PaTAVTT: A Hardware-in-the-Loop Scaled Platform for ...4 JournalofAdvancedTransportation Table1:FunctionlistofPaTAVTTplatform. Autonomousvehicletrajectorycontroltype Description Single-vehiclecontrol

Research ArticlePaTAVTT A Hardware-in-the-Loop Scaled Platform forTesting Autonomous Vehicle Trajectory Tracking

Zhigang Xu1 Mingliang Wang1 Fengzhi Zhang2 Sheng Jin3

Jin Zhang4 and Xiangmo Zhao1

1School of Information Engineering Changrsquoan University Xirsquoan Shaanxi China2Qilu Bank Corporation Limited No 176 Shunhe St Jinan Shandong China3College of Civil Engineering and Architecture Zhejiang University Hangzhou Zhejiang China4Griffith School of Engineering Griffith University Gold Coast Campus Southport 4222 QLD Australia

Correspondence should be addressed to Jin Zhang jinzhang4griffithunieduau

Received 11 May 2017 Revised 4 September 2017 Accepted 24 September 2017 Published 13 November 2017

Academic Editor Vinayak Dixit

Copyright copy 2017 Zhigang Xu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

With the advent of autonomous vehicles in particular its adaptability to harsh conditions the research and development ofautonomous vehicles attract significant attention by not only academia but also practitioners Due to the high risk high cost anddifficulty to test autonomous vehicles under harsh conditions the hardware-in-the-loop (HIL) scaled platform has been proposedas it is a safe inexpensive and effective test method This platform system consists of scaled autonomous vehicle scaled roadwaymonitoring center transmission device positioning device and computers This paper uses a case of the development processof tracking control for high-speed U-turn to build the tracking control function Further a simplified vehicle dynamics modeland a trajectory tracking algorithm have been considered to build the simulation test The experiment results demonstrate theeffectiveness of the HIL scaled platform

1 Introduction

Autonomous vehicles also known as self-driving vehicles ordriverless vehicles are capable of sensing the traffic environ-ment navigating through software algorithm and controllingvehicle movement without driverrsquos decisions and actionsSuch vehicles have been widely used in logistics and cargotransportation military purpose and planetary explorationdue to its great potential ability to improve safety increasetransportation capacity and minimize pollution [1ndash8] In thepast 40 years the development of autonomous vehicles hasbeen greatly increased Recently Google Tesla Uber andBaidu had demonstrated their autonomous cars which canrun on various roads company with live traffic [9]Thereforewith the resolution of technological societal and legal issuespeople will finally free themselves from the mental andphysical burden of driving [4]

Although autonomous vehicles have many advantagesrecent several accidents slow down their process of com-mercialization Tesla cancelled the propaganda of self-driving

function and Uber also terminated all autonomous vehicletesting In reality both government and academia havereached an agreement that the autonomous vehicle needsto conduct comprehensive systematic and rigorous testsbefore it is officially commercialized However the testingof autonomous vehicle requires extremely time-consumingwork and huge economic cost [10] An autonomous vehicleconsists of five functions (as shown in Figure 1) (1) sensingand location systems (2) global route planning (3) behaviorreasoning (4) trajectory planning (5) trajectory trackingcontrol Among these five functions the first four can besimulated and tested by using the data collected from theautonomous vehicle sensors Basically it is a test of thesoftware function of the autonomous vehicles Howeverthe trajectory tracking control process needs to be testedwith real vehicles as the vehicle kinematic and dynamicconstraints controller responsiveness will influence the reli-ability smooth and comfort of autonomous vehicles Forthe trajectory tracking control function it requires that thecontrol algorithm can provide the spatial path planning and

HindawiJournal of Advanced TransportationVolume 2017 Article ID 9203251 11 pageshttpsdoiorg10115520179203251

2 Journal of Advanced Transportation

Sensing andlocalization

systems

Global route planning

Behavior reasoning

Trajectorytracking control

Trajectory planning

Autonomous vehicle ldquoSindardquo developed by Changrsquoan University

Figure 1 The generic function chart of an autonomous vehicle

handle the directionspeed of the vehicle according to thereal-time surrounding traffic information and high-accuracymap information [10]

The main two existing testing approaches of autonomousvehicle trajectory tracking are simulation testing and realvehicles testing Although the software-based simulation hasthe advantages of low cost and high efficiency the simulationmodel is based on the ideal mathematical model whichignores many practical factors might cause large differencebetween the simulation results and real cases results It shouldbe noted that the real world testing although with muchhigher accuracy is very time-consuming expensive andlimited by weather and scenarios [11ndash13] In this regardshortening the development cycle without sacrificing accu-racy and reliability has been concerned [14] There aremany well-known testbeds around the world for testingconnected and automated vehicles such as the MCity of theUniversity of Michigan and the GoMento test site locatedin Contra Costa County California and CU CVIS testbedof Changrsquoan University in China The former two testbedsfocus on demonstration for applications of future IntelligentTransportation Systems CU CVIS focuses on the metafunc-tion testing for each part of CAVs and the comprehensiveperformance testing under the limit conditions [15]

Hardware-in-the-loop (HIL) simulation has combinedboth mathematical and mechanical models to emulate realvehicles as considering the influence of gravity resistanceand friction which may cause the inaccuracy of the modelCompared to the testing in real traffic system the HIL has themerit of low construction cost short development cycle andreproducible method [16] At present HIL-based simulationhas been widely used in the field of automotive testingDeng et al [17] proposed a HIL simulation system as anintegral part of various autonomous driving programs whichis a laboratory environment to support the developmenttest and verification of many functions and algorithmsrelated to sensor-guided autonomous driving Zulkefli et al[18] proposed a HIL testbed to evaluate the performance

of connected vehicle applications This testbed integrated alaboratory powertrain research platform with a microscopictraffic simulator (VISSIM) which could be used to testvarious ITS applications such as CACC Eco-Driving andSpeed Harmonization Gietelink et al [19] developed anindoor vehicle hardware-in-the-loop simulation system totest the advanced driver assistance systems embedded in areal vehicle To best of our knowledge most of HIL-basedsimulations embed a vehicle or vehicle parts into the systemwhich are usually complex and costly and require large spaceA research group from RWTH Aachen University Germanyproposed a hardware implementation of a platoon of four1 14 scaled trucks to test the cooperative platoon controlalgorithm [20] As considering critical safety factors HILsimulation system is also used to precrash threat assessment[21]

In the proposed paper a HIL scaled platform for test-ing autonomous vehicle trajectory tracking (PaTAVTT) ispresented which is a mechatronic testbed consists of scaledroadway scaled vehicles indoor positioning subsystem andcomputer-aided Graphical User Interfaces Compared withother HIL test systems PaTAVTT has the following advan-tages First it is equipped with an indoor ultra-wideband-(UWB-) based high-precision positioning system matchesthe GPS precision in outdoor field which can record theaccurate trajectory of the scaled vehicle in motion Thedeviation between the real trajectory and the reference wouldbe an important criterion to evaluate the performance of thetrajectory tracking algorithm Second the scaled platformbridges the software-based vehicle dynamics model with thereal vehicleThe algorithmmodules and parameters validatedby Matlab or Carsim can be downloaded into the scalevehicle After passing the tests on PaTAVTT the algorithmscan be further transplanted into the real vehicle Thirdmany external factors such as the road surface material roadgeometry and slope and static or dynamic obstacles can betested due to the low establishment and testing costs

