A Hybrid Hierarchical Rally Driver Model for Autonomous ......with Rally driving techniques. While Formula drivers operate the vehicle linearly, with smooth and gentle inputs, and

A Hybrid Hierarchical Rally Driver Model for Autonomous Vehicle AgileManeuvering on Loose Surfaces

Manuel Acosta, Stratis Kanarachos and Michael E. FitzpatrickSchool of Mechanical, Aerospace and Automotive Engineering, Coventry University, Coventry, U.K.

Keywords: Agile Maneuvering, Linear Quadratic Regulator, Drift Control, Motion Planning, ADAS.

Abstract: This paper presents a novel Hybrid Hierarchical Autonomous system for improving vehicle safety based onagile maneuvering and drift control on loose surfaces. Standard Electronic Stability Control Systems providestability by limiting the vehicle body slip, thus reducing the capability of the vehicle to generate lateral ac-celeration and follow road segments and paths with high curvature on loose surfaces. The proposed systemovercomes this shortcoming. Furthermore, it is the first time where a solution for arbitrary road geometries isproposed. The system described in this work consists of three layers. The first layer selects the driver model.The second layer selects the path to be followed and the maneuver type using a Proportional controller andmotion planning strategies. The third layer coordinates the steering and driving functions of the vehicle to per-form the maneuver, where a Gain-Scheduled Linear Quadratic Regulator is employed to achieve drift control.The hybrid system is implemented in Matlab/Simulink R© and tested in two scenarios: First, a Rally-like stageformed by a combination of clothoid and arc segments is used to study the drift-path-following capabilities ofthe system, and lastly, a lateral collision case is proposed to evaluate the suitability of the system as an ADASCo-Pilot system for lateral collision avoidance.

1 INTRODUCTION

Rallying stands out from other motorsport disciplinesdue to the complexity and peculiarities associatedwith Rally driving techniques. While Formula driversoperate the vehicle linearly, with smooth and gentleinputs, and seeking for quasi-static conditions, pro-fessional Rally drivers exhibit an aggressive behavior.They take advantage of the car non-linearities and ex-cite the yaw dynamics to generate high yaw acceler-ations and change the vehicle attitude fast (Blundelland Harty, 2004). It is remarkable how Rally driversadapt their behavior to the road friction characteristics(e.g. Tarmac, Gravel) and control the vehicle underall kind of disturbances (e.g. roots, bumps). Usingan analogy with control systems, it can be stated thatFormula drivers are very precise controllers for track-ing problems (racing line) whereas Rally drivers areoutstanding robust controllers (drift stabilization).

The problem of off-road autonomous maneuver-ing has been adressed in (Lenain et al., 2017; Lenainet al., 2012) employing kinematic and dynamic mod-els for low-speed path tracking. In order to developautonomous vehicles capable of operating the vehi-cle at higher speeds and more demanding conditions,some authors have focused their research in the study

of the dynamics behind Rally driving techniques. In(Acosta et al., 2016) the yaw acceleration requiredto perform agile maneuvers such as ScandinavianFlick or Trail Braking was studied employing the Mo-ment Method Diagram (MMD), (Milliken and Mil-liken, 1995), and a Finite State Machine (FSM) capa-ble of performing these tasks autonomously was pro-posed. In (Velenis et al., 2007) a mathematical anal-ysis of these maneuvers was presented and differenttrajectory optimization scenarios were studied using anumerical scheme. A stability analysis of aggressivedriving techniques was presented in (Yi et al., 2012;Li et al., 2011), and a stability phase portrait based onthe yaw rate and the rear wheel slip angle was pro-posed.

The analysis of drifting techniques was ap-proached in (Hindiyeh, 2013; Velenis et al., 2011;Edelmann and Plochl, 2009). In (Edelmann andPlochl, 2009), the unstable nature of the powerslidemotion was studied numerically using a two-track ve-hicle model and root locus analysis. In (Velenis et al.,2011), the stabilization of a Rear-Wheel-Drive (RWD)vehicle around the steady-state drift equilibrium wasstudied. A cascade control architecture formed by aLinear Quadratic Regulator (LQR) and a Backstep-ping controller was proposed for this purpose. The

216Acosta, M., Kanarachos, S. and Fitzpatrick, M.A Hybrid Hierarchical Rally Driver Model for Autonomous Vehicle Agile Maneuvering on Loose Surfaces.DOI: 10.5220/0006393002160225In Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2017) - Volume 2, pages 216-225ISBN: Not AvailableCopyright © 2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

same problem was investigated in (Velenis, 2011), butthis time a Front-Wheel-Drive (FWD) driveline archi-tecture was employed. In (Hindiyeh, 2013), a nested-loop structure was proposed, and an input coordina-tion scheme was suggested to integrate the lateral andlongitudinal control actions.

