IEEE TRANSACTIONS ON ROBOTICS, VOL. 30, NO. 5, OCTOBER 2014 1137

Design of a High-Performance Automatic SteeringController for Bus Revenue Service Based

on How Drivers SteerHan-Shue Tan and Jihua Huang

Abstract—This paper focuses on the design of an automatic steer-ing controller that has been implemented on an 18.3-m articulatedbus for revenue service. Compared with the typical environmentfor autonomous cars, the narrow and curving bus lane and the tightS-shape docking curves require a steering controller to consistentlyprovide high accuracy with ride comfort. While analyzing the dataof drivers steering through a double lane change course, we dis-covered and validated that driver’s steering rate is proportionalto a specific vehicle angle error. Subsequent analysis showed thatdrivers in effect execute a naturally robust controller that allowshigh-gain corrections and is insensitive to variations in vehicle dy-namics and speeds. This paper presents the first adaptation of thisdriver’s steering mechanism to a real-world challenging applica-tion. The resultant system achieved all performance requirements,and the revenue service at Eugene, OR, USA, started in June 2013.Moreover, the simple control structure greatly facilitated the designof fault detection, degraded control, and control redundancy.

Index Terms—Automated vehicle control, autonomous vehicles,bus rapid transit, driver models, intelligent vehicles.

I. INTRODUCTION

INTEREST in automated vehicles can be dated back to thelate 1930s, when the automated highway systems were

first shown as a feature of the General Motors “Futurama”exhibit at the 1939–1940 New York World’s Fair. Since then,continuous efforts have been devoted to this field [1]–[4]. Morerecently, the DARPA1 Grand Challenge and Urban Challengehave greatly boosted the technology advances in autonomousvehicles [5], [6].

During the decades of efforts, various sensing technologieshave been explored for automatic steering control. Accordingto the point of measurement of the vehicle lateral displace-ment, automatic steering control approaches can be groupedinto look-ahead and look-down systems [7]. Sensors for look-ahead systems include machine vision, radar, and LIDAR; theymeasure the lateral displacement in front of the vehicle. Sen-

Manuscript received March 7, 2014; revised May 29, 2014; accepted June11, 2014. Date of publication July 8, 2014; date of current version September30, 2014. This paper was recommended for publication by Editor B. J. Nelsonupon evaluation of the reviewers’ comments. This work was conducted underthe Vehicle Assist and Automation Project, which was sponsored by FederalTransit Administration, the Intelligent Transportation Systems Joint ProgramOffice, and the California Department of Transportation.

The authors are with California PATH Program, University of Califor-nia at Berkeley, Richmond, CA 94804 USA (e-mail: hstan@berkeley.edu;huangjihua@berkeley.edu).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TRO.2014.23310921Defense Advanced Research Projects Agency

sors for the look-down systems include electric wire guide-lines, magnetic markers, and DGPS; they measure the lateraldisplacement within or in the close vicinity of the vehicle bound-aries. In addition to sensing technologies, various control tech-niques have been investigated and applied to develop automaticsteering control.

With the great advances in vehicle automation and announce-ments of autonomous car production in the near future, auto-matic steering control may seem to be a solved problem. Manysteering controllers in autonomous applications, such as theDARPA Challenges [5], [6], are path-tracking methods for con-trolling a car along a predetermined path. Such path-trackingmethods include variations or combinations of pure pursuit [8],Stanley method [5], kinematic controllers [9], and dynamicsmodel-based controllers [10]. All of the path-tracking methodsare imperfect solutions in some way, although all can performquite well in many common scenarios. Most of the applicationsin practice still encounter challenges when high accuracy and ro-bustness are required [11]. As a result, applications that demandconsistent high-accuracy performance remain a challenge. Thispaper presents such an application, where the automatic steer-ing control system needs to provide lane keeping and precisiondocking for an 18.3-m articulated bus in revenue service alonga challenging segment on the EmX bus rapid transit (BRT) lineof the lane transit district (LTD) in Eugene, OR, USA.

The 4-km (2 km in each direction) segment chosen for the au-tomatic steering control mostly consists of narrow curvy lanes.It includes both narrow curbed lanes (typically 3.05-m wide)and mixed traffic lanes without any barriers. It has a total of36 curves (excluding seven docking entry and exit S-curves),and eight of the road curves have a radius of less than 100 m(with the smallest radius of 46.6 m). Moreover, five of the sixstations for precision docking involve sharp S-curve docking,and most stations have limited docking spaces confined by theplatform and the curb. (For example, one station requires thearticulated bus to make a full lane change within a short inter-section and pull straight immediately without touching the curbor the platform on both sides.) On top of all this, with the drivercontrolling the speed, the bus could be operated at speeds above64 km/h, and often drivers execute S-curve docking (with radiismaller than 30 m) at speeds above 32 km/h.2 In addition tolarge variations in individual drivers’ speed profiles, it is not

2This segment of the EmX BRT route was chosen for automatic steering con-trol because it has been a challenge for operators. The transit agency experienceshigh turnover and relative large amount of tire damage (as the tires frequentlytouch the curb and platform guard under manual control).

1552-3098 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

1138 IEEE TRANSACTIONS ON ROBOTICS, VOL. 30, NO. 5, OCTOBER 2014

uncommon for drivers to suddenly perform emergency brakingdue to a passenger rushing to the platform when the bus is ap-proaching to less than 5 cm to the platform. Such challengingoperating conditions require the steering controller to maintainhigh accuracy as well as ride comfort consistently, even underbad weather conditions.

Given such a challenging application and with the limita-tions of the typical steering controllers, we turned to an unusualsource for inspiration: drivers. Drivers can perform adequatesteering with relatively little practice, and they typically handlevariations in speeds and vehicle dynamics with ease. Moreover,drivers often increase their control gain whenever additionalsteering corrections are needed.

