Iterative learning control designs for autonomous driving applications

10 3 Feedback controller 14 4 Iterative Learning Control ILC 17 4.1 Overview of ILC controller.. In this thesis, we aim to generate a feedforward control signal using ILC rithms that rea

Iterative Learning Control Designs For Autonomous Driving Applications

Master Thesis

Master of Control System Engineering

HAN University of Applied Science, the Netherlands

I would like to thank my dear teacher and academic supervisor, Richarch dorp, who gave me a professional supervision with invaluable lessons Richard is awarm-hearted person and he is always willing to answer my questions and discusswith me in his classes In order to finish my thesis, he gave me useful and insightfulcomments helping me to follow the right track

Kaan-In addition, I would love to express my gratitude to my company supervisor,

Dr Son Tong He was always happy to help me solve confusions and led me toobtaining the final results of the thesis Besides, Son is an open-minded person whohas been good to me Without his encouragement, I could not finish this final work

in my master study

Furthermore, I am grateful to Thai Nguyen University of Technology (TNUT) inVietnam, where I studied and have been working for Additionally, I would like toacknowledge Prof Cuong Duy Nguyen at TNUT in Vietnam He always supportsand motivates me in my academic research I also would like to thank VietnameseGovernment for sponsoring my Master study at HAN University of Applied Science,Netherlands in form of Project 599 scholarship

Finally, I wish to thank my family Your love and belief have brought me up andgone further

Thank you!

Leuven, March 2018

Lanh Nguyen

In this master thesis, iterative learning control (ILC) is introduced to deal withthe problem of designing the most optimal control signal in autonomous driv-ing applications that require tracking a fixed reference trajectory By exploitingdata/information from the previous iterations, the learning control algorithm canobtain better tracking control performance for the next iteration, and hence out-performs conventional control approaches such as feedback control In addition, thecontrol design is based on optimization, where kinematic and dynamic constraints ofthe vehicle, such as acceleration and steering, are taken into account The learningalgorithms can also be used in combination with other traditional control techniques,for example, the conventional feedback control is designed in the first iteration, thenlearning control is applied to improve performance in the subsequent iterations Inthis thesis, we use RoFaLT, a nonlinear optimization-based learning control tool, toimplement the ILC controllers Finally, the learning control designs are simulated in

a co-simulation fashion of LMS Amesim and Prescan software in two different narios: autonomous valet parking and racing car The results show the advantages

sce-of ILC controllers in improving tracking performance while guaranteeing systemconstraints

Keywords:

Advanced Driver Assistance Systems (ADAS), Iterative Learning Control (ILC),Optimal Control

1.1 Siemens Industry Software NV 1

1.2 Autonomous Driving 1

1.3 Goal of this thesis 1

1.4 Simulation with LMS Imagine.Lab Amesim 2

1.5 Demostration with PreScan 4

2 Vehicle dynamics 5 2.1 Vehicle model 6

2.2 Tire model 7

2.3 Slip-free bicycle model 8

2.4 Valiation 10

3 Feedback controller 14 4 Iterative Learning Control (ILC) 17 4.1 Overview of ILC controller 17

4.1.1 PD-type design 18

4.1.2 Plant Inversion Methods 18

4.1.3 Quadratically Optimal Design (Q-ILC) 19

4.1.4 Current-Iterative Learning Control 19

4.2 RoFaLT tool 20

4.2.1 Model correction step 21

4.2.2 Control step 22

5 Autonomous Applications and Simulation Results 24 5.1 Application 1: Valet Parking 24

5.2 Application 2: Racing 30

6 Conclusion and recommendation 41 6.1 Conclusion 41

6.2 Recommendation 41

Cr0 Zero order friction parameter [−]

Cr2 Second order friction parameter [−]