Finally, the first pieces of evidence of autonomousor semi-autonomous systems that replicate some pat-terns exhibited by Rally drivers have been found in(Cutler and J.P.How, 2016; Gray et al., 2012). Inthe former, autonomous drifting is achieved using amethodology to incorporate Optimal Control policiesinto a Reinforcement Learning (RL) process. In (Grayet al., 2012), authors proposed a hierarchical two-level control framework composed of a high-levelmotion planner and a low-level trajectory trackingcontroller based on Model Predictive Control (MPC).

In this paper, a Rally-based driver model is pro-posed for improving the vehicle safety based on theautonomous execution of agile maneuvers and driftcontrol. The contribution of the paper is significantin what concerns driver modeling, as the drift controlaction is no longer restricted to constant radius turnsand is performed along clothoid and arc segments ofdifferent radii instead. In Section 2, the formulationemployed to model the vehicle planar dynamics, tires,and road, is presented. In addition, relevant back-ground about the Drift Equilibrium Solutions and Lin-ear Quadratic Optimal Control is provided. The struc-ture of the driver model proposed in this paper is de-scribed in Section 3. Simulation results for two sce-narios: Rally-like stage and Lateral collision avoid-ance are provided in Section 4. Finally, conclusionsand future intended steps are exposed in Section 5.

2 BACKGROUND

2.1 System Modeling

2.1.1 Single-track Vehicle Model

Following the approach proposed in previous worksto study the vehicle behavior in agile maneuvers anddrift-equilibrium problems, (Tavernini et al., 2013;Velenis et al., 2010), a single track model is employedin this research, expressions (1-3).

x1 =1m(Fx f cos(u1)−Fy f sin(u1)+Fxr)+ x2x3 (1)

x2 =1m(Fy f cos(u1)+Fx f sin(u1)+Fyr)− x1x3 (2)

x3 =1Iψ(Fy f cos(u1)l f +Fx f sin(u1)l f −Fyrlr) (3)

The vehicle longitudinal velocity (vx), lateral velocity(vy), and yaw rate (ψ), form the state vector of the sys-tem (x = vx,vy, ψ). The terms l f , lr correspond tothe distance from the front and rear axles to the centerof gravity respectively. The vehicle mass is denotedby m and Iψ is the yaw inertia of the vehicle. Thesteering wheel angle and the axle longitudinal slipsare considered inputs to the system (u = δ,λ f ,λr).Wheel rotating dynamics modeling is avoided at thisstage of the research in order to simplify the prob-lem formulation. The vehicle parameters employedin this paper are presented in Table 1, and correspondto a compact rear-wheel-drive vehicle. The tire forcesrequired to compute the system states are modeled us-ing the nonlinear expressions (4-5).

Fx,i = Fz,iµ(λi,αi), i ∈ f ,r (4)Fy,i = Fz,iµ(λi,αi) (5)

The normal load proportionality principle is as-sumed, and the tire friction coefficient is presented asa nonlinear function that depends on the axle wheelslips (α) and the axle longitudinal slips (λ). The for-mer are obtained from the geometric equations (6-7), using a small angle approximation (Kanarachos,2012).

α f = u1−x3l f

x1− x2

x1(6)

αr =−x2

x1+

x3lrx1

(7)

Finally, the tire vertical forces (Fz) are calculatedusing a simple steady-state longitudinal weight trans-fer model (8).

Fz,i = Fzi,st ±mhCoG

l f + lr(x1− x2x3) (8)

The height of the center of gravity is denoted byhCoG, and the static vertical loads are designated byFz,st .

Table 1: Parameters of the Single-Track model.