In this paper the system structure of this HIL plat-form and the implementation of each submodule havebeen described Further a new methodology of U-turn hasbeen developed and tested which can also be used in anautonomous vehicle The testing results demonstrate that theHIL platform can be used to test the trajectory planning andtracking control of an autonomous vehicle which potentiallyshorten its development cycle The remainder of this articleis organized as follows Section 2 is the overview of thePaTAVTT Section 3 presents a real-case study and themethodology of U-turnThe simulation results are presentedin Section 4 Section 5 concludes the paper

2 Overview of PaTAVTT

In this paper PaTAVTT consists of scaled roadway position-ing system scaled vehicle transmission system and softwaresimulator As can be seen in Figure 2 the scaled roadwayis a rounded rectangle platform which has two lanes andthe width of each lane is 375 cm Additionally the scaledroadways has different kinds of road infrastructures such astraffic signs and LED information board

Journal of Advanced Transportation 3

Wi-Fi hotspot

Ultra-widebandpositioning antenna

Positioning tag

Scaled autonomouscar

Network hub

Software simulator

(a) Structure diagram of platform (b) A snapshot of the platform

Figure 2 The system structure of PaTAVTT

ControllerCPUBattery

Wi-Fi communicationmodule

Steeringgear Motor

Localization tag

Optical-electricityencoder

Ultrasoundrange sensors

DataprocessingCPU

IIC

USR

AT

IO

Camera

(a) Structure diagram of scaled vehicle

CameraController

CPU

Utrasound range sensor

Steering geer

Data processingCPU

MotorBattery


Localizationtag

(b) Scaled autonomous vehicle

Figure 3 Structure of scaled autonomous vehicle

The scaled vehicles are 37 cm in length 30 cm in widthand 14 cm in height The scaled vehicle is battery poweredand the highest speed is 3msThe positioning system is pro-duced by Ubsense based on UWB wireless communicationtechnology which consists of a positioning antennamountedon the wall and a label on the vehicle Its positioning accuracyis about 30 cm which is approximately equal to the lengthof the scale vehicle At this point it matches the positioningprecision of GPS which has a precision of 3ndash5m and isclose to the length of a real vehicle Each scaled vehicle isequipped with dual controllers and dual Central ProcessingUnits (CPUs) oneCPU is used to control the vehicle steeringthe other is used to handle the output data from four kindsof sensors (UWB positioning sensor ultrasonic distancesensor cameraimage sensor and photoelectric encoder seeFigure 3) Ultrasonic distance sensors are used to detect thelocation of the front vehicle or obstacles to prevent collisionsThe image sensor is used to detect the lane line to ensurethat the vehicle is traveling within the laneThe photoelectric

encoder is used tomeasure the speed and displacement of thevehicle

The wireless communication system is realized by using80211ac wireless Wi-Fi technology Wi-Fi modules areinstalled to smart vehicles All wireless communication isconnected to a network router using Intranet It shouldbe noted that the system is able to simulate the trajectorycontroloptimization strategies

PaTAVTT platform can be used to test various typesof autonomous vehicle tracking control functions such assingle-vehicle control and platoon control Please refer toTable 1 for details

3 A Case Study of U-Turn

31 U-Turn and Its Negative Effects to Traffic DynamicsU-turn is a common traffic scenario which lowers vehiclespeeds and affects the traffic flow The U-turn signs fromdifferent countries are shown in Figure 4 It may cause


Table 1 Function list of PaTAVTT platform

Autonomous vehicle trajectory control type DescriptionSingle-vehicle control(1) Vehicle longitudinal control Start stop accelerate decelerate(2) Vehicle lateral control Turn left turn right serpentine(3) Lane-keeping control According to the image captured by the camera to keep the vehicle driving in the lane(4) U-turn control Turn the vehicle to reverse lane(5) Obstacle avoidance Decelerate and change lane when the vehicle detects an obstaclePlatoon control(6) Vehicle following control Verification of various vehicle following models(7) Lane changing controller Vehicles automatically change lane in the case of security(8) Overtaking control Vehicles overtake the front one and then return to the original lane(9) Intersection coordination Vehicles pass through the intersection in an optimal way(10)Headway control Control the vehicle headway to prevent collision

Figure 4 Different signs of U-turn

sideslip or rollover accident if the vehicle accelerates in aU-turn maneuver [22] As autonomous vehicles are able toautomatically plan and control the trajectories a proper U-turn algorithm can significantly improve the overall trafficefficiency reduce fuel consumption and minimize othernegative effects

Based on the PaTAVTT platform this paper uses U-turntrajectory tracking as a case study and builds an autonomousvehicle dynamics model We use Model Prediction Control(MPC) algorithm to perform and test the autonomousvehicles trajectory tracking control in U-turn scenario underdifferent speed conditions

32 Vehicle Dynamics Model The trajectory tracking controlof autonomous vehicles is achieved by controlling the vehiclefunction system Mathematical vehicle dynamics model isuseful in vehicle design crash simulation and kinematicbehavior analysis as it provides a quick simulation anal-ysis compared with finite element (FE) models [23] Inthis regard in this paper we use vehicle dynamics modelto be the prediction model and the autonomous vehicledynamics model can be simplified as two-wheeled bikemodel

In the plane Cartesian coordinate system (119900119909119910) thevehicle dynamics model has been shown in Figure 5 (119909119903 119910119903)and (119909119891 119910119891) are the center coordinates of the vehicle rearaxle and front axle respectively V119903 and V119891 are velocity of thevehicle rear axle and front axle respectively 120593 is the driving

l

y

o x

(xf yf)

(xr yr) rf

f

Figure 5 Vehicle dynamics model

direction of the vehicle 120575119891 is the angle of front wheel and 119897 isthe wheelbase between the front and rear axle

From Figure 5 we have

V119903 = 119903 cos120593 + 119910119903 sin120593 (1)

119903 sin120593 minus 119910119903 cos120593 = 0 (2)

V119903 = V119891 cos 120575119891 (3)

= V119891 sin120575119891119897 (4)


where 119903 and 119910119903 are the lateral velocity and the longitudinalvelocity of rear axle respectively

By combining (1) and (4) the model is simplified as

[[[119903119910119903]]]= [[[[[[

cos120593sin120593

(tan 120575119891)119897

]]]]]]V119903 (5)

The general expression of (5) is

120594 = 119891 (120594 119906) (6)

where the state variable 120594 = [119909119903 119910119903 120593]119879 and the control input119906 = [V119903 120575119891]119879Trajectory tracking control is implemented by tracking

reference vehicle Therefore assuming that the reference

vehicle follows the given path the reference vehicle willsatisfy the above equation at any time Using 0 to notate thereference vehicle

1205940 = 119891 (1205940 1199060) (7)

By using Taylor series and ignoring the higher-order func-tion (7) can be approximated by (8) as follows

120594 = 119891 (1205940 1199060) + 120597119891 (120594 119906)120597120594100381610038161003816100381610038161003816100381610038161003816120594=1205940119906=1199060 (120594 minus 1205940)

+ 120597119891 (120594 119906)120597119906100381610038161003816100381610038161003816100381610038161003816120594=1205940119906=1199060 (119906 minus 1199060) sdot sdot sdot

(8)