Subscripts

f front wheel x x axis

List of Figures

1.1 Vehicle dynamics basic [7] 2

1.2 AMEsim vehicle dynamics simulations of the vehicle chassis [7] 3

1.3 A scenario in Prescan 4

2.1 Model Coordinate System [2] 5

2.2 Bicycle model [2] 6

2.3 Geometry for bicycle model 8

2.4 Simulink model of Validation 11

2.5 Validate results when the vehicle goes forward 12

2.6 Validate results when the vehicle goes backward 12

3.1 Block diagram of feedback controller 14

3.2 Step response of PID controller 15

3.3 Result of feedback controller 16

4.1 Block diagram of basic iterative learning control 18

4.2 Current Iteration ILC architecture 20

4.3 Schematic overview of the considered two-step learning algorithms [9] 21 5.1 Parking trajectory 24

5.2 Block diagram of feed-forward controller 25

5.3 Results of ILC, forward path 26

5.4 Results of ILC, backward path 26

5.5 Result of last iteration, forward path 27

5.6 Result of last iteration, backward path 27

5.7 Correction terms and control signals of each iteration, forward path 28

5.8 Correction terms and control signals of each iteration, backward path 28 5.9 Result of ILC, full parking trajectory 29

5.10 Screenshot of demos 30

5.11 Racing trajectory 31

5.12 Block diagram of ILC-Feedback controller 31

5.13 MPC setting 1 33

5.14 MPC setting 2 33

5.15 MPC setting 3 34

5.16 Result of ILC after each iteration in normal weather 35

5.17 Result of last iteration, normal weather condition 35

5.18 Correction terms and control signals 36

5.19 Result of ILC in adverse weather 37

5.20 Result of last iteration, adverse weather 37

5.21 Tire slip in normal weather 38

5.22 Tire slip in adverse weather 38

5.23 Control signal, normal weather 39

5.24 Control signal, adverse weather 39

5.25 Screenshot of videos in Prescan 40

List of Tables

2.1 : Parameter of bicycle model 13

3.1 : Parameter of bicycle model 15

5.1 : Parameter of bicycle model 32

Chapter 1

Introduction

Siemens Industry Software NV (SISW) is a business unit of Siemens DigitalFactory Division The company provides software, services and systems in the areas

of managing the product lifecycle and management of industrial operations SISWworks collaboratively with clients to offer industrial software solutions that helpcompanies worldwide to achieve a sustainable competitive advantage by realizing,making real their important innovations

The autonomous driving technologies and systems has been developing ically recently in both research and commercial products, for example, autonomousparking technologies function in several cars, i.e Ford, Toyota Lexus, Audi A6,BMW i3 [19] Audi’s self-driving car performed an autonomous journey from SanFrancisco to Las Vegas on January, 2015 [20] and Waymo’s vehicles have been tested

dramat-on public roads without human in the driver seat from November, 2017 [21] Theseintelligent driving assist systems bring various benefits to the society, for example,removing difficulty and stress, reducing the amount of time and traffic disruption,

as well as preventing minor dents and scratches by less-skilled drivers

In this thesis, we aim to generate a feedforward control signal using ILC rithms that realize the motion of the vehicle along a given path while taking intoaccount system dynamics and constraints The reference trajectory of the vehicle ispredetermined The requirements of the control system are: smallest tracking errorwhile acceleration and steering control signals are smooth and be constrained

algo-ILC has several advantages over a well-designed feedback and feedforward troller [1] A feedback controller has to react to inputs and disturbance, therefore,always has a lag in transient tracking This lag can be eliminated by feedforwardcontroller, but only for known or measurable signals ILC is anticipatory and cancompensate for exogenous signals, such as repeating disturbances by learning from

con-previous iterations In ILC, the exogenous signals are not required to be known ormeasured but repeated from iteration to iteration.