Sym. Value Unit Sym. Value Unitl f 1.35 m lr 1.45 m

hCoG 0.55 m Iψ 1800 kgm2

m 1500 kg Drive RWD −

2.1.2 Tire Friction Model

The tire friction coefficients (µx,µy) are approximatedwith a simplified isotropic model that employs aMagic Formula-based (MF) formulation. The theo-retical longitudinal and lateral slips (σx,σy), as well as

A Hybrid Hierarchical Rally Driver Model for Autonomous Vehicle Agile Maneuvering on Loose Surfaces

217

Table 2: Pacejka tire parameters representative of gravel andasphalt surfaces, (Tavernini et al., 2013).

Surface B C D EGravel 1.5289 1.0901 0.6 -0.95084Asphalt 6.8488 1.4601 1.0 -3.6121

the equivalent slip (σ) are computed from expression(9), following the formulation presented in (Taverniniet al., 2013; Pacejka, 2012).

σx =λ

1+λ,σy =

tanα1+λ

,σ =√

σ2x +σ2

y (9)

Once the equivalent slip is calculated, the longitu-dinal and lateral friction coefficients are obtained us-ing equations (10-11).

µx =σx

σDλ sin[Cλ arctanσBλ−Eλ(σBλ

− arctanσBλ)](10)

µy =σy

σDλ sin[Cλ arctanσBλ−Eλ(σBλ

− arctanσBλ)](11)

The MF tire parameters employed in this paperare shown in Table 2, and were extracted from (Tav-ernini et al., 2013). These parameters approximate theshape of the friction-slip curves that are characteristicof gravel and asphalt surfaces.

2.1.3 Road Modeling

The position of the vehicle with respect to the ref-erence path is expressed in curvilinear coordinates,(Tavernini et al., 2013). The position of the vehiclealong the reference path Ss, the lateral deviation of thevehicle with respect to the road centerline Sn, and therotation of the vehicle with respect to the road tangentε, are computed using expressions (12-14).

Ss =V cos(ε+β)

1−Snκ(12)

Sn =V sin(ε+β) (13)

ε = ψ−κV cos(ε+β)

1−Snκ(14)

Where κ is the road curvature, V is the module ofthe velocity, and β is the vehicle body slip angle.

2.2 Drift Equilibrium Solutions

The reference solutions necessary for the drift controltask are obtained following the approach presented in

(Velenis et al., 2011). Steady-state conditions are im-posed on the vehicle planar motion states, and the ve-hicle body slip angle (β) and the road radius (R) arefixed. The Matlab R© function fsolve is used to solvethe vehicle dynamic equations (1-8). The tire rollingresistance is neglected, and the front axle longitudinalslip is set to zero (λ f = 0). In order to study the in-fluence of the tire friction characteristics on the driftequilibrium solutions, the process was repeated usingthe gravel and asphalt parameters presented in Table2, and the results depicted in Fig. 1 were obtained.

0

200

400

-200SW

A (

de

g)

-4002 4 6 8 10

Ayc

(m/s2)

2 4 6 8 10

Ayc

(m/s2)

(

de

g)

1 2 3 4

Ayc

(m/s2)

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A (

de

g)

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400

1 2 3 4

Ayc

(m/s2)

(

de

g)

0

10

-10

-20

-30

-40

Gravel Asphalt

0

10

-10

-20

-30

-40

Figure 1: Vehicle Equilibrium Solutions in gravel and as-phalt, R = 20m. In blue regular solution, in orange driftsolution. The steering wheel angle is denoted by SWA andthe centripetal acceleration by Ayc.

The multiplicity of solutions in asphalt is relatedto the shape of the friction-slip curve, Fig. 2 right,where a one-to-one mapping between the friction co-efficient (µ) and the equivalent slip (σ) does not ex-ist (same friction values can be obtained for small”before-peak” and large ”after-peak” slips). A uniqueequilibrium solution characterized by a large bodyslip angle at the limit is obtained in gravel, Fig. 1left. In order to maximize the centripetal accelera-tion, it is necessary to stabilize the vehicle around abody slip angle of -35 degrees approximately. Thischange in behavior is due to the different shape of thefriction-slip curve in gravel, Fig. 2 left. In this case,the grip scaling approach described in (Pacejka, 2012)and employed to approximate the friction forces inlow µ rigid surfaces is no longer valid, and the maxi-mum grip is developed for high slip values.