Understanding and modeling of drivers is a complex topicthat involves multiple disciplines such as cognitive science, psy-chology, physiology, and control theory. Decades of researchhave yielded rich, although sometimes contradictory, knowl-edge. Some research focused on drivers’ perception and use ofvisual information. Analysis of driver’s eye gaze in [12] sug-gested that drivers rely particularly on the tangent point on theinside of each curve, while data in [13] indicated that driversmay not always utilize the tangent point on curved roads butinstead sometimes tend to fixate on the center of the road. An-other research suggested that drivers may use two referencepoints to steer a car since their steering accuracy with the tworeferences is comparable with that with a full view [14]. Someresearch examined the effects of advanced information on themaneuver execution (such as the reaction time) [15]. Some otherresearch proposed steering models based on certain assumptionsand demonstrated their capability in performing maneuvers withcharacteristics similar to drivers [16]. However, we had yet tosee a driver steering model that could match drivers’ steeringrate (or even steering angle) in closed-loop validation.

The dynamics of perception and action can be described attwo levels of analysis: the first level characterizes the interac-tion between an agent and its environment, and the second levelcharacterizes the behavioral dynamics (i.e., the temporal evolu-tion of the behavior) [17]. It was in the second level of analysisthat we attempted to derive a dynamical model of driver’s steer-ing behavior based on vehicle test data. Through the analysisof vehicle test data from double lane change (DLC) conductedby 20 drivers of various driving skill levels, we discovered thatthe steering rate of every participating driver was proportionalto a specific vehicle angle error with respect to a moving targetahead of the vehicle [18]. This discovery suggested that driversengage a straightforward steering rate control, and the closed-loop simulations verified that this control mechanism was ableto match not only the steering angle but the steering rate ofindividual drivers on the DLC for all the 20 drivers as well. Itis important to note that the research did not make assumptionson how drivers acquire the specific information; instead, the re-search focused on identifying relationships in the test data andvalidating the causality through direct comparison of the vehicletest data and closed-loop simulation results. The direct match ofthe steering rate (and therefore the steering angle and the trajec-tory) demonstrated that the discovered control mechanism canexplain how drivers steer through the DLC course and accountfor different skill levels [18].

With sensing and actuating technologies that process muchmore accurately and quickly than human drivers, a controlleradopting the driver steering mechanism (and capturing the ex-perts’ skill) has the potential to achieve the high performanceand robustness required by our application. In this paper, wefirst transformed the driver’s steering mechanism to an equiva-lent look-down controller and identified optimal control param-eters through an automated optimization process. The controlstructure revealed that drivers in effect perform a PID controlwith speed-dependent look-ahead distances and feedback gains.The control synthesis further showed that the equivalent con-troller has desirable zeroes that help explain the stability marginnecessary to sustain higher feedback gain. This controller wasimplemented as the baseline controller, and preliminary resultsverified the capability of the controller [19]. Furthermore, sim-ilar to what a driver would do, a gain scheduling scheme wasapplied to the feedback gain when the errors get larger. The de-signed system achieved all performance requirements, and therevenue service started in June 2013. This successful applicationsuggested that the driver’s steering mechanism is directly appli-cable to automated vehicles, especially for situations requiringfast response and high accuracy.

This paper is organized as follows. Section II describes thediscovery of how drivers steer based on DLC vehicle test data.Section III details the control synthesis of the driver’s steeringmechanism and its transformation to equivalent control struc-tures implementable by both look-ahead and look-down sys-tems. Section IV describes the steering controller design usingthe equivalent control structure. Section V provides the systemperformance, and Section VI concludes this paper.

II. HOW DRIVERS STEER

This section describes the discovery of how drivers steer basedon the vehicle data of DLC maneuvers at a proving ground[18]. Our goal was to identify the relationships (i.e., differen-tial equations) that govern the behavior dynamics of drivers’steering behavior. No a priori assumptions were made aboutdrivers’ perception; the relationships were identified based ondata recorded during vehicle tests on the standard ISO DLCcourse, including vehicle positions and angles (from DGPS),steering angle at hand wheel, vehicle speed, and yaw rate. Theidentified relationships were generic to all the 20 participat-ing drivers. Moreover, the relationships were validated throughclosed-loop simulations where no recorded data except vehiclespeed were used in the simulation in order to verify the causal-ity of the relationships. This is critical since a well-matchedopen-loop relationship often fails in closed-loop validations.

The above engineering process led to a new target and control(T&C) scheme that describes the driver’s steering mechanismduring the DLC maneuver [18]. This scheme has two basic find-ings. First, during lane changes, contrary to some conventionaldriver models, typical drivers do not “plan” a trajectory andthen follow the planned trajectory; instead drivers are keen onthe angle error between where the vehicle is heading and wherethey would like the vehicle to go. Second, the analysis of theDLC data revealed that the rate of the steering angle exhibiteda proportional relationship to a specific “vehicle heading angle

TAN AND HUANG: DESIGN OF A HIGH-PERFORMANCE AUTOMATIC STEERING CONTROLLER FOR BUS REVENUE SERVICE 1139

Fig. 1. DLC target sets (dotted line along the lane centerline).

error” for almost all subject drivers.3 That is, the driver controlshow fast he/she needs to increase or reduce the steering anglebased on the angle error between where the vehicle is headingand where the vehicle should be heading to reach the desired“target.” The lane change trajectory is not a planned trajectorybut a result from the closed-loop control actions.

A. Switching Target Set

To explain this T&C scheme, we start with the DLC ma-neuvers. As the data analysis and simulations will show later,drivers use target points located along the centerline of the lanethey are changing to as references for lane change control (seeFig. 1).

As shown in Fig. 1, the DLC course can be divided into threesegments separated at the transition points P1 and P2 (the loca-tions where a driver starts changing to the next lane). Dependingon the segment the vehicle is currently in, the correspondingmoving target is described below.

1) Segment I (before transition point P1): The targets lie onthe centerline of the lane defined by the first cone set.

2) Segment II (between points P1 and P2): The targets lie onthe centerline defined by the second cone set.

3) Segment III (beyond point P2): The targets lie on thecenterline defined by the third cone set.

The maneuver in Segment I is lane keeping, while the maneu-vers in Segments II and III are lane changes. There is no explicittrajectory planning.