The objective of this master thesis is to demonstrate the potential of ILC ologies in autonomous applications via a co-simulation framework of high fidelityvehicle dynamics and traffic environment models

LMS Imagine.Lab Amesim software in Siemens Industry Software NV is a physics simulation platform that provides libraries of different physical domain, such

multi-as mechanical, electromechanical and powertrain [16] In this project, it will beused to simulate a vehicle and its dynamic for the purposes of testing ADAS controlalgorithms By connecting blocks, a complex and realistic model can easily be builtfor simulations Furthermore, a very detailed sub-model of single components can

be made

Figure 1.1: Vehicle dynamics basic [7]

Figure 1.1 presents simplified chassis models (bicycle model on the left-hand sideand four wheels steering model on the right-hand side) δ and V are steering andvelocity inputs, and the outputs are states of the car These models could be usefulfor basic functional chassis modeling and control law design, as they do not requiremany chassis parameters

Figure 1.2 shows the model of a complete vehicle system, including chassis, ertrain, braking, steering, and suspension components This model illustrates a realvehicle in very detail, so it is useful in this project

pow-Figure 1.2: AMEsim vehicle dynamics simulations of the vehicle chassis [7]

1.5 Demostration with PreScan

For demonstration purpose, we use co-simulation of AMEsim and PreScan can is a physics-based simulation platform provided by Tass International [17] It isused in the automotive industry for the development of Advanced Driver AssistanceSystems (ADAS) that are based on sensor technologies such as radar, laser, lidar,camera and GPS This software not only includes a user interface (GUI) allows us

PreS-to build scenarios and sensors, but also consists of a Matlab/Simulink interface thatenables us to add a control system This interface can be used to import existingMatlab/Simulink models such as vehicle dynamics models When running experi-ment, a realistic 3D representation of the scenario is given as shown in Figure 1.3

Figure 1.3: A scenario in Prescan

The remainder of this thesis is organized as follows: Vehicle dynamic is sented in chapter 2 Chapter 3 introduces a simple feedback controller Chapter 4details Iterative Learning Control and RoFaLT tool to solve ILC algorithm Twoautonomous applications and simulation results will be presented in chapter 5, andchapter 6 concludes the thesis

pre-Chapter 2

Vehicle dynamics

In order to execute a proper control action, a parametric model of the vehicle isneeded In this chapter, different models available from literature will be introduced,including both vehicle and tire models Then a model is selected considering thetrade-off between detailed dynamics and computational effort complexity The stepsexplained in this chapter replicates procedures discussed in [2], [3] and [4]

The considered models are assumed rear-wheel driven car with front-wheel ing The global coordinate system is defined by (X, Y, ϕ), where ϕ is the orientation

steer-of the car with respect to the positive X-axis A local moving coordinate system(x, y) is attached to the car, with the x-axis aligned with the longitudinal axis ofthe car (Figure 2.1)

Figure 2.1: Model Coordinate System [2]

2.1 Vehicle model

The car is symmetric and has standard geometric relations Furthermore, lowcenter of gravity and firm suspensions allow us to neglect the out-of-plane motionand the roll dynamics The velocity of inside and outside wheels are similar, andthe roll dynamic of the car is negligible To simplify the model, the pair of tires

at each end of the vehicle are grouped as a single tire We obtain the well-knownbicycle model or single track model, as described in Figure 2.2

Figure 2.2: Bicycle model [2]

By integrating the equations of motion, then transforming them to the globalcoordinate system using a rotation matrix, the position and orientation of the carare obtained The yaw rate ˙ϕ is the same in both local and global frames:

One important component in vehicle modelling is the tire-road interactions model

It is essential in the case if one would like to capture the force saturation (maximumforce given to powertrain) and avoid drift situations (such as wet roads in rainydays) Therefore, tire model is presented and then combined with the discussedbicycle model The detail of this model can be found in [2], [4] and [12], in whichthe complete mathematical model is given as below:

Ff,y= Df sin (Cfarctan (Bfαf)) (2.5a)

Fr,y = Drsin (Crarctan (Brαr)) (2.5b)

B: stiffness factor, slope at the origin

C: limits the range of the sine function appearing in the formula (2.5)

D: peak value of force

2.3 Slip-free bicycle model

The slip-free bicycle model assumes ideal point contact and no slip behavior andhence zero lateral speed at the rear wheel vr,y This model type is valid under thefollowing assumptions: the tire force limit is never exceeded in case of slow drivingsituations; the slip angle α ≈ 0; and the steering angle δ ≈ 0 because of smallturn action Under the above assumptions, the slip-free model can be derived inFigure 2.3, as discussed in [4]

Figure 2.3: Geometry for bicycle model

Applying these above assumptions, we get:

L and C2 =

1

L.