As can be noticed in Fig. 2 right, the equivalentslips required to achieve maximum centripetal accel-eration in asphalt remain close to 0.15 (peak frictionforce). On the other hand, these values are consider-ably higher in gravel (0.4-0.7), Fig. 2 left, and have anotable influence on the final equilibrium body slipangle. Results might differ when employing moreelaborated tire, chassis, and driveline models, but the

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1

0.6

0.2

0.8

0.4

0.5 1.51.0 2.0

!0.5 1.51.0 2.0

!

1

0.6

0.2

0.8

0.4

Gravel Asphalt

1 2 3 4

Ayc

(m/s2)0

!

0.5

1.0

1.5

2.0(a)

(b)

RearFront

(a)

(b)

RearFront

!

0.5

1.0

1.5

2.0

2 4 6 8 10

Ayc

(m/s2)

Figure 2: (a) Equivalent slip equilibrium solutions, R =20m. (b) Friction-slip curves for each surface.

physical explanation behind the large drifts exhibitedby World Rally Cars (WRC) in Finland or Argentinaremains the same.

2.3 Linear Quadratic Regulator

Linear Quadratic Control is often employed in multi-input problems to determine the optimal feedbackgain based on the optimization of a performance ob-jective function. In the following, the Infinite TimeHorizon case (LQR) is presented. For the formulationof the LQR, a Linear Time-Invariant (LTI) system ex-pressed in state-space form (15) is considered.

x = Ax+Bu (15)

Assuming that the n states of the system are avail-able for the controller, the optimal control vector thatstabilizes the plant around the origin is given by theexpression (16).

u(t) =−Kx(t) (16)

Where K is the optimal feedback gain obtainedfrom the optimization of the objective performancefunction (17).

J =∫ ∞

0(xT Qx+uT Ru)dt (17)

The terms Q and R are positive-definite Hermitianmatrices that account for the relative importance ofthe regulation error and actuator energy expenditurerespectively. Substituting the control law (16) in thecost function (17), and following the derivation pre-sented in (Ogata, 2010), the control law can by refor-mulated as:

u(t) =−R−1BT Px(t) (18)

Where the constant matrix P is the uniquepositive-definite solution to the associated steady-state Riccati equation (19).

PA+AT P−PBR−1BT P+Q = 0 (19)

The Positive-definite solution of this equation (P)always exists provided that the matrix (A−BK) is astable matrix (i.e. the closed-loop poles of the systemlie on the left side of the complex plane).

2.3.1 Gain-scheduled Linear QuadraticRegulator

In order to implement the LQR controller presentedpreviously, the vehicle dynamics equations (1-8) werelinearized around the Vehicle Equilibrium Solutions(xss,uss). The axle friction forces were linearized us-ing a first order Taylor series expansion (20).

Fi(λ,α) = Fi,0 +∂Fi

∂α∆α+

∂Fi

∂λ∆λ

= Fi,0 +Ci,α∆α+Ci,λ∆λ, i ∈ x,y(20)

Where the axle longitudinal stiffness (Cx,λ) andthe axle cornering stiffness (Cy,α) were calculatedfor each equilibrium solution using a finite differ-ences approach (21-22), and the cross-stiffness terms(Cx,α,Cy,λ) were neglected.

Cx,λ ≈Fx,λss+∆λ−Fx,λss−∆λ

2∆λ(21)

Cy,α ≈Fy,αss+∆α−Fy,αss−∆α

2∆α(22)

The Vehicle Equilibrium Solutions were found fora grid of operating conditions (βss = 0 : 5 : 30, Rss =10 : 10 : 400), and the plant (Ass) and input (Bss)matrices obtained after the system linearization wereparticularized at each operating point.

1,1

1,2

1,3

2,1

2,2

2,3

800 600 400 200 0 -40

-20

0

0.15

0.35

0.30

0.25

0.20

800600 400 200 0

-40

-20

0

800600 400 200 0

800600

400200

0

0

-10

-20

-30

-40

-20

0

-40

-20

0

800600

400 200 0

800600

400200 0

0

1

2

3

0.15

0

-0.05

0.05

0

-0.05

-0.10

-0.15

0.05

0.10

0

-0.1

-0.2

-0.3

-0.4

0

-0.1

-0.2

-0.3

0.1

-40

-20

0

Figure 3: Gain surfaces of the Gain-Scheduled LQR.