B. Preview Target Determination

At any specific time, the target is at a look-ahead distance(i.e., preview distance, possibly varying) away from the vehicleposition. Thus, given the transition locations P1 and P2, a look-ahead distance d(t), and the current vehicle position (x(t), y(t)),the preview target T (xT (t), yT (t)) can be represented as

∥∥∥∥∥∥

⎡

⎣

xT (t) − x(t)

yT (t) − y(t)

⎤

⎦

∥∥∥∥∥∥

= d(t) and

⎡

⎣

xT (t)

yT (t)

⎤

⎦ ∈ Π (1)

where the target set Π is the centerline of the lane which the ve-hicle is changing to. In this DLC maneuver, Π is a function of thevehicle current position (x(t), y(t)) and the transition locationsP1 and P2.

3Exceptions were typically observed after low-skill drivers gave up controland failed to complete the DLC course.

Fig. 2. Target heading angle.

C. Target Angle Error

With a given target, the target angle error is determined basedon a target heading angle as described below.

Definition (Target heading angle): Given vehicle current po-sition (x(t), y(t)), yaw rate ωv (t), speed v(t), and a targetT (xT (t), yL (t)) ∈ Π, and assuming the vehicle maintains itscurrent yaw rate and speed, the target heading angle θT is theheading angle that ensures the vehicle reaches target T.

Fig. 2 illustrates the target heading angle θT , correspondingto a target T; the blue curved line is a curve with a fixed radiusR(t) = v(t)/ωv (t) at the current time t; the blue dashed line istangent to the curve at the vehicle position.

Thus, the target heading angle is the desired current headingangle since the vehicle will reach the target T if it maintains itscurrent yaw rate and speed. Accordingly, the target angle erroris introduced

θe(t) = θT (t) − θv (t) (2)

where θv (t) is the vehicle heading angle. It is important to pointout that this target angle error was one of multiple errors weinvestigated. Although it is not the only error that has a distinctrelationship with the steering rate or steering angle in open-loopcomparisons, it turned out to be the only one whose relation-ship withstood the test of closed-loop comparisons. Moreover,our approach in the second level of analysis (i.e., modelingthe behavior dynamics) did not attempt to answer questions inperception. In practice, a driver may not explicitly identify thedesired target heading angles, but it is possible that he/she iskeen on this angle error based on how the vehicle is gettingclose to or away from the desired targets.

D. Steering Rate Controller

One important finding in [18] is that all DLC data from the 20participating drivers of different skill levels (at speeds from 50to 85 km/h) exhibit similar proportional relationships betweenthe steering angle rate and the target angle error. As examples,Fig. 3 shows such proportional relationships for four drivers withdifferent skill levels: expert, average, low skill, and novice. Thedashed lines are the computed target angle errors with respectto targets at three different look-ahead distances (15, 18, and21 m). It is clear that the steering rates within the blue circlesmatch well with the target angle errors for all four drivers. InFig. 3, the lane change transition points P1 and P2 (shown inFig. 1) are assumed to be at the beginning of the first and secondcone sets. The actual transition points can then be identifiedbased on the locations where the steering rate starts to matchthe target angle errors.

1140 IEEE TRANSACTIONS ON ROBOTICS, VOL. 30, NO. 5, OCTOBER 2014

Fig. 3. Steering rate versus vehicle target angle error during DLC forexpert/average/low-skill/novice drivers.

Thus, the DLC data suggest a linear relationship between thesteering rate and the target angle error

δ(t) = k(t)θe(t). (3)

To identify the parameters in the relationship, we computedδ(t) and θe(t) based on vehicle test data and used them toidentify the feedback gain k(t) and the look-ahead distance d(t)(for each driver) using the windowed least-squares estimation.To validate the relationship, the steering rate control (3) withthe identified parameters (and the transition points P1 and P2) isimplemented (as the driver model) in closed-loop simulations tonegotiate the exact same DLC course. Other than vehicle speed,the closed-loop simulations did not use any vehicle test data.

The results from the closed-loop simulation consistentlymatched well with the test data [18]. Most drivers seemed tohave a nominal gain k(t) that was approximately proportional tospeed over the look-ahead distance; drivers typically increasedk(t) when either the target angle error got too big or the ve-hicle was too close to a cone. From the control’s perspective,a driver’s (steering) skill level is a consequence of the rela-tionships among k, d, vehicle dynamics, and the timings of themaneuver decision (for example, a driver should use a larger kwhen the lane-change starts late).

Following what the data and the simulations suggested, ageneric simple control law was proposed to capture the driversteering mechanism:

δ(t) = kθe(t), where k = ki for εi ≤ |θe | < εi+1 . (4)

Typically, ε0 is 0, and only a simple gain scheduling is needed(i = 0 to 2 or 3) for most of the drivers. Fig. 4 shows theclosed-loop simulation results using the CarSim vehicle modelfor the same four drivers in Fig. 3. The nominal gains (k0 , d)used in the simulation were (0.77, 18 m), (0.92, 18 m), (0.97,18 m), and (1.15, 22 m for first lane change, and 18 m forthe second lane change) for the expert, average, low-skill, andnovice driver, respectively. The simulation results (dashed linesin Fig. 4) match very well with vehicle test data for all drivers inthe steering angle (blue lines), heading angle (magenta lines),

Fig. 4. T&C model (CarSim) simulation (dashed) versus data (solid)(expert/average/low-skill/novice drivers).

Fig. 5. T&C driver steering model based on the DLC.

and vehicle trajectory (red lines). Some small separations wereobserved after the vehicle entered the third cone set due to thefact that the drivers had no specific targets to follow from thatpoint on. The matching of the steering rates (black lines) clearlydemonstrated that this simple driver model captures how driversadjusted their steering (blue lines) during the DLC maneuvers.

E. Target and Control Driver Steering Model

In summary, the driver’s steering mechanism (3) can be rep-resented by a T&C steering model shown in Fig. 5. The T&Cmodel was shown to perform maneuvers such as lane-keep,lane-change, and left/right turns [20]. This T&C model reflectsthe following characteristics of how drivers steer.

1) Instead of planning a trajectory, drivers steer toward (mov-ing) targets at certain look-ahead distances ahead of thevehicle.

2) Drivers assess the target angle error, which is a headingangle error between where the vehicle is heading andwhere the vehicle should be heading to reach the targets.