We have:

Fdc = ma is power-train force given to the vehicle

Fdrag = m(−Cr0− Cr2vx2) is resistance force of the vehicle

Here, Cr0 and Cr2 are zero and second order friction parameters, respectively.

2.4 Valiation

In order to deriving the ODE model parameters, a validation step should be plemented This is to find the parameters of the slip-free bicycle model in Eq (2.15)and Eq (2.16) which will be used later in the control design stage While the value

im-of C2 = 1/L = 1/2.4 [m−1] can be found in AMEsim model, the other parameters,

C0, Cr0 and Cr2 are obtained by model validation The parameters tuning procedure

is implemented by comparing between the states and the outputs of the ODE model(simulated outputs) and the output of the AMEsim model (measured outputs) re-sponding to the same given input signals The differences between simulated andmeasured outputs give an impression on the accuracy of the model [6] We design

2 step inputs to both AMEsim model and ODE model: step acceleration input attime t = 5 [s] and step steering input (δ) at t = 10 [s], as shown in Figure 2.4.Initial velocity is set to 2 [m/s] The gear input is set to 1 to drive the car forwardand -1 for going backward Figure 2.5 and Figure 2.6 show the results of the ODEand AMEsim models when the car goes forward and backward, respectively

Figure 2.4: Simulink model of Validation

Figure 2.5: Validate results when the vehicle goes forward

Figure 2.6: Validate results when the vehicle goes backward

In Figure 2.5, from t = 0 to 5 [s], a and δ are set to zeros, and there are onlyfriction coefficients Cr0 and Cr2 effecting to the velocity Observing the measuredvelocity, we see that it decreases linearly from initial value 2 [m/s] to 1.9 [m/s] due

to the effect of Cr0 It means that there is almost no effect of the second orderfriction parameter on the decrease of the velocity, as a result, Cr2 ≈ 0 By changingthe value of Cr0 until the simulated velocity fits the measured velocity, we obtain

Cr0 = 0.0175.

From t = 5 to 10 [s], we set a = 0.5 [m/s] and δ = 0 Both measured velocity andsimulated velocity increase linearly and close to each other when the accelerationinput is added It verifies the validated values of Cr0 and Cr2

From t = 10 to 15 [s], we set a = 0.5 [m/s] and δ = 0.2 [rad] During this time,the steering step input is applied This input signal also effects to the velocity ofthe vehicle While C2 is known, C1 is tuned until the simulated velocity and themeasured velocity are as close as possible, resulting C1 = 0.22

In summary, 2.5 and 2.6 verify the ODE model parameters in both situations:forward and backward There is still mismatch error of around 1 [m] between trajec-tories of two models when the vehicle starts turning This error occurs due to someassumptions when deriving mathematical equations of the slip-free bicycle model,

as given in section 2.3 This mismatch model, however, could be corrected whenapplying the proposed iterative learning control framework, that will be presentedlater in chapter 4

Validated parameters of bicycle model are listed in Table 2.1:

Table 2.1: : Parameter of bicycle model

Parameter Unit Physical meaning Value

C1 - Geometrical (lr/L) 0.22

C2 m−1 Geometrical (1/L) 1/2.4

Cr0 1/m Zero order friction parameter 0.0175

Cr2 m/s2 Second order friction parameter 0.00

The second order friction parameter, Cr2, is very small and approximately equal

to zero

Chapter 3

Feedback controller

In this chapter, the traditional PID (Proportional-Integral-Derivative) controllerdesign is discussed The objective is twofold First, it aims to design a feedback con-troller that could be used in combination with ILC to stabilize system with respect

to uncertainties in measurement noise and non-repeating disturbances Second, thePID control also demonstrates limitations in obtaining satisfactory tracking controlperformance with nonlinear multiple-input multiple-output (MIMO) systems, andhence motivating a more advanced controller development such as ILC