Finally, the gain surfaces depicted in Fig. 3 wereobtained for each operating point. Following the sameformulation as (Velenis et al., 2011), the final steering


219

and rear longitudinal slip control inputs were com-puted using expression (23).

u = uss +Kss(x−xss) (23)

Where the regulation terms are added to thesteady-state open-loop inputs (uss). In order to avoidchattering, the input weighting matrix was set tentimes greater than the process weighting matrix (R =10Q,Q = In).

3 DRIVER MODEL STRUCTURE

The structure of the driver model proposed in thiswork is depicted in Fig. 4. A Hierarchical Hybridmodeling approach inspired by previous works (Ka-rimoddini et al., 2014) has been followed to combinethe path following and drift control tasks. The oper-ation of the hierarchical automaton can be describedbriefly in the following manner.

• Supervision Layer: The driver model is selecteddepending on the road geometry (radius) and theroad friction characteristics. Two driver modelsare considered in this work: a regular or low bodyslip driver model, and a drift or high body slip one.

• Path planning Layer: Four blocks are distin-guished in this layer: Straight Look-Ahead (SLA),Step Transitions (ST), Agile Transitions (AT), andCurved Look-Ahead (CLA). The blocks SLA andCLA compute the look-ahead points necessary forthe path following task. A Predictive Trajectoryalgorithm is employed to minimize the lateral de-viation error during fast transitions (change in cur-vature sign, Agile Transitions) and abrupt radiusreductions (e.g. from straight line driving to Hair-pin turn, Step Transitions).

Supervision

Layer DRIVER SELECTOR

REGULAR DRIVER DRIFT DRIVER

Low slip path following Drift path following

CLAAgile TransitionsStep Transitions

Gain-Scheduled LQR

Drift control

Path planning

Layer

Regulation

Layer

P Sat.

Road geometry

Road friction

SLA

P

Figure 4: Hierarchical Hybrid Structure, driver model.

• Regulation Layer: If the regular driver action isrequired (straight line or large radius), the steer-ing control action is carried out by a Proportionalcontroller with saturation functions (Casanova,2000). On the other hand, during lower radiuswhere large body slips maximize the lateral ac-celeration, Fig. 1, a Gain-Scheduled LQR is used.The tracking references necessary for the regula-tion task are provided by an upper-level Propor-tional controller P, which produces an output pro-portional to the lateral deviation error. Finally,during ST or AT, the drift control action is trig-gered to change the vehicle heading fast or stabi-lize the vehicle around a certain body slip.

3.1 Supervision Layer

For simplicity, constant road friction characteristicsare considered in this paper, specifically a gravel sur-face. Thus, the driver model is selected accordingto the road segment’s curvature. During large radii(R > 400m) and straight line driving, the low bodyslip driver is selected. For lower radius where drift isadvantageous for maximum centripetal acceleration,the drift driver is used.

3.2 Path Planning Layer

3.2.1 Regular Driver

In the regular driving mode, two blocks are active:SLA and ST.

• Straight Look-Ahead (SLA): This block computesthe lateral deviation error of a set of future pathcoordinates (Si) considering a straight trajectory,(Casanova, 2000). A proportional controller withsaturation functions regulates the path followingfunction (Casanova, 2000).

0

1

2

3

0

1 2

3

!0

!1

!2

!3

!0

!1

!2

!3

"0

"1

"2

"3

0

1

2

3

Straight Look-Ahead (SLA)

Curved Look-Ahead (CLA)

Figure 5: Calculation of the lateral deviation error. StraightLook-Ahead approach (Regular driver) and Curved Look-Ahead approach (Drift Driver).


220

• Step Transitions (ST): The aim of this block is toachieve a fast transition with a minimum lateraldeviation between straights and short-radius turns.This behavior is often seen in Rally drivers duringTrail braking or Scandinavian Flick maneuvers,(Acosta et al., 2016), when a high yaw momentis applied to build up a large body slip and initi-ate the drift condition. In order to model this be-havior in the autonomous system, the closed loopresponse of the Gain-Scheduled LQR was com-puted off-line under a series of Step changes inthe reference radius. The trajectories obtained inthese tests were normalized and stored in Look UpTables. The test was repeated for different radii(R = 10 : 10 : 400m), and the target body slipduring the drift stabilization was set to 20 degrees.