By substituting (8) with (7) we have

120594 = 119860120594 + 119861

where 119860 = [[[0 0 minusV0 sin12059300 0 V0 cos12059300 0 0

]]]119861 = [[[[[

[

cos1205930 0sin1205930 0(tan 1205750)119897 V0(119897 cos2 1205750)

]]]]]]

120594 = [[[ minus 0119910 minus 1199100 minus 0

]]] 120594 = [[

[119909 minus 1199090119910 minus 1199100120593 minus 1205930

]]] = [V minus V0120575 minus 1205750]

(9)

Themodel predictive control (MPC) used in this paper isa discrete time control method Let 120594 = (120594(119896 + 1) minus 120594(119896))119879where 119879 is the sampling period

Therefore we can discretize the continuous dynamicsfunction and (10) is the discrete time model which will beused as the predictive model in this research

120594 (119896 + 1) = 119860 (119896) 120594 (119896) + 119861 (119896) (119896) (10)

where 119860 and 119861 are represented by

119860 (119896) = [[[1 0 minusV0 sin12059301198790 1 V0 cos12059301198790 0 1

]]]

119861 (119896) = [[[[[[

cos1205930119879 0sin1205930119879 0(tan 1205750119879)119897 V0119879119897 cos2 1205750

]]]]]]

(11)

33 The Trajectory Tracking Control Algorithm of U-TurnBased on MPC MPC predicts the future state or outputof the system via the established prediction model whichsolves the optimal control sequence based on the constraintsand performance of vehicle dynamics It can calculate thefollowing optimal control sequence by predicting the futurestate or output of the control object under previous optimalcontrol sequence After alternating this cycle the object can

be controlled by the system MPC is effortless to be modelledand controlled and it also has good robustness Then it canbe used to solve multivariable and constrained problems andimplement online optimization [24]

As shown in Figure 6 the control strategy forMPC-basedU-turn trajectory tracking is as follows it starts from the 119896thsampling period generating a set of control increments byoptimization Δ119880lowast119896 = [Δ119906lowast119896 Δ119906lowast119896+1 Δ119906lowast119896+119873119888minus1]119879 to ensurethe predicted trajectory highly fits the reference trajectory inthe predictive time domain [119896 + 119879119870 +119873119901 times 119879] It also limitsthe minimum amount changes of controlling output 119873119888 isthe number of sampling points of control inputs and 119873119901 isthe number of predictive points of the system state outputswhich usually commits119873119901 ge 11987311988834 Objective Function Design As the objective functionneeds to ensure autonomous vehicle track the referencetrajectory quickly and smoothly the deviation of system statevariables and the optimization of control variables shouldbe considered Then the following objective function will beused to design the trajectory tracking controller

119869 (119896) = 119873119901sum119895=1

120594119879 (119896 + 119895 | 119896)119876120594 (119896 + 119895)

+ 119873119888sum119895=1

119879 (119896 + 119895 minus 1) 119877 (119896 + 119895 minus 1) (12)


Reference trajectoryPredictive trajectory

y

x

Δu(k | k)Δu(k + 1 | k)

t(k + 2 | k) (k + Nc minus 1 | k) (k + Np | k)t(k | k) tt t(k + Nc | k)t(k + 1 | k)

Δu(k + Nc minus 1 | k)

middot middot middot middot middot middot

Figure 6 Control strategy for MPC-based U-turn trajectory track-ing

where 119876 and 119877 are weight matrixes The first item reflectsthe performance of trajectory tracking the second itemreflects the constraints on changesThis function can be easilyconverted into a standard quadratic programming form [25]Therefore considering the vectors

120594 (119896 + 1) =[[[[[[[

120594 (119896 + 1 | 119896)120594 (119896 + 2 | 119896)

sdot sdot sdot120594 (119896 + 119873119901 | 119896)

]]]]]]]

119906 (119896) = [[[[[[

(119896119896) (119896 + 1119896)

sdot sdot sdot (119896 + 119873119888 minus 1119896)

]]]]]]

(13)

(12) can be represented by

119869 (119896) = 119909119879 (119896 + 1)119876119909 (119896 + 1) + 119906119879 (119896) 119877119906 (119896) (14)

with 119876 = [[119876 0 sdotsdotsdot 00 119876 sdotsdotsdot 0 d

0 0 sdotsdotsdot 119876

]]119877 = [ 119877 0 sdotsdotsdot 00 119877 sdotsdotsdot 0

d


]In order to simplify the solving to (12) assuming 119873119901 =119873119888 = 119873 we have

120594 (119896 + 1) = 119860 (119896) 120594 (119896 | 119896) + 119861 (119896) 119906 (119896) (15)

where

119860 (119896) =[[[[[[[[[

119860 (119896 | 119896)119860 (119896 + 1 | 119896) 119860 (119896 | 119896)

sdot sdot sdot119873minus1prod119894=0

119860 (119896 + 119894 | 119896)

]]]]]]]]]

119861 (119896)

=[[[[[[[[

119861 (119896119896) 0 sdot sdot sdot 0119860 (119896 + 1119896) 119861 (119896119896) 119861 (119896 + 1119896) sdot sdot sdot 0

sdot sdot sdot119860 (119896 + 119873 minus 2119896) times sdot sdot sdot times 119860 (119896 + 1119896) 119861 (119896119896)

sdot sdot sdot119860 (119896 + 119873 minus 2119896) times sdot sdot sdot times 119860 (119896 + 2119896) 119861 (119896 + 1119896)

sdot sdot sdotsdot sdot sdot

sdot sdot sdot0119860 (119896 + 119873 minus 1119896) times sdot sdot sdot times 119860 (119896 + 1119896) 119861 (119896119896) 119860 (119896 + 119873 minus 1119896) times sdot sdot sdot times 119860 (119896 + 2119896) 119861 (119896 + 1119896) sdot sdot sdot 119861 (119896 + 119873 minus 1119896)

]]]]]]]]

(16)

From (15)sim(16) the objective function can be convertedinto a standard quadratic form

119869 (119896) = 119906119879 (119896)119867 (119896) 119906 (119896) + 119891119879 (119896) 119906 (119896) + 119871 (119896) (17)where

119867(119896) = (119861119879 (119896) 119876119861 (119896) + 119877)119891 (119896) = 2 (119861 (119896)119879119876119860 (119896) 120594 (119896 | 119896))119871 (119896) = 120594119879 (119896 | 119896) 119860119879 (119896) 119876119860 (119896) 120594 (119896 | 119896)

(18)

119871(119896) can be ignored as it is independent of and can not affectthe determination of 119906lowast

Thus we can redefine the function as

1198691015840 (119896) = 119906119879 (119896)119867 (119896) 119906 (119896) + 119891119879 (119896) 119906 (119896) (19)This above function is expressed in standard form which

can be solved by online QP problems solver such as MatlabThe amplitude constraints in the control variables of (19) canbe represented as

119906min minus 1199060 (119896 + 119895) le (119896119896 + 119895) le 119906max minus 1199060 (119896 + 119895) (20)


After solving (19) the control inputs sequence can be derivedas

119880lowast119896 = [lowast119896 lowast119896+1 lowast119896+119873minus1]119879 (21)

Thefirst element in119880lowast119896 is applied to the system to get an actualcontrol increment which is

Δ119906lowast119896 = lowast (119896) minus (119896 minus 1) (22)

After entering the next control cycle we repeat the abovecycle processes to achieve the whole tracking control system

