Winter Test of ABD Steering Robot

RESEARCH REPORT

Department of Computer Science, Electrical and Space Engineering Division of EISLAB

ISSN: 1402-1528 ISBN 978-91-7439-845-8 (pdf) Luleå University of Technology 2014 Winter test of ABD steering robot

Håkan Fredriksson Niclas Engström Jeremy Ash

June 19, 2013, rev 1.0 Winter test of ABD steering robot

H˚akan Fredrikssona, Niclas Engstr¨oma, Jeremy Ashb aLule˚aUniversity of Technology bAnthony Best Dynamics

Supported by: ISSN: 1402-1528 ISBN 978-91-7439-845-8 (pdf) Luleå 2014 www.ltu.se Preface

This report comprise the winter test of a steering robot that were performed during the winter 2012/2013 in Sweden. The scope for the test was to evaluate if, and subsequently how, a path-following steering robot can be used for winter test of cars. This work was performed within the Centre for Automotive Systems Technologies and Testing (CASTT) at Lule˚aUniversity of Technology, together with Anthony Best Dynamics. The objective was to support the vehicle test region in the northern part of Sweden by elaborating new test tools and methods. The work was funded by the European Regional Development Fund (ERDF). The main author is H˚akan Fredriksson. Niclas Engstr¨om has been involved in the planning and execution of the experiments and partly writing of the report. Jeremy Ash supplied training on the steering robot and participated in early parts of the tests.

Lule˚aJune 2013 H˚akan Fredriksson

iii iv Abstract

This report highlights the use of a steering robot with path-following for car testing in winter conditions. The steering robot was provided from Anthony Best Dynamics. Experiments have been made with a couple of commonly used test sequences (lane change, dual lane change, constant radius circle, handling), the result from these test are shown and discussed. The path-following algorithm gives steering commands to the car (replace the human driver), these commands affect how the car will move; hence, the car performance is affected by the behaviour of the path-following algorithm. The settings of the path-following algorithm greatly affect the car response in different situations. This is especially noticeable when the car starts to slide, a situation common when driving on a slippery winter road. The main focus for this report is to describe what happens when you push the path-following system to, and beyond, the physical limitations concerning road grip and vehicle speed. A theoretical analysis of the path-following algorithm and how it reacts on large lateral errors and high sideslip angles was done. As shown in the results, the evaluated path-following test sequences in general did work out well. Some characteristics of the algorithm, especially noticeable when driving in winter condition, were found and discussed. The overall impression is that the ABD steering robot with path-following can indeed be useful for repetitive test in winter conditions with bad road grip.

v vi Contents

Preface iii

Abstract v

Contents vii

1 Introduction 1 1.1 Steeringrobot...... 1 1.2 ABDpath-following ...... 2 1.3 Relatedwork ...... 3 1.4 Thisreport ...... 3

2 Method 4 2.1 Equipment ...... 4 2.2 Testsite...... 6 2.3 Testprocedure ...... 6 2.4 Dataprocessing...... 7

3 Result 8 3.1 Theoreticalanalysis ...... 8 3.2 Experimentaltests ...... 11 3.2.1 Testmanoeuvres ...... 11 3.2.2 PF-settings ...... 13 3.2.3 Othernotes...... 17

4 Discussion 19 4.1 Conclusion ...... 19 4.2 Futurework...... 20

Bibliography 20

Appendices

A Single Lane Change 22

B Double Lane Change 31

C Constant Radius Circle 33

D Handling Track 34

vii viii Chapter 1

Introduction

This report discusses the experience of using one of Anthony Best Dynamics (ABD) steering robots, with path-following capability, for winter test of a car. The ABD steering robots are commonly used for vehicle testing in situations where high repeatability is of importance and/or the safety of a human driver is in danger.

1.1 Steering robot

A steering robot is a device that can be mounted inside of a vehicle, on top of, or instead of, the steering wheel, see Figure 1.1. The device is controlled by a programmable computer and replaces the steering input that the human driver normally gives as input when driving. Using the steering robot system a steering manoeuvre can be repeated over and over again in a precise manner.

Figure 1.1: ABD SR30 steering robot installed in a Volvo V70.

There are mainly two approaches when using a steering robot for vehicle testing. The ﬁrst is open loop control, and the second is closed loop control, of the angle of the steering wheel.

1 1.2. ABD PATH-FOLLOWING CHAPTER 1. INTRODUCTION

Table 1.1: List of symbols.

α Angle to aimpoint Θ Vehicle heading offset γ Angular error due to lateral offset b Lateral offset q Projected lateral error due to heading offset v Vehicle forward velocity lad look ahead distance Kp(v) Proportional gain function p(v) Preview distance function LAC Look Ahead Constant P Proportional gain I Integral gain D Differential gain

Using the open loop control the steering wheel is turned in an exact predefined pattern. There are today several different test sequences defined for these kinds of static steering manoeuvres, Sine-dwell and the Fishhook test are two examples of such tests. Using closed loop control the vehicle position and orientation is continually compared with a predefined drive path, i.e. path-following. If the vehicle deviates from the path, the controller tries to compensate for this and strives to steer the car back to the track.

1.2 ABD path-following

The path-following algorithm in the ABD robot controller is primarily implemented according to paper [1]. It is described as ”...essentially a proportional feedback controller on ’path error’...” [1] where the path error is defined as the projected lateral position offset at a specified distance in front of the vehicle. I.e. the algorithm utilise a look ahead distance, lad to find out if the vehicle, given its current position and orientation, will end up on the defined track at a certain distance ahead. If not, the controller will control the steering angle to steer the vehicle back towards the track. A list of the most commonly used symbols throughout the report is shown in Table 1.1. The path-following controller is implemented as a PID-controller, using the projected path error as input. Figure 1.2 shows the key aspects on how the error is defined. The path error can be divided into two parts: the lateral error b due to the vehicle not located on the path, and the projected lateral error q due to the vehicle heading not pointing in the desired travel direction. Hence, the total path error used as input to the controller is b + q. Regarding path-following, there are mainly four parameters to tune when setting up the ABD steering robot in a new vehicle, the Proportional gain P , Integral gain I, Differential gain D, and the Look ahead constant LAC. As described in the paper [1], both the proportional gain, as well as the look ahead distance (a.k.a. preview distance), are speed dependent according to given functions, namely

2 Kp(v)= −0.99v − 7.1v + 602.2, v ≤ 15m/s 2 Kp(v) = 61380/v , v> 15m/s (1.1) and 2 p(v) = 0.0227v − 0.0671v + 1.6781 (1.2) respectively.

2 CHAPTER 1. INTRODUCTION 1.3. RELATED WORK

Y Aimpoint b q

α γ ϴ lad

Figure 1.2: Description of the path error used in the path-following controller. The vehicle (shown as a tricycle) is set to follow a straight line located on the y-axis.