Step transitions

Agile transitions

Minimum

Drift Control

Minimum

Drift Control

!"

!"

Figure 6: Step transitions and agile transitions. Optimumtiming for the application of the yaw moment Mz.

In order to determine the optimum timing to trig-ger the Step Transition, the area (A) enclosed be-tween the predicted trajectory and the referencepath is computed. When the minimum value isfound, the step input (yaw moment Mz) is appliedand the drift control is switched on. A memoryblock is employed for this purpose, and the areacomputed at the current time-step (Ak) is com-pared to the minimum value calculated in pre-vious steps Amin. If the current value is lower,Amin is updated. Otherwise, the minimum isfound and the Step Transition is triggered. It isassumed that a priori information regarding thearc radius after the transition is available, andthus the trajectory τi corresponding to this radiuscan be selected from the total set of trajectories(Ω = τ10, ...,τ400). In future investigations, thisrequirement will be eliminated by evaluating alarger number of candidate trajectories.

3.2.2 Drift Driver

Two blocks are active during the action of the driftdriver: CLA and Agile Transitions.

• Curved Look-Ahead (CLA): The action of thisblock is analogous to the SLA block. As the driftdriver is active during short radii, it is necessaryto consider the curvature of the vehicle trajectoryin order to avoid large errors, Fig. 5. The mathe-matics and geometry involved in the calculation ofthe lateral deviation error are omitted due to spacelimitations.

• Agile Transitions (AT): The purpose of this blockis to concatenate body slip angles of opposite signwith minimum lateral deviation, Fig. 6. This ac-tion is performed by Rally drivers when short-radius turns of opposite sign are concatenated(e.g. a sequence of Hairpin Turns). The blockis implemented following the same principle thanthe ST block, and the closed loop response ofthe Gain-Scheduled LQR is evaluated off-line fora range of radii. At each radius, the simulationstarts in drift equilibrium conditions, with the ve-hicle body slip stabilized around 20 degrees. Thesign of the target body slip is changed suddenly,and the closed-loop response of the system is sim-ulated. The trajectories are then normalized andstored in Look Up tables. At each time-step, thecandidate trajectory (τi) is translated to the vehi-cle center of gravity and rotated according to thevehicle heading angle.

*Remark: As was shown in (Velenis et al., 2011),the body slip at which the lateral acceleration is maxi-mized varies with the radius of the turn. Thus, in orderto guarantee minimum time maneuvering it would benecessary to adjust the target body slip angle accord-ing to the current radius. For simplicity, it is assumedthat near optimal conditions are achieved for a uniquetarget body slip angle.

3.3 Regulation Layer

Two driver models are implemented in the regulationlayer: low body slip steering control and high bodyslip drift control.

3.3.1 Low Body Slip Steering Control

The low body slip steering control was extracted from(Casanova, 2000), and its construction is oriented toracing-line path following problems. In essence, thecontroller attempts to minimize the heading and lat-eral deviation errors using proportional gains and sat-uration functions. The gain values were obtained


221

from (Casanova, 2000). Concerning the longitudinalcontrol action, a PID is employed to track a targetspeed profile. The generation of the target speed pro-file is omitted due to space limitations. For simplicity,a constant target speed was considered during the ac-tion of the Regular driver.

3.3.2 High Body Slip Drift Control

The function of the high body slip drift controlleris more involved, and two blocks are implementedin cascade to achieve the path following and driftcontrol tasks: path following P controller and Gain-Scheduled LQR, Fig. 7.

P

Target

Drift Equilibrium Solutions

!!

target

-

+

"#!!

$!!

CLA

vehicle trajectoryRef. path

#!!

%!!

Gain-Scheduled LQR

$ "#

&0 '

0

&1 '

1

&( '

(

.

.

.

.

∑&2 '

2

Proportional Curvature correction

DRIFT REGULATION

Figure 7: High body slip regulation. Proportional curvaturecontroller and Gain-Scheduled LQR.

• Path Following (P) Controller: As was seen inSection 2.2, for each pair (βss,κss) a set of Vehi-cle Equilibrium states (xss) and equilibrium inputs(uss) exist. In this paper, the path following task issituated in an upper level, and the final target cur-vature is formed by the reference curvature (κre f )and a correction term (∆κ), proportional to the lat-eral deviation error (24).