4 Simulation and Testing on PaTAVTT

According to the road design standards as considering thevehicle sideslip the formula to calculate the road safety speedwith large transverse gradients is

V119904 = radic 120583 + tan (120573)1 minus 120583 tan (120573)119892119877119888 (23)

where 120583 is the tire-road adhesion coefficient 120573 is the trans-verse gradient of road 119877119888 is the radius of curvature 119892 is thegravitational acceleration [26]

When the vehicle is driving on the road with large tire-road adhesion coefficient under high-speed condition thevehicle will have an overturning moment which is causedby centrifugal force and lateral adhesion The overturningmoment may result in the gravity of the vehicle to shift to theoutside tire (ie the phenomenon of lateral-load transfer)Once the overturning moment is increased to the extentthat makes the inside tire leaves off the road the untrippedrollover will occur The critical rollover speed of the vehicleon the load with large tire-road adhesion coefficient V119903 is

V119903 = radic119861 + 2ℎ tan (120573)2ℎ minus 119861 tan (120573)119892119877 (24)

where119861 is the wheel-track and ℎ is the center of gravity height[27]

The main factor of vehicle rollover is the center of gravityheight ℎ and if the center of gravity height is lower enoughthe rollover will not occur In this paper the research objectis small vehicles which usually have relatively low center ofgravity height Therefore the road safety speed V119903 is greaterthan V119901

In this case study the following parameters are used 120583 =065 120573 = 3∘ 119892 = 98ms2 ℎ = 07m 119877 = 10m andV119901 = 8442ms The simulation trajectory tracking resultsbased on MPC under different vehicle speed conditions areshown in Figure 7 The speed varied from 84ms to 36mswith a negative step ofminus03 From the figure we see that whenthe vehicle speed decreases the vehicle movement trajectorygets closer to the reference trajectory

The snapshots of lab tests are presented in Figure 8 Usingthe simulation results we deploy 5 scaled vehicles to conductthe trajectory tracking experiment and we set the desiredspeed of the vehicles the one tenth of the simulation reference

Table 2 Statistical results of the trajectories of 5 homogenous scaledvehicles

Veh Trajectory overlapratio (TOR) Travel time (s) Average speed (s)

(1) 899 38 062(2) 863 37 061(3) 894 41 059(4) 883 40 061(5) 902 41 058

Table 3 Statistical results of a real autonomous vehicle for 10rounds

Round Trajectory overlapratio (TOR)

Travel time(s)

Average speed(ms)

(1) 967 116 63(2) 991 120 61(3) 982 121 59(4) 963 136 66(5) 976 141 58(6) 948 116 62(7) 965 122 59(8) 957 126 64(9) 978 127 61(10) 980 128 61

speed (V = 06ms) The testing results on PaTAVTTplatform are shown in Figure 9 As can be seen in thefigure the trajectories are pretty closewhich demonstrates theeffectiveness of the proposed testing platform

Furthermore we calculated the parameters of the trajec-tories of 5 homogenous vehicles as shown in Table 2 Thetrajectory overlap ratio (TOR) is defined as follows

TOR = 119873119887119873 (25)

where 119873 is the number of the total trajectory points ata sampling period of 004 s and 119873119887 is the number of thetrajectory points located in the reference trajectory bufferwhich is a stripe with a width equal to the scaled vehicleand takes the reference trajectory as its mean axle From thetable it can be concluded that the proposed U-turn algo-rithm does well in repeatability robustness and trajectorytracking

We further apply the proposed algorithm to real worldtesting environments (see Figure 10) and conduct the sameU-turn trajectory experiment for 10 times Experimental results(see Figure 11) show that the algorithm can generate veryconsistent resultsThis further demonstrates the effectivenessof the proposed methodology and the scaling effect can becontrolled Moreover the control effect of the same MPCalgorithm on a real vehicle is better than that on a scaledvehicle (see Table 3) mainly because the real vehicle isequipped with ESP and other electronic devices to helpcontrol the stability of the vehicle


Y versus X-trajectory (different velocity)

0

5

10

15

20

25

Glo

bal Y

coor

dina

te (m

)

10 15minus15 minus10 minus5minus25 minus20minus30 0 5Global X coordinate (m)

84 ＧＭ

36 ＧＭ

(a)

Real longitudinal speedReference longitudinal speed

2022242628303234363840

Long

itudi

nal s

peed

(km

h)

50 15 20 2510Time (sec)

Speed error when vehicle speed = 8442ms

(b)

minus505

101520253035404550

Yaw

rate

(deg

s)

50 15 20 2510Time (sec)

Yaw angles-deg vehicle speed = 8442ms

(c)

0 5 15 20 25 3010t (s)

minus3

minus2

minus1

0

1

2

3Longitudinal position error vehicle speed = 8442ms

e(x)

(m)

(d)

minus3

minus2

minus1

0

1

2

3

0 5 15 20 25 3010t (s)

Lateral position error vehicle speed = 8442ms

e(y)

(m)

(e)

Figure 7 U-turn trajectory tracking results based on MPC (a) The simulation trajectory tracking results based on MPC under differentvehicle speed conditions (b) Longitudinal speed error (vehicle speed = 844ms) (c) Yaw angle of the trajectory (vehicle speed = 844ms)(d) Longitudinal position error (vehicle speed = 844ms) (e) Lateral position error (vehicle speed = 844ms)


Figure 8 A snapshot of the testing process

Figure 9 U-turn trajectory tracking results on PaTAVTT platform

5 Conclusion

It is difficult to test real autonomous vehicle under harshconditions Using the hardware-in-loop scaled platform totest scaled autonomous vehicle becomes an apparent alter-native In this paper we use the HIL platform to test theslip of scaled autonomous passing through U-turn underhigh-speed condition After comparing its result with the realvehicle testing we have proved the feasibility of using HILscaled platform as surrogates of the real autonomous vehiclefor testing automated vehicle Note that the proposed testplatform has a very high flexibility in simulating real worldtraffic operations including those with purely traditionalvehicles For example it can be used for conducting trafficcapacity analysis [28ndash30] LongDistanceCommuter lane (Quand Wang 2015) traffic oscillations [31 32] traffic safetyanalysis [33ndash35] and others At the end of this paper we use asimple case study of high-speed U-turn to build the trackingcontrol function A simplified vehicle dynamics model and atrajectory tracking algorithm have been considered to buildthe simulation test The experiment results demonstrate theeffectivity of HIL scaled platform

In the future we will continue this research on threeaspects Firstly we will theoretically discuss the factors thatresult in the trajectory difference between scaled vehiclesand real vehicles with the same trajectory tracking algo-rithm Secondly we will test scaled vehicles on its dynamictrajectory planning and tracking performance under trafficdisturbances Last but not least we will utilize PaTAVTTto conduct experiments and validations on the trajectory

Figure 10 U-turn trajectory tracking testing on CU CVIS testbed

0 5 10 15 20 25 30 35minus5

Global X coordinate (m)

minus20

minus15

minus10

minus5

0

5

Glo

balY

coor

dina

te (m

)

Figure 11 U-turn trajectories of a real autonomous vehicle for 10rounds

optimization and control of multiple scaled and connectedvehicles

Notations

(119909119903 119910119903) The center coordinates of the vehicle rearaxle(119909119891 119910119891) The center coordinates of the vehicle frontaxle