3) Instead of steering to specific steering angles, drivers de-termine how much and how fast they need to adjust thesteering angle based on the target angle error and executethe steering adjustment accordingly. As a result, driversexecute a linear rate control (with simple gain scheduling)to regulate the target angle error.

TAN AND HUANG: DESIGN OF A HIGH-PERFORMANCE AUTOMATIC STEERING CONTROLLER FOR BUS REVENUE SERVICE 1141

Fig. 6. Application of T&C steering model to automated vehicles.

Fig. 6 shows a block diagram of applying this T&C steer-ing model to an autonomous vehicle. Maneuver decisions aremade based on commands from navigation and obstacle detec-tion modules. A target set can then be dynamically determinedbased on the look-ahead sensors (and/or map). The target an-gle error can be estimated at any look-ahead distance using themeasurements from the look-ahead sensors as well as vehicleyaw rate and speed. The steering command is generated byan integrator with simple gain scheduling. Parameters reflectingdriving styles and skills could be incorporated in real time basedon the operational scenarios.

Besides being a simple, robust, and flexible steering con-troller, the proposed steering mechanism has the following po-tential advantages for autonomous vehicle applications.

1) Without explicitly following a trajectory, unnecessaryovershoots could be reduced in high-gain control for crit-ical scenarios such as emergency maneuvers.

2) With the targets being determined dynamically and thesimple steering rate control being executed to always steera vehicle toward the targets, the control system couldfunction more efficiently and produce a smoother ride.

3) The identified steering mechanism is also capable of mim-icking different driving styles, which may facilitate thepersonalization of autonomous vehicles.

III. CONTROL SYNTHESIS OF THE DRIVER STEERING MODEL

To analyze this T&C driver steering model, the model is for-mulated into a standard state feedback for lane-keeping control.4

In this scenario, the target set is the centerline of the lane. Fig. 7shows a vehicle traveling on a curved road. The points in thefigure are as follows:

1) Point V (xr , yr ): the current vehicle position with respectto the current road reference;

2) Point T (Tx, Ty ): preview target at look-ahead distance d;3) Point A (Ax,Ay ): the location the vehicle will be if it

travels the distance d while keeping its current headingangle, θr , with respect to the current road reference;

4) Point B (Bx,By ): the location the vehicle will be if ittravels the look-ahead distance d while keeping its currentyaw rate and speed;

4The control synthesis aims to deepen our understanding of the driver steeringmodel and to facilitate its implementation with different sensor configurations.It does not suggest drivers literally estimate vehicle states and execute the statefeedback.

Fig. 7. Target angle error computation.

5) Point O: the center of the curve corresponding to the ve-hicle trajectory if it keeps its current yaw rate and speed.R is the radius of the curve;

The road coordinates are used with the origin at the lanecenter. yr is, therefore, the vehicle lateral deviation from thelane center.

Assuming the (vehicle) radius R is much larger than the look-ahead distance d, the travel distance from V to B is approxi-mately the distance between V and B. Therefore, by rotating thecurve between V and B by an angle of θe , point B will be at thelocation of point T. Thus, the angle θe is the target angle error.The coordinates of point T can then be calculated as

{

Tx = xr + d cos (θr + β + θe)

Ty = yr + d sin (θr + β + θe) .(5)

By assuming that the vehicle heading angle θr and the targetangle error θe are both small, we have

⎧

⎪⎪⎪⎨

⎪⎪⎪⎩

Tx = xr + d

(

1 − d

2Rθe −

d

2Rθr − θeθr

)

Ty = yr + d

(

θr −d

2Rθeθr +

d

2R+ θe

)

.(6)

Ignoring the higher order term θeθr and letting R = v/ωv

(ωv is the vehicle yaw rate), we have⎧

⎪⎪⎪⎨

⎪⎪⎪⎩

Tx = xr + d

(

1 − dωv

2vθe −

dωv

2vθr

)

Ty = yr + d

(dωv

2v+ θe + θr

)

.(7)

On the other hand, given a constant road curvature ρroad =1/Rroad and Rroad � d, the target T should satisfy

⎧

⎪⎨

⎪⎩

Tx = xr + d cos βroad ≈ xr + d

Ty = d sin βroad = d

(d

2Rroad

)

=d2ρroad

2.

(8)

Combining (7) and (8), we have

θe =d

2ρroad −

(1dyr +

d

2vωv + θr

)

. (9)

Correspondingly, we have the control law as follows:

δ = kθe = k

(d

2ρroad −

(1dyr +

d

2vωv + θr

))

. (10)

1142 IEEE TRANSACTIONS ON ROBOTICS, VOL. 30, NO. 5, OCTOBER 2014

Fig. 8. Closed-loop diagram of the driver steering model.

Fig. 9. Closed loop with the driver steering model.

In other words, the steering rate control [in (1), (2), and (4)] isa feedback control based on the lateral deviation yr , the yaw rateωv , and the heading angle θr . Fig. 8 shows the block diagramof the steering controller equivalent to that of the driver T&Cmodel, where Gv represents vehicle dynamics.

The equivalent controller of the T&C model in lane-keepingmaneuvers can be described by (11) with the overall closed-loopdiagram shown in Fig. 9

C(s) =k

s

(

s2 + 2 vd s + 2

(vd

)2)

2 vd s2 . (11)

The above control synthesis of the T&C model reveals severaladvantages of the driver’s steering mechanism. First, the equiv-alent controller has two zeroes at (− v

d ± vd i), which have a

constant damping at 0.707. As the control gain gets larger, twoof the dominant closed-loop poles approach these two open-loop zeroes that have favorable damping. That is, the controlleris likely to sustain higher gains without sacrificing the stability.Thus, it provides a nice reservoir of stability margin that allowsdrivers to increase control gains when needed. That explainswhy the driver can increase the control gain momentarily with-out creating instability. (Professional drivers may keep such ahigher gain for a longer period of time.) This is a desirableproperty for a baseline controller to engage gain scheduling forvarious operational exceptions such as preventing hitting theplatforms or curbs.

Second, the controller is inherently linear time varying withrespect to speed, which enables drivers to drive the vehicle ata relatively wide range of speeds with relative ease. By lettingd ∝ v, the dominant poles and damping ratio of the closed-loopsystem would remain similar for different speeds.

