2009, European commission - Directorategeneral for energy.

[3] A. Alam, Fuel-Efficient Distributed Control for Heavy Duty Vehicle Platooning,Licentiate thesis, Royal Institute of Technology, SE-100 44 Stockholm, Sweden,2011.

[4] A. Alam and A. Gattami and K. H. Johansson Suboptimal Decentralized Con-troller Design for Chain Structures: Applications to Vehicle Formations, 50thIEEE Conference on Decision and Control and European Control Conference,Orlando, FL, USA, 2011.

[5] A. Alam, A. Gattami, K. H. Johansson, and C. J. Tomlin. Establishing safetyfor heavy duty vehicle platooning: A game theoretical approach. In 18th IFACWorld Congress. Milan, Italy, 2011.

[6] R. E. Bellman and S. E. Dreyfus. Applied Dynamic Programming. PrincetonUniversity Press, Princeton, New Jersey, 1962.

[7] D. J. Chang and E. K. Morlok. Vehicle speed profiles to minimize work and fuelconsumption. Journal of transportation engineering, 131(3): 173- 181, 2005.

[8] A. Fröberg, E. Hellström, and L. Nielsen. Explicit fuel optimal speed profilesfor heavy trucks on a set of topographic road profiles. In SAE World, Congress2006, number 2006-01-1071.

[9] A. Fröberg and L. Nielsen. Optimal fuel and gear ratio control for heavy truckswith piece wise linear engine characteristics. In 5th IFAC Symposium on Ad-vances in Automotive Control, Monterey, CA, USA, 2007.

[10] E. Hellström, M. Ivarsson, J. Aslund, and L. Nielsen. Look-ahead control forheavy trucks to minimize trip time and fuel consumption. Control EngineeringPractice, 17(2):345-254,2009.

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[11] E. Hellström, J. Aslund, and L. Nielsen. Design of an efficient algorithm forfuel-optimal look-ahead control. Control Engineering Practice, in press, 2010.

[12] E. Holma. Data Requirements for a Look-Ahead System. Master thesis,Linköpings universitet, SE-581 83 Linköping, Sweden (2011).

[13] W. Huang, D. M. Bevly, S. Schnick, and X. Li. Using 3D road geometry tooptimize heavy truck fuel efficiency. Proceedings of the 11th International IEEEConference on Intelligent Transportation Systems, Beijing, China, October 12-15, 2008.

[14] Y. Kuwata and J. P. How. Robust Cooperative Decentralized Trajectory Op-timization using Receding Horizon MILP. Proceedings of the 2007 AmericanControl Conference Marriott Marquis Hotel at Times Square New York City,USA, July 11-13, 2007.

[15] W. Levine and M. Athans. On the optimal error regulation of a string of movingvehicles. IEEE Transactions on Automatic Control, 11(3): 355- 361, 1966.

[16] K.-Y. Liang. Linear Quadratic Control for Heavy Duty Vehicle Platooning.Master thesis, Royal Institue of Technology, Osquldas väg 10, 100 44 Stock-holm, Sweden (2011).

[17] J. Morimoto, G. Zeglin, C. G. Atkeson. Minimax Differential Dynamic Pro-gramming: An Application to Robust BipedWalking, in Advances in NeuralInformation Processing Systems 14, 2002.

[18] J. Rich, C. O. Hansenfreight transport trends for 2020, 2030 and 2050„ Euro-pean commission DG TREN 7th research framework programme.

[19] A. Schwarzkopf and P. Leipnik. Control of highway vehicles for minimum fuelconsumption over varying terrain. Transportation Research, 11(4): 279- 286,1977.

[20] P. Varaiya. Smart cars on smart roads: Problem of control. IEEE Transactionson Automatic Control, 38(2), 1993.

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