κ = κre f −∆κ (24)

The curvature imposed by the upper level P con-troller is used in combination with the targetbody slip (βss) to determine the reference statesand reference inputs of the Gain-Scheduled LQR(βss,λr,ss,δss,rss,Vss).

• Gain-Scheduled LQR: This block tracks the ref-erence states (xss) and inputs (uss) dictated by theupper level path-following controller, Fig. 7. De-tails regarding the implementation of this blockwere provided in Section 2.3.1.

4 RESULTS

4.1 Rally Stage

The driver model was implemented inMatlab/Simulink R© using the vehicle and tireparameters presented in Tables 1 and 2. At thisresearch stage, perfect knowledge of the vehicle pa-rameters, road-friction characteristics, and full statefeedback is assumed. The robustness of the controlleragainst uncertainties in the vehicle parameters androad friction characteristics will be addressed infutures stages of this research. A Rally-like stage wasconstructed using a combination of clothoid, arc, andstraight line segments to test the performance of theHybrid Driver model, Fig. 8.

0 100 200 600

-600

-400

-200

0

200

S1

S2

S3

x (m)

y (

m)

-800300 400 500 700

ST

AT

ST

Figure 8: Rally-like segment. Detail of Agile transitions ATand Step transitions ST.

For simplicity, a target body slip of ±20 degreeswas set during this simulation. Further steps in thisresearch will explore the combination of path follow-ing and non-constant body slip tracking. The stageconsists of 3 Sectors: S1, S2, S3, and the results ob-tained in Matlab R© are presented in the following.In order to explain the behavior of the Hybrid sys-tem, the following nomenclature has been employedfor the FLAGS shown in Figures 9-11: (ST) Steptransitions, (AT) Agile transitions, (P) Proportionalcontroller ON, (DRIFT) Drift driver model ON, and(REG) Regular driver model ON. The LQR referencesignals are denoted as (Ref ), the Regular driver speedreference by (REGspd), and the vehicle states and in-puts by (Sim).

During the first sector, the vehicle starts in astraight line and executes a ST to follow a large left-handed turn (t ≈ 18). The vehicle is stabilized inDRIFT mode and the P controller switches on to startthe path following task (t ≈ 19.5). After (t ≈ 40),an AT is performed to track a large right-handedclothoid. The P controller is switched off during the


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stabilization of the vehicle around the new operatingcondition and becomes active in (t ≈ 42) to track theclothoid transition (R = 200 to R = 100).

(

de

g)

time (s)

10 20 30 40 50 60 70

20

-20

1

0

FL

AG

S

(k

ph

)

200

! (

de

g/s

) 100

-100

SWA

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-)

1

-1

#$ (

m) 5

-5

100

0

0

0

0

Ref. Sim.P. REG.AT. DRIFT.ST.

REGspd

Figure 9: Results of Sector 1.

time (s)70 80 90 100 110 120

(

de

g) 20

-20

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0

FL

AG

S

(k

ph

)

200

! (

de

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0


REGspd


In the second sector, the system tracks a concate-nation of turns. The following sequence (AT - P OFF- Stabilization - P ON) is repeated through the sec-tor. As can be noticed in Fig. 10, the Hybrid systemgenerates large yaw accelerations (yaw rate peaks) tochange the vehicle attitude fast. This behavior resem-bles the driving style of Rally drivers (yaw-sideslipexcitation, (Blundell and Harty, 2004)), in which the

time (s)

120 130 140 150 160 170 180 190


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vehicle is operated in the upper and lower regions ofthe yaw acceleration versus lateral acceleration plot.

Finally, the results obtained in the third sector areportrayed in Fig. 11. During the first part of thesector, the system tracks a concatenation of R = 50mturns (t ≈ 120 to t ≈ 150), followed by a clothoid tran-sition and an arc segment (R = 60m). After that, theREG driver model switches on to drive the vehicle inthe straight segment (t ≈ 165) and goes off again in(t ≈ 170) when the ST action is triggered. Overall, theHybrid System exhibited a remarkable performanceto track the reference body slip angle with minimumlateral deviation.