If desired by the user, these functions may be adjusted. However, throughout the tests presented in this report these functions where left unchanged. When changing the parameters P or LAC, the output from these two functions is scaled accordingly. Hence, the look ahead distance lad is calculated with LAC ∗ p(v) and the proportional gain used in the controller is P ∗ Kp(v).

1.3 Related work

So far there is not much written knowledge and experience for the use of steering robot in winter conditions. The Swedish research institute VTI has made some experiments aiming at testing the ESP system of a car [2] and provoking over steering on ice and snow with diﬀerent winter tires [3]. However, in these tests they only use static pre-programmed steering manoeuvres (sine with dwell). No feedback control based on the vehicle position is used.

1.4 This report

The experiments described in this report focus on the use of closed loop control of the steering angle of the car, i.e. path-following, on road surfaces like snow and ice. Extensive tests have been performed on a test track located on a frozen lake. Several diﬀerent test manoeuvres has been performed and evaluated. The main question this report tries to answer is: • What happen when you push the path-following system to, and beyond, the physical limitations concerning road grip and vehicle speed? This is something that does indeed occur when driving during winter conditions on low friction surfaces such as ice and snow. One important part when winter testing cars is to provoke the car in such a manner so that the Electronic Stability Control (ESC) of the car is activated. How well does the path-following algorithm cope with under-steering and over-steering behaviour of the car? To fully understand the details in this report it is necessary to know how the path-following algorithm used in the ABD steering robot works. This is described in paper [1].

3 Chapter 2

Method

This chapter describes the prerequisite for the test and evaluation of the ABD steering robot with path-following in winter conditions.

2.1 Equipment

For the tests, a steering robot system was made available by ABD. The steering robot mounted in the test vehicle can be seen in Figure 1.1. A motion pack from Oxford Technical Solution (OxTS) is used to keep track of the vehicle position and orientation (pose). A reliable and accurate estimate of the vehicle pose is crucial for the path-following algorithm to function properly. Figure 2.1 show the drive electronics for the steering robot and the OxTS motion pack mounted in the trunk of the test vehicle.

Figure 2.1: OxTS motion pack (red box), battery unit (silver box) and control electronics (blue box) for the steering robot, ﬁrmly secured to the ﬂoor in the trunk of the test vehicle.

As test vehicle the Volvo V70 station wagon seen in Figure 2.2 was obtained. This vehicle was chosen since it is a common car in Sweden and it has good load capability. Furthermore, two diﬀerent tires were used during the tests presented in this report: the Standard Reference Test Tire, and the Bridgestone Blizzak Nordic, non-studded winter tire.

4 CHAPTER 2. METHOD 2.1. EQUIPMENT

Figure 2.2: Winter test of ABD steering robot in a Volvo V70 station wagon. The tests were performed on an ice track located on a frozen lake.

Details about the equipment used are found in the following bullet list.

• Steering robot system

– SR 30, ABD Steering robot [4]

– Omni(3), ABD control unit

– P3821C Battery unit

• Motion pack (Inertial and GPS)

– RT2002, Oxford Technical Solutions [5]

– GPS-Base, Oxford Technical Solutions [6]

– Satel radio modem

• Test vehicle and tires

– Volvo V70 Station wagon Year 2011 DRIVe, diesel engine Front wheel drive

– Standard Reference Test Tire (SRTT) Non-studded tire Dimension: 225/60 R16

– Bridgestone Blizzak Nordic (Blizzak) Non-studded winter tire Dimension: 205/55 R16

5 2.2. TEST SITE CHAPTER 2. METHOD

2.2 Test site

The tests were performed at a test site, owned and maintained by the company LAPICE, located in the village Mal˚ain the northern part of Sweden. The actual test site was located on top of the ice of the frozen Mal˚alake. As seen in Figure 2.3, the tracks consisted of a large open area, approximately 400m long and 60m wide, and a 1.1km long handling track. Due to the characteristics of the surface (packed snow) and the fact that a path-following steering robot makes the test vehicle drive more or less on the same spot over and over again, the surface of the tracks needs to be maintained from time to time. Figure 2.4 shows the preparation of the handling track.

Track layout 50

Polished ice 0 Packed snow

−50 Handling start

−100

−150 Position [m]

−200

−250

−300 0 50 100 150 200 250 300 350 400 450 500 Position [m]

Figure 2.3: Track layout of the test site in Mal˚a, one large open area and one handling track. The areas surrounded by red lines consists of polished ice, all other surfaces consist of packed snow on top of rough ice. The circle on the left side of the large open area is used for constant radius tests.

2.3 Test procedure

In order to get a solid understanding of the path-following behaviour when driving on roads with bad grip, four different test manoeuvres where performed. Focus for the tests has been to provoke the test vehicle into heavy under- or over-steering behaviour, i.e. the combination of tire-road grip, steering command, and vehicle speed should be kept at a level where it is not physically possible to follow the predefined path. In this way the behaviour of the path-following steering robot, when used for winter test of cars, can be studied. The steering robot system used during these tests only control the steering wheel. Gear-change, throttle, and brake have to be manually manoeuvred. Hence, the human driver is necessary and plays an important role in maintaining the requested vehicle speed. The four different test manoeuvres were Single lane change, Double lane change, Constant radius circle, and Handling. Details about the different manoeuvres can be found in the following list.

6 CHAPTER 2. METHOD 2.4. DATA PROCESSING

Figure 2.4: Preparation of the handling track. The wheel loader scrapes the surface with the blade. Behind the wheel loader, not visible in the picture, is several old truck tires that are pulled along to pack the surface.

• Single lane change Surface: Polished ice Dimension: 3m sideways movement in 20m Tires: SRTT Variations: Speed and PF-settings • Double lane change Surface: Packed snow Dimension: ISO 3888-2 (moose test) Tires: Blizzak Variations: Speed • Constant radius circle Surface: Packed snow Dimension: Radius: 42m Tires: SRTT Variations: Speed • Handling course Surface: Packed snow Dimension: 1.1km Tires: Blizzak Variations: Speed

2.4 Data processing

During the tests a substantial amount of data has been captured. This data has been processed in Matlab. To be able to draw rational conclusions when analysing the captured data, a lot of eﬀort has been put into understanding of the path-following algorithm.

7 Chapter 3

Result

This chapter show the results from the diﬀerent path-following experiments that were made.