Proceeding further from (10), we have

δ =k

s

(d

2ρroad −

(1dyr +

d

2vωv + θr

))

. (12)

Fig. 10. Feedback controller equivalent to the T&C controller.

Since ωr

s = θr , θr

s = yr

v , and ωr = ωv − vρroad , we have

δ =−k

v

(

yr +(v/d

s

)

yr +d

2θr

)

. (13)

Equation (13) reveals that the T&C driver model is in essencea PID controller with speed-dependent gains and a “look-ahead”characteristic (yr + d

2 θr ), which introduces phase lead for sta-bility margins. Fig. 10 shows the block diagram of this equiva-lent steering controller.

Based on the above discussions, the T&C driver steeringmodel has at least three equivalent structures that support dif-ferent implementations: (2) and (4) as well as (10) and (13).An autonomous vehicle with camera or radar/LIDAR may di-rectly use the steering rate controller in its original form [(2) and(4)] without planning a specific trajectory. A vehicle with GPSor magnetic sensing system can implement the equivalent PIDcontroller (13) and benefits from the robustness and flexibilityof the T&C driver model as well.

Although the control synthesis decomposes the controllerinto feedbacks of vehicle states, it does not suggest that driversaccurately estimate all the vehicle states and literally execute thestate feedback control. In fact, the DLC vehicle test data suggestthat drivers have a relatively good sense of where the vehicle isgoing (θr ) and how well the vehicle is aligned with the desiredheading (θT ) toward the targets. In other words, drivers couldsense the target angle error (2) intuitively and adjust the steeringangle accordingly [as indicated by (3)].5

In the sense of closed-loop control, the difference betweenan expert driver and a low-skill one lies in how the controlparameters k and d are chosen with respect to vehicle speedand dynamics [18]. Thus, k and d of an automatic controllerneed to be properly designed in order to achieve all the desiredperformance, which will be discussed in the next section.

IV. DESIGN OF THE AUTOMATIC STEERING CONTROL

FOR BUS REVENUE SERVICE

The automatic steering control system is to provide lane keep-ing and precision docking (with speed controlled by the driver)for an 18.3-m New Flyer articulated bus on the Franklin EmX

5A study on human walking towards goals [17] suggested that humans seemto have the capability of assessing the angle error between their heading and thedesired heading toward the goal and then aligning their heading with the desiredheading. The driver’s steering mechanism [see (2) and (3)] suggests a similarcapability in human driving, which further involves moving targets and vehicledynamics.

TAN AND HUANG: DESIGN OF A HIGH-PERFORMANCE AUTOMATIC STEERING CONTROLLER FOR BUS REVENUE SERVICE 1143

Fig. 11. Configuration of an articulated bus.

BRT route of the LTD in Eugene, OR. This section describesthe control system design based on the driver’s steering mecha-nism. The system safety and redundancy design for the revenueservice operation is provided in [21].

A. Performance Requirements

Since the automated bus will carry paying passengers underday-to-day operations for an extensive period of time, the controlsystem, in addition to the safety requirements, is required tooperate in all possible operating and weather conditions withouttouching curbs or platforms.

According to the Americans with Disability Act, the hori-zontal gap between station and vehicle floor shall be less than7.62 cm. The system thus needs to align both sections of thearticulated bus to the platform within 7.62 cm [standard devia-tion (STD) � 1.27 cm], without touching the platform or curb,despite variations in the driver’s speed profile.

For the 2.6-m-wide bus riding on a 3.05-m narrow lane, themaximum allowable lateral deviation is 22.8 cm. Therefore, thelane keeping shall have a STD less than 7.6 cm when the bus iswithin the curbed corridor. In fact, for certain curves, the frontpart of the bus needs to get much closer to one side of the curbin order for the rear wheel not to touch the curb.

To ensure a good ride quality, the lateral acceleration shallbe no greater than 0.12 g more than (v2ρroad ) and the lateraljerk shall be no greater than 0.24 g/s [22]. In short, the resultantlateral acceleration should be at least at the same level as that ofa trained bus operator but with significantly better and consistentaccuracies.

B. Dynamic Model of Articulated Bus

With an additional degree of freedom introduced by the trailersection, the dynamics of an 18.3-m articulated bus are differentfrom a single-section vehicle (see Fig. 11). This is especiallytrue when the articulated bus makes lane changes and docks atthe station.

The dynamic model of an articulated bus can be developedbased on Kane’s equation [23]. If we assume a small steeringangle and a small articulation angle, the lateral dynamics of anarticulated bus can be written as

Mq + Dq + Kq = E1ρ + E2δ (14)

where q =[yr θr θa

]T, and yr represents the lateral displace-

ment of the bus front section CG with respect to the lane center-line, θr is the yaw angle of bus front section with respect to thelane centerline, and θa is the articulation angle shown in Fig. 11.

ρ is the road curvature, and δ is the front wheel steering angle.The matrices are defined as follows with the assumption of asmall articulation angle:

M =

⎡

⎢⎢⎣

m1 + m2 −m2(d1 + d3) −m2d3

−m2(d1 + d3) M22 M23

−m2d3 M23 Iz2 + m2d23

⎤

⎥⎥⎦

(15)

with

⎧

⎨

⎩

M22 = Iz1 + Iz2 + m2(d1 + d3)2

M23 = Iz2 + m2d23 + m2d1d3

D =2v

⎡

⎢⎢⎣

H11 H12 −Cαtl3

H12 H22 Cαt(d1 + l3)l3

−Cαtl3 Cαt(d1 + l3)l3 Cαtl23

⎤

⎥⎥⎦

(16)

with

⎧

⎪⎪⎨

⎪⎪⎩

H11 = Cαf + Cαr + Cαt

H12 = Cαf l1 − Cαr l2 − Cαt(d1 + l3)

H22 = Cαf l21 + Cαr l22 + Cαt(d1 + l3)2

K = 2

⎡

⎢⎢⎣

0 0 −Cαt

0 0 Cαt(d1 + l3)

0 0 Cαtl3

⎤

⎥⎥⎦

(17)

E1 =

⎡

⎢⎢⎢⎢⎢⎢⎣

(m1 + m2)v +2v

(Cαf l1 − Cαr l2 +Cαt(d1 +l3))