V119903 Velocity of the vehicle rear axleV119891 Velocity of the vehicle front axle120593 The driving direction of the vehicle120575119891 The angle of front wheel119897 The wheelbase between the front and rear

axle119903 The lateral velocity of rear axle119910119903 The longitudinal velocity of rear axle120594 The configuration (position andorientation) of the center of the axis of thewheels1205940 State output of the reference vehicle119906 Control input1199060 Control input of the reference vehicle


120594 The convergence of 120594 to 1205940 Associated perturbation control input ofthe reference vehicle119879 The sampling period119896 The sampling timeΔ119880lowast119896 Control increments119873119888 The number of sampling points of controlinputs119873119901 The number of predictive points of thesystem state outputs119876 Weight matrix119877 Weight matrix1198691015840(119896) Objective function119867(119896) (A Hessian matrix) the quadratic part ofthe objective function119891(119896) The linear part120583 Tire-road adhesion coefficient120573 Transverse gradient of road119877119888 Radius of curvature119892 Gravitational acceleration

V119904 The road safety speed with large transversegradients

V119903 The critical rollover speed of the vehicleon the load with large tire-road adhesioncoefficient119861 Wheel-trackℎ The center of gravity height119873 The number of the total trajectory pointsat a sampling period119873119887 The number of the trajectory pointslocated in the reference trajectory buffer119906min Lower bound of the input vector119906max Upper bound of the input vector

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The research is supported by the National Natural ScienceFoundation of China (no 51278058) the Fundamental Appli-cation Research Program of China Ministry of Transport(no S2013JC9397) the 111 Project (no B14043) the Fundsfor Key Scientific and Technological Innovation Team of theShaanxi Province (no 2017KCT-29) the Zhejiang ProvincialNatural Science Foundation (no LY16E080003) and the JointLaboratory of Internet of Vehicles sponsored by Ministry ofEducation and China Mobile

References

[1] D Bullock B Johnson R B Wells M Kyte and Z LildquoHardware-in-the-loop simulationrdquo Transportation ResearchPart C Emerging Technologies vol 12 no 1 pp 73ndash89 2004

[2] L Li W Huang Y Liu N Zheng and F Wang ldquoIntelligencetesting for autonomous vehicles a new approachrdquo IEEE Trans-actions on Intelligent Vehicles vol 1 no 2 pp 158ndash166 2016

[3] X Li Z Xu R Wang H Min and X Zhao ldquoCU-CVIS testbed a test bed of cooperative vehicle-infrastructure system inchangrsquoan universityrdquo in Proceedings of the DEStech Transactionson Engineering and Technology Research (ictim) 2016

[4] Y Ma Q Wu X Yan and Z Huang ldquoThe Hardware-in-the-loop Simulator A Mechatronic Testbed for CooperativeVehicles Maneuversrdquo International Journal of Intelligent Trans-portation Systems Research vol 11 no 1 pp 11ndash22 2013

[5] L Du L Han and S Chen ldquoCoordinated online in-vehiclerouting balancing user optimality and system optimalitythrough information perturbationrdquo Transportation ResearchPart B Methodological vol 79 pp 121ndash133 2015

[6] F Zhou X Li and J Ma ldquoParsimonious shooting heuristic fortrajectory design of connected automated traffic part I theoret-ical analysis with generalized time geographyrdquo TransportationResearch Part B Methodological vol 95 pp 394ndash420 2017

[7] M Zhou X Qu and S Jin ldquoOn the impact of cooperativeautonomous vehicles in improving freewaymerging amodifiedintelligent driver model based approachrdquo IEEE Transactions onIntelligent Transportation Systems vol 18 no 6 pp 1422ndash14282017

[8] J Ma X Li F Zhou J Hu and B B Park ldquoParsimoniousshooting heuristic for trajectory design of connected automatedtraffic part II computational issues and optimizationrdquo Trans-portation Research Part B Methodological vol 95 pp 421ndash4412017

[9] L Li and D Wen ldquoParallel systems for traffic control arethinkingrdquo IEEE Transactions on Intelligent TransportationSystems vol 17 no 4 pp 1179ndash1182 2016

[10] X Li Z Sun D Cao D Liu and H He ldquoDevelopment of a newintegrated local trajectory planning and tracking control frame-work for autonomous ground vehiclesrdquoMechanical Systems andSignal Processing vol 87 pp 118ndash137 2017

[11] F Michaud P Lepage P Frenette D Letourneau and NGaubert ldquoCoordinated maneuvering of automated vehiclesin platoonsrdquo IEEE Transactions on Intelligent TransportationSystems vol 7 no 4 pp 437ndash446 2006

[12] P Fernandes andUNunes ldquoPlatooning of autonomous vehicleswith intervehicle communications in SUMO traffic simulatorrdquoin Proceedings of the 13th International IEEE Conference onIntelligent Transportation Systems ITSC 2010 pp 1313ndash1318September 2010

[13] B Vanholme D Gruyer S Glaser and S Mammar ldquoFastprototyping of a highly autonomous cooperative driving systemfor public roadsrdquo in Proceedings of the 2010 IEEE IntelligentVehicles Symposium IV 2010 pp 135ndash142 June 2010

[14] S Brennan and A Alleyne ldquoThe Illinois Roadway SimulatorA mechatronic testbed for vehicle dynamics and controlrdquoIEEEASMETransactions onMechatronics vol 5 no 4 pp 349ndash359 2000

[15] Z Xu X Li X Zhao M H Zhang and Z Wang ldquoDSRCversus 4G-LTE for connected vehicle applications a study onfield experiments of vehicular communication performancerdquoJournal of Advanced Transportation vol 2017 pp 1ndash10 2017

[16] Y Ma Y Xu and Q Wu ldquoA review of cooperative driving forvehicle-platoon hybrid controlrdquo Chinese Journal of AutomotiveEngineering vol 4 no 1 pp 1ndash13 2014

[17] W Deng Y H Lee and A Zhao ldquoHardware-in-the-loopsimulation for autonomous drivingrdquo in Proceedings of the 34thAnnual Conference of the IEEE Industrial Electronics SocietyIECON 2008 pp 1742ndash1747 November 2008


[18] M A M Zulkefli P Mukherjee Z Sun J Zheng H X Liuand P Huang ldquoHardware-in-the-loop testbed for evaluatingconnected vehicle applicationsrdquoTransportation Research Part CEmerging Technologies vol 78 pp 50ndash62 2017

[19] O Gietelink J Ploeg B de Schutter andM Verhaegen ldquoDevel-opment of advanced driver assistance systems with vehiclehardware-in-the-loop simulationsrdquo Vehicle System Dynamicsvol 44 no 7 pp 569ndash590 2006

[20] H Diab M G Chavez Grunewald I Ben Makhlouf D Abeland S Kowalewski ldquoA testing platform for cooperative vehicleplatoon controllersrdquo in Proceedings of the 13th InternationalIEEE Conference on Intelligent Transportation Systems ITSC2010 pp 1718ndash1723 September 2010

[21] D Bohmlander V Yano T Brandmeier et al ldquoA novel approachfor intelligent pre-crash threat assessment systemsrdquo in Proceed-ings of the 2014 17th IEEE International Conference on IntelligentTransportation Systems ITSC 2014 pp 954ndash961 October 2014

[22] C Sun C Wu D Chu M Zhong Z Hu and J Ma ldquoRiskprediction for curve speed warning by considering humanvehicle and road factorsrdquo Transportation Research Record vol2581 pp 18ndash26 2016