3.1 Theoretical analysis

To illustrate how different settings of the ABD path-following algorithm influence the vehicle motion, the theoretical output from the controller is compared with the geometrical problem of making a tricycle drive to a specific destination/aimpoint. Analysing Figure 1.2 strictly geometrically and neglecting slip between tire and road; if the front end of the tricycle is set to reach the aimpoint, the angle α of the steered front wheel must be pointing directly towards that location at all time. The purpose of the controller is to maintain α pointing in that direction as the vehicle moves. If done properly, the end destination will at some point be reached. The steering angle α is calculated as the sum of the angle γ, induced by the lateral position error b, and the current heading Θ of the vehicle, α =Θ+ γ. (3.1) Using trigonometry it can be shown that the angle γ can be calculated by b γ = arctan , (3.2) lad where lad (look ahead distance) is the distance to the aimpoint. To compare the tricycle model with, for instance a normal car, the concept of effective steering angle is introduced. For a tricycle, assuming no slip, a given steering angle α will result in the rear axle of the vehicle tracking a circle with radius L r = vehicle , (3.3) circle sin(α) where Lvehicle is the distance from the rear to the front axle. Thus, for a normal car with two rear wheels and two steered front wheels, the effective steering angle αeffective is the angle of a imaginary wheel in the middle between the two front wheels. If for a given steering command, the circle radius for the centre of the rear axis rcircle is measured, the effective steering angle can be calculated using Lvehicle αeffective = arcsin . (3.4) rcircle Moreover, if the forward velocity v and the rotation velocity ω of the vehicle is known the effective steering angle can be estimated while driving using ωL α = arctan vehicle . (3.5) effective v

8 CHAPTER 3. RESULT 3.1. THEORETICAL ANALYSIS

More or less, this is the problem that the ABD path-following controller is taking care of. However, a few differences can be noted. At first, the aimpoint is continually pushed forward and thus, it should never be reached. Secondly, the ABD steering robot does control the angle of the steering wheel. Hence, the correlation between the angle α (effective steering angle) and the output from the controller might not be linear, and it is definitely vehicle dependent. Two things that do affect the correlation are the steering geometry and speed dependent progressive steering available on some car models.

Figure 3.1 shows the difference between the geometrical findings and the ABD gain function Kp(v) (eq 1.1). To compare the controller gain Kp with the angle γ the relationship between the angle of the steering wheel and the effective steering angle α is assumed to be linear, hence, γ is multiplied with the scale factor noted in the figure. The scale factor is chosen such that the two curves will match at 10m/s, this gives a factor of 25.5, which can be interpreted as one full turn on the steering wheel (360◦) resulting in an effective steering angle of 360/25.5 = 14.1◦. The scale factor is probably a little bit high compared to the car used in the test (Volvo V70), however, still fairly reasonable. Assuming a fixed lateral error when calculating γ (eq 3.2), the curve form of the ABD gain actually match the geometrical curve pretty well, however, not shown in the figure, the match vary depending on the chosen lateral error.

Controller gain 1000 K (v) p 800 γ(p(v)) @ b=1m (scale 25.5) 600

Gain 400

200

0 0 5 10 15 20 25 30 Speed [m/s] Controller gain 1000 K (lad) p 800 γ(lad) @ b=1m (scale 25.5) 600

Gain 400

200

0 0 5 10 15 20 25 Look ahead distance [m]

Figure 3.1: Top plot: Output from ABD controller compared to scaled output from Eq 3.2 (lad = p(v)) versus vehicle speed. Bottom plot: Output from ABD controller compared to scaled output from Eq 3.2 versus look ahead distance.

The ABD path-following controller uses the projected lateral error b+q as input to the feedback loop. Doing so, the controller does indeed take the offset in both vehicle position as well as vehicle heading into account. When further analysing the geometrical properties in Figure 1.2 it can be shown that the relationship between projected lateral error b+q and the angle α is not strictly proportional. While the projected lateral error b is directly proportional to the current lateral offset, a heading offset Θ does result in a error q as

q = tan(Θ) · lad. (3.6)

Strictly geometrical, a lateral position oﬀset should give rise to an angle according to equation 3.2 and a heading error should be compensated with a 1 to 1 relationship.

9 3.1. THEORETICAL ANALYSIS CHAPTER 3. RESULT

Figure 3.2 illustrates the difference between the output of the ABD controller and the geometrical relationship. The output from the controller is scaled with the same factor as in Figure 3.1. With the PF-settings used when creating the figure (P=1, LAC=1), it can be noted that when driving at a speed of 10m/s, the steering angle from the ABD controller does correspond well to the geometrical properties up to a lateral offset of about 1.5m or a heading offset of app. 20◦. This match is due to the fact that the output from the controller is scaled to fit the geometrical properties at that speed. However, as the speed increases, the controller overestimates the steering angle, and when the speed decreases the steering angle is underestimated. This implies that the faster the vehicle drives, the more aggressive the steering will become.

Speed 5 m/s Speed 5 m/s

Controller output (scale 1/25.5) 40 40 Angle to aimpont α 30 30

20 20

Angle [degree] 10 Angle [degree] 10

0 0 0 0.5 1 1.5 2 2.5 3 0 10 20 30 40 Lateral offset [m] Heading offset [degree] Speed 10 m/s Speed 10 m/s

40 40

30 30

20 20

Angle [degree] 10 Angle [degree] 10

0 0 0 0.5 1 1.5 2 2.5 3 0 10 20 30 40 Lateral offset [m] Heading offset [degree] Speed 15 m/s Speed 15 m/s

40 40

30 30

20 20

Angle [degree] 10 Angle [degree] 10

0 0 0 0.5 1 1.5 2 2.5 3 0 10 20 30 40 Lateral offset [m] Heading offset [degree]

Figure 3.2: ABD controller output scaled by the constant noted in the plot, compared with the geometrically calculated angle α, calculated at three different speeds (5-10-15m/s). The plots show the lateral offset (left) and the heading offset (right) influence on the steering angle.

Increasing the LAC (look ahead constant) will make the controller aim further ahead, hence, the minimum curve radius that the vehicle can track will be increased and the vehicle will start to cut corners. It can be noted that assuming a fixed lateral offset, if the LAC is increased the angle α to the aimpoint is decreased (Eq 3.2), and vice versa. However, the output from the controller (error b) stays the same, all other variables fixed. Furthermore, assuming a fixed heading offset, if LAC is increased, the output from the controller is also increased (error q, Eq 3.6), though the angle to the aimpoint is the same. All in all, increasing the look ahead constant will make the steering more sensitive to both a lateral error, as well as a heading error. This is also shown experimentally further on in the report. To maintain the controller sensitivity to a specific error, lateral or heading, when the LAC constant is changed, the proportional gain P can be changed in the opposite direction. As example, if LAC is doubled (from 1 to 2) and P is halved (from 1 to 0.5), the increased controller output due to increased LAC will be fully compensated by the reduced proportional gain P .

10 CHAPTER 3. RESULT 3.2. EXPERIMENTAL TESTS

3.2 Experimental tests

To evaluate the ABD steering robot in winter conditions four diﬀerent test manoeuvres were performed. Three diﬀerent path-following parameters have been particularly examined, namely the Proportional gain P , the Integral gain I, and the Look ahead constant LAC. Other notes from the test period are also mentioned.