−m2(d1 + d3)v +2vH22

−m2d3v +2vCαtl3(d1 + l3)

⎤

⎥⎥⎥⎥⎥⎥⎦

(18)

E2 = 2[Cαf Cαf l1 0]T (19)

where m1 and m2 represent the mass of the bus’s frontand articulated sections, respectively; Iz1 and Iz2 repre-sent moment of inertia of the front and articulated sec-tions, respectively. Cαf ,Cαr , and Cαt represent cornering stiff-ness of front, rear, and trailer tires, respectively. With x =[yr θr θa yr θr θa ]T as the state and the steering angleδ as the control input, the lateral dynamics of the articulated buscan be written in the state space as

x = Ax + Bδ + Eρ + n (20)

where

A =[

0 I−M−1K −M−1D

]

, B =[

0M−1E2

]

E =[

0M−1E1

]

and n represents the disturbances that cannot be modeled.

1144 IEEE TRANSACTIONS ON ROBOTICS, VOL. 30, NO. 5, OCTOBER 2014

Fig. 12. Frequency responses: steering angle to front yaw rate (left); steeringangle to trailer yaw rate (right).

Fig. 12 shows the frequency responses from the bus steeringangle to the yaw rates of the front and trailer sections at differentlongitudinal speeds. As vehicle longitudinal speed increases,resonant peaks appear at around 0.4 Hz especially for the trailersection yaw rate.

C. Controller Design

The automatic steering system adopts the magnetic sensingtechnology, in which magnetometers mounted on the bus mea-sure the magnetic field strength of magnetic markers installedunder the roadway and the lane position is determined basedon the measured magnetic field strength. With two embeddedmagnetometer sensor bars installed under the bus, one underthe front door and the other under the middle door, yr and θr

can be derived based on the lateral deviations measured at thetwo sensor locations. Thus, the driver steering model can beimplemented using the structure shown in (13) and Fig. 10. Thecontrol design then focused on the determination of the controlparameters [the look-ahead distance (d) and the feedback gain(k)] that would satisfy the performance requirements (e.g., likean expert driver).

One way to identify the appropriate look-ahead distance andfeedback gain is to evaluate the closed-loop poles (which rep-resent the stability and damping characteristics of the resultantclosed-loop system). Fig. 13 shows an example of the criticalclosed-loop poles with different look-ahead distances and gainsfor four different speeds: 5, 10, 15, and 20 m/s. In each subplot,three look-ahead distances were selected: d = v (blue dots), d= 2v (black dots), and d = 3v (red dots). For each look-aheaddistance, the feedback gain was increased from 0 to 6, and thepole locations marked with 1, 2, and 3 correspond to feedbackgain equal to 1, 2, and 3, respectively.

We could compute the pole locations for any given look-ahead distance and feedback gain at any given speed. Thus,given predefined criteria, the pair of look-ahead distance andfeedback gain that yields the best combination of closed-looppoles can be automatically determined. For example, the criteriacan include 1) all poles should have a minimum damping of0.5, 2) the system should be stable with gains ranging from

Fig. 13. Dominant closed-loop poles for different look-ahead distance (d/v =1 (blue), 2 (black), 3 (red)) and gain (k = 0–6).

Fig. 14. Look-ahead distances and feedback gains.

0.5k to 2k, and 3) the damping of the dominant poles shouldbe maximized. Accordingly, an automatic process that sweepsthrough all d and k within the design range for every speedwas devised to identify the optimal control parameters for eachspeed. The resulting selections are shown in Fig. 14.

Those parameters were then implemented in the baselinecontroller as the nominal look-ahead distances and feedbackgains. As the closed-loop system provides adequate stabilitymargin, the feedback gains can be further increased with arelatively straightforward gain-scheduling mechanism when-ever the current or predicted errors become large. Such pro-tection is a necessary feature for an automated vehicle carryingpassengers to ensure high-accuracy performance without com-promising the stability, despite variations in drivers’ speed pro-file. Such high-accuracy performance is important for the busto avoid hitting stations or curbs at tight curves, which hasbeen a major cause of tire damages under manual driving, aswell as a main cause of driver stress on the challenging EmXroute.

TAN AND HUANG: DESIGN OF A HIGH-PERFORMANCE AUTOMATIC STEERING CONTROLLER FOR BUS REVENUE SERVICE 1145

Fig. 15. Automated steering system for new flyer 60’ bus.

V. IMPLEMENTATION OF TARGET AND CONTROL CONTROLLER

FOR AN AUTOMATED BUS IN REVENUE SERVICE

A. System Implementation and Bus Integration

The automatic steering controller was implemented on the18.3-m articulated bus (see Fig. 15). The system consists of twocontrol computers and two human machine interface units forredundancy, a steering actuator and processor, two embeddedmagnetometer sensor bars, a yaw rate gyro, and redundant powersupplies.

The steering actuator includes an actuator assembly mountedon the steering column and an embedded controller for servocontrol and relevant fault detection and management. The actua-tor assembly includes a small DC motor, gears, and steering an-gle sensors. Each embedded magnetometer sensor bar consistsof multiple magnetometer sensors to provide adequate sensingrange and redundancy, while the gyro serves as a supplementaland redundant sensor. Vehicle speed is read from the vehicle’sJ1939 CAN bus. Except for the two sensor bars, the steering ac-tuator mechanical assembly, and the dual LED lights, buzzers,and control switches/buttons, all other components were in-stalled on one shelf in the instrument cabinet (23 cm × 15 cm× 28 cm).

B. Field Operational Results

From June to August 2013, over 14 operators were trainedand had used the automated bus in revenue service. The initialanalysis used 546 round trips made by the equipped bus; amongthem, 256 round trips were under automatic steer. The manualtrips were made by operators before they were fully trained. Cur-rently, all operators assigned to this bus have been trained andthe bus is under automated control whenever it passes throughthe corridor.

The revenue-service data showed that the final systemachieved lateral positions of about 7.1 cm STD (including theS-curve docking), which satisfies the requirements and is lessthan half of the STD (16.7 cm) achieved by manual driving.Fig. 16 shows the position error, speed, and hand wheel angle ofa west-bound (WB) run with respect to the travel distance fromthe beginning of the magnet track. The steering angle reached

Fig. 16. EmX WB run: lateral position error, hand wheel angle, and speed(distance based).