Intuitively, the PID control assumes decoupled MIMO system, and design ing input to follow the path and acceleration (throttle) input to track the referencevelocity Therefore, we separate the control laws into two single-input single-outputcontrollers: velocity based PID controller that designs acceleration input, and apsi-error based PID controller that calculates steering angle input The schematicdiagram of feedback controller is shown in Figure 3.1

steer-Figure 3.1: Block diagram of feedback controller

As the first step, we validate the response of closed loop system to velocity stepinput at t = 3 [s] and steering step input at t = 6 [s] Since the system is nonlinearand MIMO, well-known techniques to design feedback controller for linear systems,such as root locus technique and frequency response technique, are not suitable.Manual tuning method is used to find PID parameters so that the following controlspecifications are satisfied: steady state error is less than 3 %; overshoot smaller

than 5 %; and settling time tsis smaller than 1 [s] The tuning approach is achieved

by arranging the parameters according to the system response [18] By observingsystem behavior, Kp, Ki and Kd are changed until the desired system response isobtained Table 3.1 lists value of PID parameters

Table 3.1: : Parameter of bicycle model

illus-of the vehicle reach their steady state quickly, after 1 [s] for both signals withoutovershoot In addition, we can see the effect of steering input to velocity, leading to

a significant decrease in velocity when the vehicle start to turn at t = 6 [s] Thisadverse effect, however, can be addressed by feedback controller

Figure 3.2: Step response of PID controller

Next, the designed feedback controller is applied to drive the vehicle along a givenreference path The position error is expected to smaller than 0.05 [m] when thecar runs at a parking speed of 3 [m/s] Simulation results are shown in Figure 3.3.The figure demonstrates that measured velocity and yaw angle are able to tracktheir references and the vehicle follows the trajectory stably However, there were

a noticeable lagging in measured velocity when it increases and decreases This

lagging leads to a large position error, from 0.5 [m] at t = 5 [s] to 2.5 [m] at t = 15[s] and 3.2 [m] at t = 25 [s] Thus, the results do not meet our expectation Thisillustrates the difficulty in using a PID controller for a nonlinear, MIMO system,

in which the number of outputs is higher than the number of inputs In the nextchapter, iterative learning control and RoFaLT tool will be introduced to addressthis problem

Figure 3.3: Result of feedback controller

Chapter 4

Iterative Learning Control (ILC)

This chapter presents an overview of ILC and RoFaLT tool Section 4.1 duces the main concept of ILC and popular ILC designs Theoretical background

intro-of RoFaLT, a tool used in this thesis to implement ILC, will be explained in section4.2

The overview of ILC controller is presented mainly based on the survey paper

of D Bristow et al [1] The main idea of ILC is based on the notion that theperformance of a system that executes the same task multiple times can be improved

by learning from previous executions Robot arm manipulators, chemical batchprocesses are typical examples of systems that operate in a repetitive manner Inthese tasks, the systems are required to perform the same action over and overagain with high precision This type of learning in ILC differs from other learningstrategies such as neural network and adaptive controller That is, instead of learningthe model or controller, which is a system, ILC learns the control input, which is asignal

Consider the discrete-time, linear time-invariant (LTI) system:

yj(k) = P (q)uj(k) + d(k), (4.1)

where k labels time instants, j denotes iteration number, q is the forward time-shiftoperator: qx(k) ≡ x(k + 1) Here, yj(k) is output, uj(k) is control input, and d isthe repeated exogenous signal (disturbance) The plant P (q) is a proper rationalfunction of q and has a delay

The basic structure of an ILC is shown in Figure 4.1 The input signal uj(k) andthe error signal ej(k) between reference trajectory yd(k) and system output yj(k)are stored in memory The input signal for the next iteration is computed based on

uj(k) and ej(k + 1) That is: uj+1(k) = f (uj(k), ej(k + 1))