3.2.1 Test manoeuvres

Single lane change

The single lane change is an eﬀective way to provoke the car and its ESC system. The ﬁrst turn normally is no problem, however, in the second turn the load transfer in the car will cause the tire grip to change and the car will most likely not be able to make the turn (assuming quite high speed). When so, the ESC system gets activated and applies brake force on some of the wheels to make the car turn in the desired direction. In this situation it is important that the driver (steering robot) keeps the angle of the front wheels pointing in the desired travel direction, otherwise the ESC system does not know in what way to turn the vehicle.

The single lane change has been used to evaluate how diﬀerent settings for the Proportional gain P (Figure 3.3), the Integral gain I (Figure 3.4), and the Look ahead constant LAC (Figure 3.5), aﬀect the path-following algorithm. The result is discussed further on in the report. More data from the tests can be found in Appendix A.

Run 1, (P=0.75, I= 0, LAC=1.5) Run 2, (P=0.75, I= 0, LAC=1.5) Run 3, (P=0.75, I= 0, LAC=1.5) 15 15 15 Front axle 14 14 14 Rear axle Yaw angle 13 13 13 Desired path

12 12 12 Position [m] Position [m] Position [m] 11 11 11

10 10 10 200 220 240 260 280 300 320 200 220 240 260 280 300 320 200 220 240 260 280 300 320 Position [m] Position [m] Position [m] Run 4, (P=0.5, I= 0, LAC=1.5) Run 5, (P=0.5, I= 0, LAC=1.5) Run 6, (P=0.5, I= 0, LAC=1.5) 15 15 15

14 14 14

13 13 13

12 12 12 Position [m] Position [m] Position [m] 11 11 11

10 10 10 200 220 240 260 280 300 320 200 220 240 260 280 300 320 200 220 240 260 280 300 320 Position [m] Position [m] Position [m] Run 7, (P=0.25, I= 0, LAC=1.5) Run 8, (P=0.25, I= 0, LAC=1.5) Run 9, (P=0.25, I= 0, LAC=1.5) 15 15 15

14 14 14

13 13 13

12 12 12 Position [m] Position [m] Position [m] 11 11 11

10 10 10 200 220 240 260 280 300 320 200 220 240 260 280 300 320 200 220 240 260 280 300 320 Position [m] Position [m] Position [m]

Figure 3.3: The figure illustrates the influence of the Proportional gain on the path-following behaviour. Through all tests the vehicle was driving at a speed of approximately 10m/s. In- creasing the proportional gain (three plots on top) resulted in a smaller lateral offset with a skittish behaviour. As can be seen in the three bottom plots, lowering the proportional gain will result in a larger lateral error and a slowly oscillating behaviour.

11 3.2. EXPERIMENTAL TESTS CHAPTER 3. RESULT

Test 1, (P=0.5, I=0.1, LAC=1.5) Test 2, (P=0.5, I= 0, LAC=1.5) Test 3, (P=0.75, I= 0, LAC=1.5) Front axle position Front axle position Front axle position

15 15 15 Run 1 Run 1 Run 1 Run 2 Run 2 Run 2 14 Run 3 14 Run 3 14 Run 3 Desired path Desired path Desired path

13 13 13 Position [m] Position [m] Position [m] 12 12 12

11 11 11 200 220 240 260 280 200 220 240 260 280 200 220 240 260 280 300 320 Position [m] Position [m] Position [m]

Path following error Path following error Path following error

0.2 0.2 0.2 0.1 0.1 0.1 0 0 0 −0.1 −0.1 −0.1 −0.2 −0.2

Error [m] −0.2 Error [m] Error [m] −0.3 −0.3 −0.3 −0.4 −0.4 −0.4 −0.5 −0.5 −0.5 200 220 240 260 280 200 220 240 260 280 200 220 240 260 280 300 320 Position [m] Position [m] Position [m]

Figure 3.4: The ﬁgure illustrates the inﬂuence of the Integral gain on the path-following behaviour. In the three testruns shown to the left a small integral gain (I=0.1) was used, after the lane change ( 260m and onwards) there is a small remaining path-following error that does not show up when the integral gain is set to zero.

Double lane change

The double lane change (ISO 3888-2) is a test that is used to subjectively determine the obstacle avoidance performance of a vehicle [7]. It is more complex than the single lane change since it consists of not two, but three turns that are quite close to each other. For the test to be approved the vehicle must traverse the track without driving on any the surrounding cones. When the test is executed at high speed on dry tarmac the forces induced are so high that some vehicles actually might roll over. Figure 3.6 shows the result of this test, performed at four diﬀerent speeds on packed snow. At low speed the vehicle can traverse the track ﬂawlessly. As the speed increases the vehicle starts to slide when cornering. When the speed is maximized the vehicle more or less completely misses the track and drives straight forward. More data from the tests can be found in Appendix B.

Constant radius circle

The constant radius circle test was performed on a surface consisting of packed snow. At ﬁrst the vehicle were driven at such a low speed that the circle could be traversed without sliding. After that the speed were increased to maximum feasible due to the current tire-road grip. This was achieved by pushing the throttle to the ﬂoor and allowing the ESC system of the car to control the speed while the steering robot controlled the steering angle.

The result of the test can be seen in Figure 3.7. At the low speed test the vehicle did track the desired path on the inner side of the circle. This is expected as a result of the look ahead distance that the path-following controller utilises. At full throttle the ESC system were constantly acting to compensate for the vehicle sliding sideways. As can be seen in the ﬁgure, the vehicle is in this case driving on the outside of the desired path. In this case the ESC system on the car and the steering robot co-operate to make the vehicle heading pointing towards the aim-point on the desired path. Detailed data from the tests can be found in Appendix C.

12 CHAPTER 3. RESULT 3.2. EXPERIMENTAL TESTS

Run 1, (P=0.375, I= 0, LAC= 3) Front axle 15 Rear axle Yaw angle 14 Desired path 13 Look ahead Position [m] 12

200 210 220 230 240 250 260 270 280 290 300 310 Position [m] Run 2, (P=0.5, I= 0, LAC= 3) 15

13 Position [m] 12 200 210 220 230 240 250 260 270 280 290 300 310 Position [m] Run 3, (P=0.5, I= 0, LAC=1.5) 15 14 13 12

Position [m] 11

200 210 220 230 240 250 260 270 280 290 300 310 Position [m] Run 4, (P=0.5, I= 0, LAC=0.75)

10 Position [m]

8 200 210 220 230 240 250 260 270 280 290 300 310 Position [m]

Figure 3.5: The ﬁgure illustrates the inﬂuence of the Look Ahead Constant LAC on the path- following behaviour. A high LAC will make the vehicle cut corners and a low LAC will introduce oscillations in the path-following.