[23] M Elkady A Elmarakbi J MacIntyre and M AlharirildquoCollision mitigation and vehicle transportation safety usingintegrated vehicle dynamics control systemsrdquo Journal of Trafficand Transportation Engineering (English Edition) vol 4 no 1pp 41ndash60 2017

[24] D Hrovat S di Cairano H E Tseng and I V KolmanovskyldquoThe development of model predictive control in automotiveindustry a surveyrdquo in Proceedings of the IEEE InternationalConference on Control Applications (CCA rsquo12) pp 295ndash302October 2012

[25] F Kuhne W F Lages da Silva Jr and J G ldquoModel predictivecontrol of a mobile robot using linearizationrdquo in Proceedingsof the In Proceedings of mechatronics and robotics pp 525ndash5302004

[26] K W Ogden ldquoSafer roads a guide to road safety engineeringrdquoEvaluation 1996

[27] A A Aljanahi A H Rhodes and A V Metcalfe ldquoSpeed speedlimits and road traffic accidents under free flow conditionsrdquoAccident Analysis amp Prevention vol 31 no 1-2 pp 161ndash168 1999

[28] B van Arem M M Abbas X Li et al ldquoIntegrated traffic flowmodels and analysis for automated vehiclesrdquo in Lecturer Notesin Mobility pp 249ndash258 2016

[29] X Qu SWang and J Zhang ldquoOn the fundamental diagram forfreeway traffic a novel calibration approach for single-regimemodelsrdquo Transportation Research Part B Methodological vol73 pp 91ndash102 2015

[30] X Qu J Zhang and S Wang ldquoOn the stochastic fundamentaldiagram for freeway traffic Model development analyticalproperties validation and extensive applicationsrdquo Transporta-tion Research Part B Methodological vol 104 pp 256ndash271 2017

[31] X Li X Wang and Y Ouyang ldquoPrediction and field validationof traffic oscillation propagation under nonlinear car-followinglawsrdquo Transportation Research Part B Methodological vol 46no 3 pp 409ndash423 2012

[32] X Li J Cui S An and M Parsafard ldquoStop-and-go trafficanalysis theoretical properties environmental impacts andoscillationmitigationrdquoTransportation Research Part BMethod-ological vol 70 no 1 pp 319ndash339 2014

[33] Y Kuang X Qu and S Wang ldquoA tree-structured crash surro-gate measure for freewaysrdquo Accident Analysis amp Prevention vol77 pp 137ndash148 2015

[34] X Qu Y Yang Z Liu S Jin and J Weng ldquoPotential crash risksof expressway on-ramps and off-ramps a case study in BeijingChinardquo Safety Science vol 70 pp 58ndash62 2014

[35] XQuYKuang EOh and S Jin ldquoSafety evaluation for express-ways a comparative study for macroscopic and microscopicindicatorsrdquo Traffic Injury Prevention vol 15 no 1 pp 89ndash932014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Sensing andlocalization

systems

Global route planning

Behavior reasoning

Trajectorytracking control

Trajectory planning

Autonomous vehicle ldquoSindardquo developed by Changrsquoan University

Figure 1 The generic function chart of an autonomous vehicle

handle the directionspeed of the vehicle according to thereal-time surrounding traffic information and high-accuracymap information [10]

The main two existing testing approaches of autonomousvehicle trajectory tracking are simulation testing and realvehicles testing Although the software-based simulation hasthe advantages of low cost and high efficiency the simulationmodel is based on the ideal mathematical model whichignores many practical factors might cause large differencebetween the simulation results and real cases results It shouldbe noted that the real world testing although with muchhigher accuracy is very time-consuming expensive andlimited by weather and scenarios [11ndash13] In this regardshortening the development cycle without sacrificing accu-racy and reliability has been concerned [14] There aremany well-known testbeds around the world for testingconnected and automated vehicles such as the MCity of theUniversity of Michigan and the GoMento test site locatedin Contra Costa County California and CU CVIS testbedof Changrsquoan University in China The former two testbedsfocus on demonstration for applications of future IntelligentTransportation Systems CU CVIS focuses on the metafunc-tion testing for each part of CAVs and the comprehensiveperformance testing under the limit conditions [15]

Hardware-in-the-loop (HIL) simulation has combinedboth mathematical and mechanical models to emulate realvehicles as considering the influence of gravity resistanceand friction which may cause the inaccuracy of the modelCompared to the testing in real traffic system the HIL has themerit of low construction cost short development cycle andreproducible method [16] At present HIL-based simulationhas been widely used in the field of automotive testingDeng et al [17] proposed a HIL simulation system as anintegral part of various autonomous driving programs whichis a laboratory environment to support the developmenttest and verification of many functions and algorithmsrelated to sensor-guided autonomous driving Zulkefli et al[18] proposed a HIL testbed to evaluate the performance

of connected vehicle applications This testbed integrated alaboratory powertrain research platform with a microscopictraffic simulator (VISSIM) which could be used to testvarious ITS applications such as CACC Eco-Driving andSpeed Harmonization Gietelink et al [19] developed anindoor vehicle hardware-in-the-loop simulation system totest the advanced driver assistance systems embedded in areal vehicle To best of our knowledge most of HIL-basedsimulations embed a vehicle or vehicle parts into the systemwhich are usually complex and costly and require large spaceA research group from RWTH Aachen University Germanyproposed a hardware implementation of a platoon of four1 14 scaled trucks to test the cooperative platoon controlalgorithm [20] As considering critical safety factors HILsimulation system is also used to precrash threat assessment[21]

In the proposed paper a HIL scaled platform for test-ing autonomous vehicle trajectory tracking (PaTAVTT) ispresented which is a mechatronic testbed consists of scaledroadway scaled vehicles indoor positioning subsystem andcomputer-aided Graphical User Interfaces Compared withother HIL test systems PaTAVTT has the following advan-tages First it is equipped with an indoor ultra-wideband-(UWB-) based high-precision positioning system matchesthe GPS precision in outdoor field which can record theaccurate trajectory of the scaled vehicle in motion Thedeviation between the real trajectory and the reference wouldbe an important criterion to evaluate the performance of thetrajectory tracking algorithm Second the scaled platformbridges the software-based vehicle dynamics model with thereal vehicleThe algorithmmodules and parameters validatedby Matlab or Carsim can be downloaded into the scalevehicle After passing the tests on PaTAVTT the algorithmscan be further transplanted into the real vehicle Thirdmany external factors such as the road surface material roadgeometry and slope and static or dynamic obstacles can betested due to the low establishment and testing costs

In this paper the system structure of this HIL plat-form and the implementation of each submodule havebeen described Further a new methodology of U-turn hasbeen developed and tested which can also be used in anautonomous vehicle The testing results demonstrate that theHIL platform can be used to test the trajectory planning andtracking control of an autonomous vehicle which potentiallyshorten its development cycle The remainder of this articleis organized as follows Section 2 is the overview of thePaTAVTT Section 3 presents a real-case study and themethodology of U-turnThe simulation results are presentedin Section 4 Section 5 concludes the paper

2 Overview of PaTAVTT

In this paper PaTAVTT consists of scaled roadway position-ing system scaled vehicle transmission system and softwaresimulator As can be seen in Figure 2 the scaled roadwayis a rounded rectangle platform which has two lanes andthe width of each lane is 375 cm Additionally the scaledroadways has different kinds of road infrastructures such astraffic signs and LED information board