4.2 ADAS System for Lateral CollisionAvoidance

During the previous subsection, the Hybrid System(Fig. 4) was studied as an entire Autonomous Sys-tem. In this subsection, however, the system is pre-sented as an ADAS, which takes control of the vehicleduring critical situations. Now, it is assumed that theresponses from the Regular Driver block approximatethe behavior of a vehicle equipped with a stability sys-tem that tries to mitigate the maximum body slip (i.e.ESP, (Zanten, 2002)).

In order to compare the performance of the vehi-cle equipped with a ”traditional” stability system, andthat using the proposed ADAS system, the test casepresented in Fig. 12 is evaluated. The car circulatesat a constant speed and approaches a left-handed turn(R = 50m) in a gravel surface. An initial test is per-


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REG

ST

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Straight line Clothoid transition

Arc segment

200 250 300 350150 400

x(m)

y(m

)

150

50

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P+LQR

LQRDRIFT STABILIZATION

AT

ADAS operation

Figure 12: State-Transition diagram of the ADAS hybridsystem.

formed switching off the drift driver model (”tradi-tional” stability system) and the same simulation isrepeated with the full ADAS system active.

50

100

300 420320 340 360 380 400

0

() ADAS ON

( ) ADAS OFF

x (m)

y (

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lateral deviation

Reference path

Vehicle trajectory

Vehicle heading

Figure 13: Vehicle trajectories obtained for (a) ADAS ON,(b) ADAS OFF.

As can be noticed in Fig. 13, the vehicle mini-mizes the lateral deviation when the ADAS system isactive. The system triggers the ST action, (t ≈ 26.5,Fig. 14) and switches on the drift control. As wasexplained in Section 2.2, large body slips are requiredin gravel in order to maximize the lateral acceleration(Figures 1-2). On the other hand, when the ADAS isOFF and the Regular driver model is active, the lattersystem tries to minimize the heading error, keepingthe vehicle attitude parallel to the tangent of the path(low body slip). This results in a low lateral acceler-ation, and the vehicle deviates abruptly from the ref-erence path. In order to negotiate the turn, the vehicleshould approach the curve with a much lower speed,thus limiting the lateral acceleration demand.

To summarize, when the ADAS system is active,the centripetal acceleration is maximized, and the ve-hicle can negotiate the turn at a higher speed thanwhen the system is switched off. This could po-tentially prevent the risk of lateral collision in loose

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Figure 14: Results obtained with the ADAS ON.

surfaces (deep snow or gravel) when a vehicle ap-proaches a turn at an excessive speed.

5 CONCLUSIONS

In this paper, an innovative Hierarchical HybridDriver model for autonomous vehicles has been pre-sented. The aim of the structure is to reproduce thebehavior of professional Rally drivers, and employadvanced driving skills such as drift control to en-hance vehicle safety when path following is requiredunder tight conditions.

The main contribution of this work is that the drift-like driving control is no longer restricted to constantradius turns, but to complex paths formed by clothoid,arcs, and straight line segments. In order to inte-grate robustly the body slip control and path follow-ing tasks, a hierarchical structure formed by a P con-troller and a Gain-Scheduled LQR has been proposed.The path planning modules (Agile transitions) and(Step transitions) have been incorporated in the sec-ond layer of the structure, in order to drive the vehi-cle through a concatenation of turns and alternate thebody slip fast with minimum lateral deviation, such asRally Drivers do.

The system has been implemented in Simulink R©,and tests have been carried out in a Rally-like stageand a lateral collision scenario. Results evidence theability of the system to track complex paths while op-erating the vehicle with large body slips.

Finally, it has been demonstrated that when the ve-hicle is driven on loose surfaces (centripetal acceler-


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ation is maximized with large body slip angles), thedrift control action can reduce the risk of lateral colli-sion and prevent the vehicle from lane departure. Therefinement of the motion planning algorithms and theevaluation of the robustness of the system under un-certain friction characteristics will be pursued duringthe next steps of this research.

ACKNOWLEDGEMENTS

This project is part of the Interdisciplinary Train-ing Network in Multi-Actuated Ground Vehicles(ITEAM) European program and has received fund-ing from the European Unions Horizon 2020 researchand innovation program under the Marie Skodowska-Curie grant agreement No 675999. M. E. Fitzpatrickis grateful for funding from the Lloyds Register Foun-dation, a charitable foundation helping to protect lifeand property by supporting engineering-related edu-cation, public engagement and the application of re-search.

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