Handling track

The test on the handling track consisted of driving three laps with varying speeds, see Figure 3.8. Since the speed was not computer controlled the human driver had to adjust the speed for each turn manually, hence, it was difficult to achieve the same speed twice in the same curve. It can be noted that the path following error shows clear resemblance between the three laps. However, a few differences can be seen in (and directly after) some of the turns, this is mainly due to the vehicle having different speed when entering the curve and starts to slide. More data from the test can be found in Appendix D.

3.2.2 PF-settings

Altering the PF-settings aﬀect the path-following controller and in turn, the vehicle motion. The focus for these tests have been on the proportional gain, integral gain, and the look ahead constant.

13 3.2. EXPERIMENTAL TESTS CHAPTER 3. RESULT

Run 1. Average speed: 3.83 m/s. −14

−16

−18

−20 Position [m] −22

140 150 160 170 180 190 200 210 220 230 Position [m] Run 2. Average speed: 9.11 m/s. −14

−16

−18

−20 Position [m] −22

140 150 160 170 180 190 200 210 220 230 Position [m] Run 3. Average speed: 10.61 m/s. −14

−16

−18

−20 Position [m] −22

140 150 160 170 180 190 200 210 220 230 Position [m] Run 4. Average speed: 17.08 m/s. −14

−16

−18

−20 Position [m] −22

140 150 160 170 180 190 200 210 220 230 Position [m]

Figure 3.6: The double lane change test, a.k.a. moose-test (ISO 3888-2), performed at four diﬀerent speeds. The vehicle is driving from left to right in the ﬁgure. (PF-settings: P=0.5, I=0.1, LAC=1.5)

Proportional gain

Figure 3.3 shows diﬀerent settings of the proportional gain. A small gain makes the vehicle turn too late since the error has to grow large before the controller gives suﬃcient steering output. This causes the vehicle to slowly oscillate around the given track after the second turn. A too small proportional gain also provokes the vehicle to second, and even a third, spin, before the path-following system stabilise.

A large proportional gain makes the vehicle turn too much since even a small error produces a large steering output. This causes the vehicle to oscillate fast around the given track. In contrast to this, a high proportional gain does seem to suppress the second spin of the vehicle. A large proportional gain also provokes a larger spin in the second corner.

Integral gain

Figure 3.4 illustrates a problem with using integral gain when the vehicle is sliding. After a large path-following error (induced by sliding in a sharp turn) it seems like there will be a small

14 CHAPTER 3. RESULT 3.2. EXPERIMENTAL TESTS

Front axle position

40 Run 1, average speed 9.4 m/s Run 2, average speed 10.8 m/s Desired path

Position and orientation 22 20

10 21.5

0 21 Position [m]

−10 20.5

−20 20 10 10.5 11 11.5 12

−30

−40

10 20 30 40 50 60 70 80 90 Position [m]

Figure 3.7: Constant radius circle at two different speeds (app. 9m/s and 11m/s). The triangle shows the start of the dataset and the drive direction of the vehicle (upwards in the figure). The figure in the middle shows a zoom in of one part of the circle. (PF-settings: P=0.75, I=0, LAC=1.5) remaining offset in the path-following. The offset will become smaller and smaller and finally disappear. When the integral is set to zero this phenomenon has not been observed. This problem can also be seen in Figure 3.8, the handling track, after the first turn during the third run there is a remaining error in the path-following. After approximately 200m the error has disappeared.

Look Ahead Constant

The look ahead distance sets how far in front of the vehicle the path-following controller should look when calculating how to turn the steering wheel, hence, it aﬀects the turning radius of the vehicle. As described in Chapter 1 the look ahead distance in the ABD controller is speed dependent according to a given function. The Look Ahead Constant (LAC) proportionally scales the output from this look ahead function. In general, a large LAC will suppress sudden changes in the track trajectory, i.e. the vehicle cut corners, and a small LAC will make the path-following more pronounced. At high speed a small LAC may result in problems to enter curves with relative small radius in a controlled manner. The controller reacts too late to the upcoming turn, and hence, over shoot in the path-following may occur.

15 3.2. EXPERIMENTAL TESTS CHAPTER 3. RESULT

Handling track

−100 Run 1 −150 Run 2 −200 Run 3 −250 Position [m] −300 100 200 300 400 500 Position [m] Total vehicle speed

10 Speed [m/s] 5

100 200 300 400 500 600 700 800 900 1000 1100 Distance travelled [m] Steering wheel angle 400 200 0 −200 Angle [degree] −400 100 200 300 400 500 600 700 800 900 1000 1100 Distance travelled [m] Slipangle 10 5 0 −5

Angle [degree] −10 100 200 300 400 500 600 700 800 900 1000 1100 Distance travelled [m] Path following error

1 0.5 0 −0.5 Error [m] −1

100 200 300 400 500 600 700 800 900 1000 1100 Distance travelled [m]

Figure 3.8: Three laps on the handling track. On top; the triangle shows the start of the track, each red star represents 100m on the track (the blue star is a 500m mark). (PF-settings: P=0.5, I=0.1, LAC=1.5)

With a small LAC one problem occurs when a large lateral error is introduced in the path- following, for example when the vehicle starts to slide in a tight corner, see Figure 3.5. A small LAC will then make the look ahead distance to get close to, or even smaller than, the projected path-following error. The car will then strive to drive straight back towards the track, perpendicular to the track direction, and it will not be able to catch the turn to get back on the desired path. Consequently, the vehicle will for some time oscillate back and forth around the path. In order to properly test the vehicle ESP system such large errors must be permitted, hence, the look ahead distance must be kept at a quite high value.

16 CHAPTER 3. RESULT 3.2. EXPERIMENTAL TESTS

Furthermore, as noted in the geometrical analysis in section 3.1, when increasing the look ahead constant, while keeping all other parameters constant, the sensitivity to heading error is also increased. This can be seen in the tests shown in Figure 3.5. While the vehicle will cut corners, it will have a tendency for small, relatively fast, oscillations around the path.

Forward velocity

The path-following controller uses the vehicle forward velocity v as input when calculating the proportional gain Kp(v) and look ahead distance p(v). When the vehicle turns into a spin and start to slide sideways (high slip angles) the total velocity of the vehicle stays more or less constant but the forward velocity may go down substantially. During the experiments slip angles of up to more than 45◦ has been reached. At those angles the forward velocity is approximately 30% (1-cos(45)) lower than the total vehicle speed, thus, the controller considers the vehicle driving slower than it actually is. This will make the controller both reducing the look ahead distance as well as increasing the proportional gain, leading to the steering to be more sensitive to controller errors. Solely the reduced look ahead distance will to some extent introduce the same problem as using a low LAC, the vehicle strives to drive too narrowly back towards the desired path. This may actually exacerbate the over-steering behaviour and increase the slip angle of the vehicle due to the ESC system on the car is trying to make the car go in the direction that the front wheels are pointing. The increased proportional gain may also enhance this behaviour. All in all, this is a problem only noticed at high slip angles when the forward velocity diﬀers signiﬁcantly from the total vehicle speed.