Wi-Fi hotspot


Positioning tag


Network hub

Software simulator





Steeringgear Motor

Localization tag



DataprocessingCPU

IIC

USR

AT

IO

Camera


CameraController

CPU


Steering geer

Data processingCPU

MotorBattery


Localizationtag

















l

y

o x

(xf yf)

(xr yr) rf

f




V119903 = 119903 cos120593 + 119910119903 sin120593 (1)

119903 sin120593 minus 119910119903 cos120593 = 0 (2)

V119903 = V119891 cos 120575119891 (3)

= V119891 sin120575119891119897 (4)




[[[119903119910119903]]]= [[[[[[

cos120593sin120593

(tan 120575119891)119897

]]]]]]V119903 (5)


120594 = 119891 (120594 119906) (6)




1205940 = 119891 (1205940 1199060) (7)


120594 = 119891 (1205940 1199060) + 120597119891 (120594 119906)120597120594100381610038161003816100381610038161003816100381610038161003816120594=1205940119906=1199060 (120594 minus 1205940)


(8)


120594 = 119860120594 + 119861


]]]119861 = [[[[[

[

cos1205930 0sin1205930 0(tan 1205750)119897 V0(119897 cos2 1205750)

]]]]]]


]]] 120594 = [[


]]] = [V minus V0120575 minus 1205750]

(9)



120594 (119896 + 1) = 119860 (119896) 120594 (119896) + 119861 (119896) (119896) (10)


119860 (119896) = [[[1 0 minusV0 sin12059301198790 1 V0 cos12059301198790 0 1

]]]

119861 (119896) = [[[[[[

cos1205930119879 0sin1205930119879 0(tan 1205750119879)119897 V0119879119897 cos2 1205750

]]]]]]

(11)




119869 (119896) = 119873119901sum119895=1

120594119879 (119896 + 119895 | 119896)119876120594 (119896 + 119895)

+ 119873119888sum119895=1

119879 (119896 + 119895 minus 1) 119877 (119896 + 119895 minus 1) (12)



y

x

Δu(k | k)Δu(k + 1 | k)






120594 (119896 + 1) =[[[[[[[

120594 (119896 + 1 | 119896)120594 (119896 + 2 | 119896)

sdot sdot sdot120594 (119896 + 119873119901 | 119896)

]]]]]]]

119906 (119896) = [[[[[[

(119896119896) (119896 + 1119896)


]]]]]]

(13)


119869 (119896) = 119909119879 (119896 + 1)119876119909 (119896 + 1) + 119906119879 (119896) 119877119906 (119896) (14)




d



120594 (119896 + 1) = 119860 (119896) 120594 (119896 | 119896) + 119861 (119896) 119906 (119896) (15)

where

119860 (119896) =[[[[[[[[[

119860 (119896 | 119896)119860 (119896 + 1 | 119896) 119860 (119896 | 119896)


119860 (119896 + 119894 | 119896)

]]]]]]]]]

119861 (119896)

=[[[[[[[[






]]]]]]]]

(16)


119869 (119896) = 119906119879 (119896)119867 (119896) 119906 (119896) + 119891119879 (119896) 119906 (119896) + 119871 (119896) (17)where

119867(119896) = (119861119879 (119896) 119876119861 (119896) + 119877)119891 (119896) = 2 (119861 (119896)119879119876119860 (119896) 120594 (119896 | 119896))119871 (119896) = 120594119879 (119896 | 119896) 119860119879 (119896) 119876119860 (119896) 120594 (119896 | 119896)

(18)
























(1) 899 38 062(2) 863 37 061(3) 894 41 059(4) 883 40 061(5) 902 41 058



Travel time(s)

Average speed(ms)

(1) 967 116 63(2) 991 120 61(3) 982 121 59(4) 963 136 66(5) 976 141 58(6) 948 116 62(7) 965 122 59(8) 957 126 64(9) 978 127 61(10) 980 128 61



TOR = 119873119887119873 (25)





0

5

10

15

20

25

Glo

bal Y

coor

dina

te (m

)


84 ＧＭ

36 ＧＭ

(a)


2022242628303234363840

Long

itudi

nal s

peed

(km

h)

50 15 20 2510Time (sec)


(b)

minus505

101520253035404550

Yaw

rate

(deg

s)

50 15 20 2510Time (sec)


(c)

0 5 15 20 25 3010t (s)

minus3

minus2

minus1

0

1

2


e(x)

(m)

(d)

minus3

minus2

minus1

0

1

2

3

0 5 15 20 25 3010t (s)


e(y)

(m)

(e)





5 Conclusion




0 5 10 15 20 25 30 35minus5


minus20

minus15

minus10

minus5

0

5

Glo

balY

coor

dina

te (m

)



Notations










Acknowledgments


References





































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Wi-Fi hotspot


Positioning tag


Network hub

Software simulator





Steeringgear Motor

Localization tag



DataprocessingCPU

IIC

USR

AT

IO

Camera


CameraController

CPU


Steering geer

Data processingCPU

MotorBattery


Localizationtag

















l

y

o x

(xf yf)

(xr yr) rf

f




V119903 = 119903 cos120593 + 119910119903 sin120593 (1)

119903 sin120593 minus 119910119903 cos120593 = 0 (2)

V119903 = V119891 cos 120575119891 (3)

= V119891 sin120575119891119897 (4)




[[[119903119910119903]]]= [[[[[[

cos120593sin120593

(tan 120575119891)119897

]]]]]]V119903 (5)


120594 = 119891 (120594 119906) (6)




1205940 = 119891 (1205940 1199060) (7)


120594 = 119891 (1205940 1199060) + 120597119891 (120594 119906)120597120594100381610038161003816100381610038161003816100381610038161003816120594=1205940119906=1199060 (120594 minus 1205940)


(8)


120594 = 119860120594 + 119861


]]]119861 = [[[[[

[

cos1205930 0sin1205930 0(tan 1205750)119897 V0(119897 cos2 1205750)

]]]]]]


]]] 120594 = [[


]]] = [V minus V0120575 minus 1205750]

(9)



120594 (119896 + 1) = 119860 (119896) 120594 (119896) + 119861 (119896) (119896) (10)


119860 (119896) = [[[1 0 minusV0 sin12059301198790 1 V0 cos12059301198790 0 1

]]]

119861 (119896) = [[[[[[

cos1205930119879 0sin1205930119879 0(tan 1205750119879)119897 V0119879119897 cos2 1205750

]]]]]]

(11)




119869 (119896) = 119873119901sum119895=1

120594119879 (119896 + 119895 | 119896)119876120594 (119896 + 119895)

+ 119873119888sum119895=1

119879 (119896 + 119895 minus 1) 119877 (119896 + 119895 minus 1) (12)



y

x

Δu(k | k)Δu(k + 1 | k)






120594 (119896 + 1) =[[[[[[[

120594 (119896 + 1 | 119896)120594 (119896 + 2 | 119896)

sdot sdot sdot120594 (119896 + 119873119901 | 119896)

]]]]]]]

119906 (119896) = [[[[[[

(119896119896) (119896 + 1119896)


]]]]]]

(13)


119869 (119896) = 119909119879 (119896 + 1)119876119909 (119896 + 1) + 119906119879 (119896) 119877119906 (119896) (14)




d



120594 (119896 + 1) = 119860 (119896) 120594 (119896 | 119896) + 119861 (119896) 119906 (119896) (15)

where

119860 (119896) =[[[[[[[[[

119860 (119896 | 119896)119860 (119896 + 1 | 119896) 119860 (119896 | 119896)