Fig. 17. EmX EB run: lateral position error, hand wheel angle, and speed(distance based).

its maximum of 213° during the sharp turn (35-m radius) fromFranklin Blvd. to E11 St. Large steering angles also occurredat the curves into and out of Walnut station, the sharp S-curveleading to Agate station, and the docking curve to Dad’s Gatestation. On the other hand, the lateral error never exceeded 20 cmexcept on the sharp docking curve leading to Dad’s Gate station.

Fig. 17 shows the position error, speed, and hand wheel angleof an east-bound (EB) run. Except on docking curves, the lateralerror never exceeded 20 cm. The horizontal gaps at the stationswere 4.6 cm at Walnut station, 4.7 cm at Agate station, and4.2 cm at Dad’s Gate station.

Fig. 18 shows the data for WB runs from revenue service inJuly 2013. Other than two locations (at 650 and 1600 m) andon docking curves, the lateral position error was within 20 cm.The two specific locations above are part of continuous curveswhere the front part of the bus was deliberately offset to avoid

1146 IEEE TRANSACTIONS ON ROBOTICS, VOL. 30, NO. 5, OCTOBER 2014

Fig. 18. EmX WB runs in July 2013: lateral position error, hand wheel angle,and vehicle speed (distance based).

Fig. 19. Docking performance at EB agate station (left) and EB walnut station(right) (one day’s data).

the rear articulation section touching the curb and the amountof offset depended on vehicle speed.

Precision docking was performed at six stations (three sta-tions in each direction). Since some docking curves are chal-lenging for drivers, LTD had placed yellow strips made of adurable material at wheel height along the platforms to guidebuses for many years. Therefore, the target horizontal gap forprecision docking is defined to be between the vehicle floor andthe yellow strips (instead of the platform) and set to be 4 cm.Our measurements at stations indicate that the horizontal gap isusually between 3 and 5 cm at both the front and the rear tirelocations at all stations. Data from revenue service confirmedthat the position errors are almost all within 2.5 cm (i.e., STDabout 0.8 cm) of the nominal 4 cm. More specifically, the STDsat the six stations were 1.01, 0.77, 0.85, 0.79, 0.45, and 0.93 cm,respectively.

Fig. 19 shows the docking performance at the two most chal-lenging stations: EB Agate station and EB Walnut station forone day. The top subplot plots the position error measured bythe front (blue lines) and rear (red lines) sensor bars. The speed

shown in the bottom subplot illustrates the variation in drivers’speeds. Drivers entered the docking curve at speeds as high as40 km/h and reached the platform at 24 km/h (see the bottomleft subplot). The control system performs steering correctionsto pull the bus straight at the platform (see that both positionerrors go to 0). In addition, as the bus was pulling straight atthe station, the steering angle exhibited larger variations (seecircled areas), demonstrating the effects of the controller’s gainscheduling to avoid hitting the platform while achieving theconsistently tight docking gap. It is worthwhile noticing that thebus/tires never touched the platform/strip or curb in the revenueservice.

VI. CONCLUSION

Most drivers acquire steering skills without extensive train-ing, and they exhibit relatively good robustness in complex en-vironments. Our analysis of the DLC data revealed that, insteadof planning a specific trajectory and then following it, driversuse targets as references and assess the error in vehicle headingangle for reaching the targets. This discovery led to a simplelinear steering rate control law, which implies that drivers donot determine and execute a desired steering angle. Instead,they determine how fast the changes in the steering angle areneeded based on the target angle error and move the hand wheelto increase or reduce the steering angle accordingly. Controlsynthesis indicates that this driving mechanism has desirablezero locations (that provide adequate stability margin to sustainhigher gains) and is inherently time varying and insensitive tovehicle speeds.

With sensing and actuating technologies that process muchmore accurately than drivers can, this driver’s steering mecha-nism has the potential to be a high-performance steering con-troller for challenging applications. In this paper, we trans-formed the driver’s steering mechanism to an equivalent look-down controller and revealed that drivers in effect perform a PIDcontrol with speed-dependent look-ahead distances and feed-back gains. The optimized control gains were obtained and thecontrol law was successfully implemented for the lane keepingand precision docking of an articulated bus in a narrow curvy buslane with sharp docking curves. The resultant system achievedall performance targets required for carrying passengers, andthe revenue service under daily operations started in June 2013.This successful application also implies that this driver steer-ing mechanism is a good steering controller candidate for au-tonomous vehicles, especially in situations (such as emergencymaneuvers) that demand high accuracy and robustness.

REFERENCES

[1] K. Gardels, “Automatic car controls for electronic highways,” GeneralMotors Res. Lab., Warren, MI, USA, Tech. Rep. GMR-276, 1960.

[2] V. K. Zworykin and L. E. Flory, “Electronic control of motor vehicleson the highways,” in Proc. 37th Annu. Meeting Highway Res. Board,Washington, DC, USA, Jan. 6–10, 1958, pp. 436–451.

[3] R. E. Fenton and R. J. Mayhan, “Automated highway studies at the Ohiostate university—An overview,” IEEE Trans. Veh. Technol., vol. 40, no. 1,pp. 100–113, Feb. 1991.

[4] S. E. Shladover, C. A. Desoer, J. K. Hedrick, M. Tomizuka, J. Walrand,W.-B. Zhang, D. H. McMahon, H. Peng, S. Sheikholeslam, and

TAN AND HUANG: DESIGN OF A HIGH-PERFORMANCE AUTOMATIC STEERING CONTROLLER FOR BUS REVENUE SERVICE 1147

N. McKeown, “Automated vehicle control development in the PATH pro-gram,” IEEE Trans. Veh. Technol., vol. 40, no. 1, pp. 114–130, Feb. 1991.