3.2.3 Other notes

The regular surface of a winter test track on lake ice is rather soft compared to for instance tarmac. Rugged ice, polished ice, or packed snow; all surfaces will wear when driving on them. Depending on the tires used, weather conditions, and the surface structure, the number of time it is possible to drive on the same spot before the surface gets substantial damaged vary. Figure 3.9 shows a part of the test track that was used as start for the path-following lead in to the single lane change test. This specific part of the track were passed more than 40 times. As can be seen in the figure the damage is significant. If, for instance, a lane change test would be executed at that location, the test would most likely be affected by the difference in surface structure.

17 3.2. EXPERIMENTAL TESTS CHAPTER 3. RESULT

Figure 3.9: Wear of winter test track when driving on the same spot over and over again. (More than 40 times) This actual tire track were created when using the lead in functionality in the steering robot system. The car enters the lead in track in the foreground of the image.

18 Chapter 4

Discussion

This chapter encapsulates the experience from using an ABD steering robot with path-following in winter conditions.

4.1 Conclusion

As presented in the report, four diﬀerent test sequences have been performed and the result from these are analysed. To fully understand how the path-following controller aﬀect the steering of the vehicle a geometrical analysis of the path-following algorithm was done.

The setting of the path-following algorithm greatly aﬀects the car response in diﬀerent situations. This is especially noticeable when the car starts to slide, a situation common when driving on a slippery winter road. As a summary of the work presented in this report follows a number of paragraphs to consider when setting up the system in a new vehicle:

• Avoid integral gain since it will introduce a remaining oﬀset in the path-following after large lateral and/or heading errors (i.e. the vehicle sliding due to entering a sharp corner at high speed)

• Look ahead constant should be kept at a rather high value to allow for the vehicle to get back on the desired path nicely after large lateral errors or high slip angles.

• Proportional gain should be adjusted such that reasonable vehicle behaviour occurs.

• The single lane change is a suitable test sequence when evaluating how diﬀerent path- following settings aﬀect the controller’s ability to cope with large lateral errors and high slip angles. If the speed is kept high enough, the vehicle will turn into a spin in the second turn. Since the sequence ends with a long straight line there is lot of time for the system to catch up and get back on the desired path.

• To accomplish large path-following errors without the speed getting excessively high the test can be performed at very low friction surface with tires not suitable for the surface, i.e. non-studded tires on polished ice.

With an appropriate choice of path-following parameters the system performs predictable and satisfying. The overall impression is that the ABD steering robot can indeed be useful for repetitive test in winter conditions with bad road grip.

19 4.2. FUTURE WORK CHAPTER 4. DISCUSSION

4.2 Future work

This section presents some ideas for future work that have emerged during the experiments and analysis of the data. The ideas are ranging from more or less possible to implement and test directly, to real long-shot that might not be feasible at all.

Algorithm adjustments

• Today the ABD path-following system uses the vehicle forward velocity as reference when calculating the look ahead distance and the controller gain. It would be interesting to test if there is a noticeable difference in the vehicle behaviour at large slip angles if the total velocity were used instead. • During the analysis of the path-following algorithm there has been indications that when the system is tuned in an appropriate manner the controller actually makes the effective steering angle pointing towards the aimpoint. Using subjective measurement (human sense during tests); with a too small steering angle the vehicle is considered to react too slow, and with too large steering angle it is perceived to react nervously. However, to make this claim properly this must be evaluated further. • If the above statement is correct the tuning of the path-following system could be revised. Assuming that the correlation between angle of steering wheel and the effective steering angle could be obtained, and by choosing a reference speed (affect the look ahead distance and the controller gain) and a desired look ahead constant, it should be possible to calculate the required proportional gain.

Steering robot in winter test

• Safety is an important concern, especially when testing for lose snow accumulation or other conditions with limited visibility and high speed. A path-following steering robot, combined with speed control (mainly throttle and brake), could be used to maintain the vehicle position close behind a truck while the visibility is limited. • As shown in the result section the track does get damaged when driving at the same spot over and over again. The track usage could be increased as the positioning of the vehicle is so precise. For each test the desired path could be moved such that the vehicle is always driving on a new surface. • Investigate new test methodology for a path-following steering robot that can be used to perform objective test of, for instance, dynamic car behaviour, ESC systems, or tires.

20 Bibliography

[1] H. Tseng, J. Asgari, D. Hrovat, P. V. der Jagt, A. Cherry, and S. Neads, “Evasive manoeuvres with a steering robot,” Vehicle system dynamics, vol. 43, pp. 199–216, March 2005. [2] S. M˚ardh, H. Andersson, M. Hjort, and J. Jansson, “En testmetod för utvärdering av säkerhetsaspekter för personbilar utrustade med esc - ett prototypförslag,” report, VTI, Linkping, 2009. [3] H. Andersson, M. Hjort, and F. Bruzelius, “Overstyrning¨ p˚ais och snömed olika vinterdäck - metodutveckling och fältstudie,” report, VTI, Linkping, 2011. [4] Anthony Best Dynamics, “Steering robot systems: Driving robot systems.” http://www.abd.uk.com/en/driving robots/steering robots, May 2013. [5] Oxford Technical Solutions, “Rt2000 family products.” http://www.oxts.com/default.asp?pageRef=57, May 2013. [6] Oxford Technical Solutions, “Gps-base.” http://www.oxts.com/default.asp?pageRef=91, May 2013. [7] International Organization for Standardization, “Iso 3888-2:2011, passenger cars - test track for a severe lane-change manoeuvre - part 2: Obstacle avoidance.” http://www.iso.org/iso/catalogue detail.htm?csnumber=57253, May 2013.

21 Appendix A

Single Lane Change

Front axle position Run 1 (P=0.5, I=0.1, LAC=1.5) 15 Run 2 (P=0.5, I=0.1, LAC=1.5) Run 3 (P=0.5, I=0.1, LAC=1.5) 14 Desired path 13 12 Position [m] 11

200 210 220 230 240 250 260 270 280 Position [m] Total vehicle speed 13 12 11 10

Speed [m/s] 9 8 200 210 220 230 240 250 260 270 280 Position [m] Steering wheel angle Max 145, Min −97 Max 191, Min −264 200 Max 240, Min −235 100 0 −100

Angle [degree] −200

200 210 220 230 240 250 260 270 280 Position [m] Slipangle Max 2.8, Min −6.2 Max 8.1, Min −12.5 10 Max 11.7, Min −8.8 5 0 −5

Angle [degree] −10

200 210 220 230 240 250 260 270 280 Position [m] Path following error Max 0.07, Min −0.46

1 Max 0.14, Min −0.73 0.5 Max 0.23, Min −1.18 0

Error [m] −0.5 −1

200 210 220 230 240 250 260 270 280 Position [m]

Figure A.1: Single lane change.

22 APPENDIX A. SINGLE LANE CHANGE

Front axle position Run 1 (P=0.5, I=0.1, LAC=1.5) 15 Run 2 (P=0.5, I=0.1, LAC=1.5) Run 3 (P=0.5, I=0.1, LAC=1.5) 14 Desired path 13

Position [m] 12

200 210 220 230 240 250 260 270 280 Position [m] Total vehicle speed 15

5 Speed [m/s]

200 210 220 230 240 250 260 270 280 Position [m] Steering wheel angle Max 130, Min −103 Max 88, Min −82 200 Max 183, Min −272

−200 Angle [degree]

200 210 220 230 240 250 260 270 280 Position [m] Slipangle Max 0.4, Min −1.1 Max 1.2, Min −2.3 10 Max 4.8, Min −14.3

−10 Angle [degree]

200 210 220 230 240 250 260 270 280 Position [m] Path following error Max 0.02, Min −0.17

0.5 Max 0.11, Min −0.22 Max 0.14, Min −0.51 0 Error [m] −0.5

200 210 220 230 240 250 260 270 280 Position [m]

Figure A.2: Single lane change.

23 Appendix A

Front axle position Run 1 (P=0.5, I= 0, LAC=1.5) 15 Run 2 (P=0.5, I= 0, LAC=1.5) 14 Run 3 (P=0.5, I= 0, LAC=1.5) Desired path 13 12 Position [m] 11

200 210 220 230 240 250 260 270 280 Position [m] Total vehicle speed

Speed [m/s] 8

200 210 220 230 240 250 260 270 280 Position [m] Steering wheel angle Max 195, Min −230 400 Max 269, Min −390 200 Max 223, Min −207 0 −200 Angle [degree] −400 200 210 220 230 240 250 260 270 280 Position [m] Slipangle Max 6.7, Min −14.9 Max 17.7, Min −16.5 10 Max 11.9, Min −11.5

−10 Angle [degree]

200 210 220 230 240 250 260 270 280 Position [m] Path following error Max 0.21, Min −0.98

Max 0.24, Min −1.32 1 Max 0.25, Min −1.45 0

Error [m] −1

200 210 220 230 240 250 260 270 280 Position [m]

Figure A.3: Single lane change.

24 APPENDIX A. SINGLE LANE CHANGE

Front axle position Run 1 (P=0.75, I= 0, LAC=1.5) 15 Run 2 (P=0.75, I= 0, LAC=1.5) Run 3 (P=0.75, I= 0, LAC=1.5) 14 Desired path 13 12 Position [m]

11 200 220 240 260 280 300 320 Position [m] Total vehicle speed 13 12 11 10

Speed [m/s] 9 8 200 220 240 260 280 300 320 Position [m] Steering wheel angle Max 291, Min −486 500 Max 175, Min −307 Max 319, Min −392

0 Angle [degree] −500 200 220 240 260 280 300 320 Position [m] Slipangle Max 3.8, Min −22.5

20 Max 2.8, Min −13.6 Max 6.0, Min −22.3 10 0 −10

Angle [degree] −20

200 220 240 260 280 300 320 Position [m] Path following error Max 0.10, Min −1.12

1 Max 0.06, Min −0.42 0.5 Max 0.30, Min −0.75 0

Error [m] −0.5 −1

200 220 240 260 280 300 320 Position [m]

Figure A.4: Single lane change.

25 Appendix A

Front axle position Run 1 (P=0.25, I= 0, LAC=1.5) 15 Run 2 (P=0.25, I= 0, LAC=1.5) 14 Run 3 (P=0.25, I= 0, LAC=1.5) Desired path 13 12

Position [m] 11

200 220 240 260 280 300 320 Position [m] Total vehicle speed

Speed [m/s] 8

200 220 240 260 280 300 320 Position [m] Steering wheel angle Max 149, Min −162 200 Max 155, Min −112 100 Max 150, Min −170

−100 Angle [degree] −200 200 220 240 260 280 300 320 Position [m] Slipangle Max 13.3, Min −8.5 Max 14.2, Min −10.7 10 Max 15.6, Min −9.4

−10 Angle [degree]

200 220 240 260 280 300 320 Position [m] Path following error Max 0.71, Min −1.65 2 Max 0.55, Min −1.81 1 Max 0.93, Min −1.76 0

Error [m] −1

−2 200 220 240 260 280 300 320 Position [m]

Figure A.5: Single lane change.

26 APPENDIX A. SINGLE LANE CHANGE

Front axle position Run 1 (P=0.5, I=0.5, LAC=1.5) Run 2 (P=0.5, I=0.5, LAC=1.5) 14 Run 3 (P=0.5, I=0.5, LAC=1.5) 12 Desired path 10

Position [m] 8 6 200 220 240 260 280 300 320 340 Position [m] Total vehicle speed 12 10 8 6 4 Speed [m/s] 2 200 220 240 260 280 300 320 340 Position [m] Steering wheel angle Max 334, Min −406 500 Max 502, Min −502 Max 502, Min −501

0 Angle [degree] −500 200 220 240 260 280 300 320 340 Position [m] Slipangle Max 22.0, Min −13.0 50 Max 30.6, Min −40.1 Max 40.6, Min −49.6

0 Angle [degree] −50 200 220 240 260 280 300 320 340 Position [m] Path following error Max 2.24, Min −1.56

5 Max 3.23, Min −3.45 Max 2.81, Min −5.61 0 Error [m] −5

200 220 240 260 280 300 320 340 Position [m]

Figure A.6: Single lane change.

27 Appendix A

Front axle position Run 1 (P=0.5, I= 0, LAC= 3) 15 Run 2 (P=0.5, I= 0, LAC= 3) Run 3 (P=0.5, I= 0, LAC= 3) 14 Desired path

13 Position [m] 12

200 210 220 230 240 250 260 270 280 290 Position [m] Total vehicle speed 12

Speed [m/s] 6

200 210 220 230 240 250 260 270 280 290 Position [m] Steering wheel angle Max 36, Min −49

100 Max 60, Min −96 50 Max 60, Min −96 0 −50

Angle [degree] −100

200 210 220 230 240 250 260 270 280 290 Position [m] Slipangle Max 1.2, Min −1.1 Max 1.6, Min −1.6 2 Max 1.6, Min −1.6

−2 Angle [degree]

200 210 220 230 240 250 260 270 280 290 Position [m] Path following error Max 0.36, Min −0.55

Max 0.50, Min −0.79 0.5 Max 0.50, Min −0.79 0

Error [m] −0.5

200 210 220 230 240 250 260 270 280 290 Position [m]

Figure A.7: Single lane change.