[5] S. Thrun, M. Montemerlo, H. Dahlkamp, D. Stavens, A. Aron, J. Diebel,P. Fong, J. Gale, M. Halpenny, G. Hoffmann, K. Lau, C. Oakley,M. Palatucci, V. Pratt, P. Stang, S. Strohband, C. Dupont, L.-E. Jendrossek,C. Koelen, C. Markey, C. Rummel, J. van Niekerk, E. Jensen, P. Alessan-drini, G. Bradski, B. Davies, S. Ettinger, A. Kaehler, A. Nefian, and P.Mahoney, “Stanley: The robot that won the DARPA grand challenge,” J.Field Robot., vol. 23, no. 9, pp. 661–692, 2006.

[6] C. Urmson, J. Anhalt, D. Bagnell, C. Baker, R. Bittner, M. N. Clark,J. Dolan, D. Duggins, T. Galatali, C. Geyer, M. Gittleman, S. Harbaugh,M. Hebert, T. M. Howard, S. Kolski, A. Kelly, M. Likhachev, M. Mc-Naughton, N. Miller, K. Peterson, B. Pilnick, R. Rajkumar, P. Rybski, B.Salesky, Y.-W. Seo1, S. Singh, J. Snider, A. Stentz, W. “Red” Whittaker,Z. Wolkowicki, J. Ziglar, H. Bae, T. Brown, D. Demitrish, B. Litkouhi, J.Nickolaou, V. Sadekar, W. Zhang, J. Struble, M. Taylor, M. Darms, andD. Ferguson, “Autonomous driving in urban environment: Boss and theurban challenge,” J. Field Robot., vol. 25, no. 8, pp. 425–466, 2008.

[7] S. Patwardhan, H.-S. Tan, and J. Guldner, “A general framework forautomatic steering control: System analysis,” in Proc. Amer. Control Conf.,Albuquerque, NM, USA, 1997, pp. 1598–1602.

[8] O. Amidi, “Integrated mobile robot control,” Robot. Inst., Carnegie MellonUniv., Pittsburgh, PA, USA, Tech. Rep. CMU-RI-TR-90-17, 1990.

[9] A. De Luca, G. Oriolo, and C. Samson, “Feedback control of a nonholo-nomic car-like robot,” in Robot Motion Planning and Control. Berlin,Germany: Springer, 1998, ch. 4, pp. 171–249.

[10] H. Peng, T. Hessburg, M. Tomizuka, W.-B. Zhang, Y. Lin, P. Devlin, S. E.Shladover, and A. Arai, “A theoretical and experimental study on vehiclelateral control,” in Proc. Amer. Control Conf., Chicago, IL, USA, 1992,pp. 1738–1742.

[11] J. Snider, “Automatic steering methods for autonomous automobile pathtracking,” Robot. Inst., Carnegie Mellon Univ., Pittsburgh, PA, USA, Tech.Rep. CMU-RI-TR-09-08, 2009.

[12] M. F. Land and D. N. Lee, “Where we look when we steer,” Nature,vol. 369, pp. 742–744, 1994.

[13] R. M. Wilkie and J. P. Wann, “Eye movements aid the control of locomo-tion,” J. Vision, vol. 3, pp. 677–684, 2003.

[14] M. Land and J. Horwood, “Which parts of the road guide steering,” Nature,vol. 377, pp. 339–340, 1995.

[15] P. Hofmann, G. Rinkenauer, and D. Gude, “Preparing lane changes whiledriving in a fixed-base simulator: Effects of advance information aboutdirection and amplitude on reaction time and steering kinematics,” Transp.Res. Part F: Traffic Psychol. Behaviour, vol. 13, no. 4, pp. 255–268, 2010.

[16] D. D. Salvucci and R. Gray, “A two-point visual control model of steering,”Perception, vol. 33, pp. 1233–1248, 2004.

[17] B. R. Fajen and W. H. Warren, “Behavioral dynamics of steering, obstacleavoidance, and route selection,” J. Exp. Psychology: Human PerceptionPerform., vol. 29, no. 2, pp. 343–362, 2003.

[18] H.-S. Tan and J. Huang, “Experimental development of a new target andcontrol driver steering model based on DLC test data,” IEEE Trans. Intell.Transp. Syst., vol. 13, no. 1, pp. 375–384, Mar. 2012.

[19] J. Huang and H.-S. Tan, “Design of an automatic steering controller forbus revenue service based on drivers’ steering mechanism,” in Proc. Amer.Control Conf., Portland, OR, USA, 2014, pp. 3930–3935.

[20] J. Huang, H.-S. Tan, and F. Bu, “Preliminary steps in understanding atarget & control based driver steering model,” in Proc. Amer. ControlConf., San Francisco, CA, USA, 2011, pp. 5243–5248.

[21] H.-S. Tan and J. Huang, “The design and implementation of an automatedbus in revenue service on a bus rapid transit line,” in Proc. Amer. ControlConf., Portland, OR, USA, 2014, pp. 5288–5293.

[22] W. C. Caywood, H. L. Donnelly, and N. Rubinstein, “Guideline for ride-quality specifications based on TRANSPO ‘72 test data,” Appl. Phys.Lab., John Hopkins Univ., Laurel, MD, USA, Tech. Rep. APL/JHU CP060/TPR039, Oct. 1977.

[23] H. Baruh, Analytical Dynamics. New York, NY, USA: McGraw-Hill, 1998.

Han-Shue Tan received the M.S. and Ph.D. degreesin mechanical engineering from the University ofCalifornia at Berkeley, Richmond, CA, USA.

He worked with the Space and CommunicationGroup, Hughes Aircraft Company, Hughes MissileSystems Company, from 1988 to 1994. He joinedthe California PATH Program with the University ofCalifornia at Berkeley in 1994. He has technicallyled a wide range of projects related to automated ve-hicle controls, driver dynamics, and heavy vehicles;he has also successfully demonstrated many vehicle

guidance and control applications. His main research interests include under-standing and solving real-world vehicle dynamics and control problems.

Jihua Huang received the Ph.D. degree in mechan-ical engineering from the University of California atBerkeley, Richmond, CA, USA, in 2004.

She was a Senior Researcher with General Mo-tors R&D, Warren, MI, USA, before she joined theCalifornia PATH Program with the University ofCalifornia at Berkeley in 2008. He has conducted re-search in three main areas: automated and advancedvehicle systems, driver-in-the-loop vehicle control,and automated system safety.