28 APPENDIX A. SINGLE LANE CHANGE

Front axle position Run 1 (P=0.375, I= 0, LAC= 3) Run 2 (P=0.375, I= 0, LAC= 3) 15 Run 3 (P=0.375, I= 0, LAC= 3) 14 Desired path

13 Position [m] 12

200 220 240 260 280 300 Position [m] Total vehicle speed 13

10 Speed [m/s] 9 200 220 240 260 280 300 Position [m] Steering wheel angle Max 28, Min −42 Max 28, Min −43 50 Max 27, Min −43

Angle [degree] −50

200 220 240 260 280 300 Position [m] Slipangle Max 0.4, Min −0.7 2 Max 0.5, Min −0.6 1 Max 0.5, Min −0.6

−1 Angle [degree] −2 200 220 240 260 280 300 Position [m] Path following error Max 0.46, Min −0.86

1 Max 0.48, Min −0.79 0.5 Max 0.48, Min −0.82 0

Error [m] −0.5

−1 200 220 240 260 280 300 Position [m]

Figure A.8: Single lane change.

29 Appendix A

Front axle position Run 1 (P=0.5, I= 0, LAC=0.75) Run 2 (P=0.5, I= 0, LAC=0.75) 14 Run 3 (P=0.5, I= 0, LAC=0.75) 12 Desired path 10

Position [m] 8

200 220 240 260 280 300 320 340 Position [m] Total vehicle speed 12 10 8 6 Speed [m/s] 4 200 220 240 260 280 300 320 340 Position [m] Steering wheel angle Max 488, Min −502 500 Max 502, Min −502 Max 502, Min −502

0 Angle [degree] −500 200 220 240 260 280 300 320 340 Position [m] Slipangle Max 29.1, Min −45.4

40 Max 24.7, Min −36.0 Max 40.2, Min −21.5 20 0 −20

Angle [degree] −40

200 220 240 260 280 300 320 340 Position [m] Path following error Max 1.13, Min −1.78

5 Max 3.50, Min −2.93 Max 2.49, Min −5.49 0 Error [m]

−5

200 220 240 260 280 300 320 340 Position [m]

Figure A.9: Single lane change.

30 Appendix B

Double Lane Change

Front axle position Run 1 (P=0.5, I=0.1, LAC=1.5)

−16 Run 2 (P=0.5, I=0.1, LAC=1.5) −17 Desired path −18 −19

Position [m] −20

140 150 160 170 180 190 200 210 220 230 Position [m] Total vehicle speed

5 Speed [m/s] 0 140 150 160 170 180 190 200 210 220 230 Position [m] Steering wheel angle Max 132, Min −154

200 Max 327, Min −270

−200 Angle [degree]

140 150 160 170 180 190 200 210 220 230 Position [m] Slipangle Max 1.0, Min −1.5

5 Max 5.3, Min −5.7

Angle [degree] −5

140 150 160 170 180 190 200 210 220 230 Position [m] Path following error Max 0.18, Min −0.17 0.5 Max 0.30, Min −0.45

0 Error [m] −0.5

140 150 160 170 180 190 200 210 220 230 Position [m]

Figure B.1: Double lane change data.

31 Appendix B

Front axle position Run 1 (P=0.5, I=0.1, LAC=1.5)

−16 Run 2 (P=0.5, I=0.1, LAC=1.5) Desired path −18

−20 Position [m]

−22 140 150 160 170 180 190 200 210 220 230 240 250 Position [m] Total vehicle speed 20

10 Speed [m/s]

140 150 160 170 180 190 200 210 220 230 240 250 Position [m] Steering wheel angle Max 502, Min −343 500 Max 279, Min −348

0 Angle [degree] −500 140 150 160 170 180 190 200 210 220 230 240 250 Position [m] Slipangle Max 20.8, Min −15.2 20 Max 14.9, Min −9.4 10 0 −10 Angle [degree] −20 140 150 160 170 180 190 200 210 220 230 240 250 Position [m] Path following error Max 1.03, Min −1.71 2 Max 3.63, Min −1.58

Error [m] −2

140 150 160 170 180 190 200 210 220 230 240 250 Position [m]

Figure B.2: Double lane change data.

32 Appendix C

Constant Radius Circle

Total vehicle speed 12

[m/s] 8

0 50 100 150 200 250 Distance travelled [m] Steering wheel angle

200

0 [degree] −200

0 50 100 150 200 250 Distance travelled [m] Slipangle 15 10 5 0

[degree] −5 −10 −15 0 50 100 150 200 250 Distance travelled [m] Path following error

0.5

0 [m]

−0.5

0 50 100 150 200 250 Distance travelled [m]

Figure C.1: Constant radius circle data.

33 Appendix D

Handling Track

Speed [m/s] 17 −100 15.4 13.8 −150 12.1 10.5 −200 8.88 Position [m] −250 7.25 5.63 −300 4 50 100 150 200 250 300 350 400 450 500 Position [m]

Slip angle [degree] 8 −100 7 6 −150 5 4 −200 3 Position [m] −250 2 1 −300 0 50 100 150 200 250 300 350 400 450 500 Position [m]

Path follwing error [m] 0.5 −100 0.438 0.375 −150 0.313 0.25 −200 0.188 Position [m] −250 0.125 0.0625 −300 0 50 100 150 200 250 300 350 400 450 500 Position [m]

Figure D.1: Handling track, lap 1.

34 APPENDIX D. HANDLING TRACK

Speed [m/s] 16 −100 14.8 13.5 −150 12.3 11 −200 9.75 Position [m] −250 8.5 7.25 −300 6 50 100 150 200 250 300 350 400 450 500 Position [m]

Slip angle [degree] 10 −100 8.75 7.5 −150 6.25 5 −200 3.75 Position [m] −250 2.5 1.25 −300 0 50 100 150 200 250 300 350 400 450 500 Position [m]

Path follwing error [m] 0.75 −100 0.656 0.563 −150 0.469 0.375 −200 0.281 Position [m] −250 0.188 0.0938 −300 0 50 100 150 200 250 300 350 400 450 500 Position [m]

Figure D.2: Handling track, lap 2.

35 Appendix D

Speed [m/s] 17 −100 15.8 14.5 −150 13.3 12 −200 10.8 Position [m] −250 9.5 8.25 −300 7 50 100 150 200 250 300 350 400 450 500 Position [m]

Slip angle [degree] 13 −100 11.4 9.75 −150 8.13 6.5 −200 4.88 Position [m] −250 3.25 1.63 −300 0 50 100 150 200 250 300 350 400 450 500 Position [m]

Path follwing error [m] 1.25 −100 1.09 0.938 −150 0.781 0.625 −200 0.469 Position [m] −250 0.313 0.156 −300 0 50 100 150 200 250 300 350 400 450 500 Position [m]

Figure D.3: Handling track, lap 3.