119860 (119896 + 119894 | 119896)

]]]]]]]]]

119861 (119896)

=[[[[[[[[






]]]]]]]]

(16)


119869 (119896) = 119906119879 (119896)119867 (119896) 119906 (119896) + 119891119879 (119896) 119906 (119896) + 119871 (119896) (17)where

119867(119896) = (119861119879 (119896) 119876119861 (119896) + 119877)119891 (119896) = 2 (119861 (119896)119879119876119860 (119896) 120594 (119896 | 119896))119871 (119896) = 120594119879 (119896 | 119896) 119860119879 (119896) 119876119860 (119896) 120594 (119896 | 119896)

(18)
























(1) 899 38 062(2) 863 37 061(3) 894 41 059(4) 883 40 061(5) 902 41 058



Travel time(s)

Average speed(ms)

(1) 967 116 63(2) 991 120 61(3) 982 121 59(4) 963 136 66(5) 976 141 58(6) 948 116 62(7) 965 122 59(8) 957 126 64(9) 978 127 61(10) 980 128 61



TOR = 119873119887119873 (25)





0

5

10

15

20

25

Glo

bal Y

coor

dina

te (m

)


84 ＧＭ

36 ＧＭ

(a)


2022242628303234363840

Long

itudi

nal s

peed

(km

h)

50 15 20 2510Time (sec)


(b)

minus505

101520253035404550

Yaw

rate

(deg

s)

50 15 20 2510Time (sec)


(c)

0 5 15 20 25 3010t (s)

minus3

minus2

minus1

0

1

2


e(x)

(m)

(d)

minus3

minus2

minus1

0

1

2

3

0 5 15 20 25 3010t (s)


e(y)

(m)

(e)





5 Conclusion




0 5 10 15 20 25 30 35minus5


minus20

minus15

minus10

minus5

0

5

Glo

balY

coor

dina

te (m

)



Notations










Acknowledgments


References





































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















l

y

o x

(xf yf)

(xr yr) rf

f




V119903 = 119903 cos120593 + 119910119903 sin120593 (1)

119903 sin120593 minus 119910119903 cos120593 = 0 (2)

V119903 = V119891 cos 120575119891 (3)

= V119891 sin120575119891119897 (4)




[[[119903119910119903]]]= [[[[[[

cos120593sin120593

(tan 120575119891)119897

]]]]]]V119903 (5)


120594 = 119891 (120594 119906) (6)




1205940 = 119891 (1205940 1199060) (7)


120594 = 119891 (1205940 1199060) + 120597119891 (120594 119906)120597120594100381610038161003816100381610038161003816100381610038161003816120594=1205940119906=1199060 (120594 minus 1205940)


(8)


120594 = 119860120594 + 119861


]]]119861 = [[[[[

[

cos1205930 0sin1205930 0(tan 1205750)119897 V0(119897 cos2 1205750)

]]]]]]


]]] 120594 = [[


]]] = [V minus V0120575 minus 1205750]

(9)



120594 (119896 + 1) = 119860 (119896) 120594 (119896) + 119861 (119896) (119896) (10)


119860 (119896) = [[[1 0 minusV0 sin12059301198790 1 V0 cos12059301198790 0 1

]]]

119861 (119896) = [[[[[[

cos1205930119879 0sin1205930119879 0(tan 1205750119879)119897 V0119879119897 cos2 1205750

]]]]]]

(11)




119869 (119896) = 119873119901sum119895=1

120594119879 (119896 + 119895 | 119896)119876120594 (119896 + 119895)

+ 119873119888sum119895=1

119879 (119896 + 119895 minus 1) 119877 (119896 + 119895 minus 1) (12)



y

x

Δu(k | k)Δu(k + 1 | k)






120594 (119896 + 1) =[[[[[[[

120594 (119896 + 1 | 119896)120594 (119896 + 2 | 119896)

sdot sdot sdot120594 (119896 + 119873119901 | 119896)

]]]]]]]

119906 (119896) = [[[[[[

(119896119896) (119896 + 1119896)


]]]]]]

(13)


119869 (119896) = 119909119879 (119896 + 1)119876119909 (119896 + 1) + 119906119879 (119896) 119877119906 (119896) (14)




d



120594 (119896 + 1) = 119860 (119896) 120594 (119896 | 119896) + 119861 (119896) 119906 (119896) (15)

where

119860 (119896) =[[[[[[[[[

119860 (119896 | 119896)119860 (119896 + 1 | 119896) 119860 (119896 | 119896)


119860 (119896 + 119894 | 119896)

]]]]]]]]]

119861 (119896)

=[[[[[[[[






]]]]]]]]

(16)


119869 (119896) = 119906119879 (119896)119867 (119896) 119906 (119896) + 119891119879 (119896) 119906 (119896) + 119871 (119896) (17)where

119867(119896) = (119861119879 (119896) 119876119861 (119896) + 119877)119891 (119896) = 2 (119861 (119896)119879119876119860 (119896) 120594 (119896 | 119896))119871 (119896) = 120594119879 (119896 | 119896) 119860119879 (119896) 119876119860 (119896) 120594 (119896 | 119896)

(18)
























(1) 899 38 062(2) 863 37 061(3) 894 41 059(4) 883 40 061(5) 902 41 058



Travel time(s)

Average speed(ms)

(1) 967 116 63(2) 991 120 61(3) 982 121 59(4) 963 136 66(5) 976 141 58(6) 948 116 62(7) 965 122 59(8) 957 126 64(9) 978 127 61(10) 980 128 61



TOR = 119873119887119873 (25)





0

5

10

15

20

25

Glo

bal Y

coor

dina

te (m

)


84 ＧＭ

36 ＧＭ

(a)


2022242628303234363840

Long

itudi

nal s

peed

(km

h)

50 15 20 2510Time (sec)


(b)

minus505

101520253035404550

Yaw

rate

(deg

s)

50 15 20 2510Time (sec)


(c)

0 5 15 20 25 3010t (s)

minus3

minus2

minus1

0

1

2


e(x)

(m)

(d)

minus3

minus2

minus1

0

1

2

3

0 5 15 20 25 3010t (s)


e(y)

(m)

(e)





5 Conclusion




0 5 10 15 20 25 30 35minus5


minus20

minus15

minus10

minus5

0

5

Glo

balY

coor

dina

te (m

)



Notations










Acknowledgments


References





































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












[[[119903119910119903]]]= [[[[[[

cos120593sin120593

(tan 120575119891)119897

]]]]]]V119903 (5)


120594 = 119891 (120594 119906) (6)




1205940 = 119891 (1205940 1199060) (7)


120594 = 119891 (1205940 1199060) + 120597119891 (120594 119906)120597120594100381610038161003816100381610038161003816100381610038161003816120594=1205940119906=1199060 (120594 minus 1205940)


(8)


120594 = 119860120594 + 119861


]]]119861 = [[[[[

[

cos1205930 0sin1205930 0(tan 1205750)119897 V0(119897 cos2 1205750)

]]]]]]


]]] 120594 = [[


]]] = [V minus V0120575 minus 1205750]

(9)



120594 (119896 + 1) = 119860 (119896) 120594 (119896) + 119861 (119896) (119896) (10)


119860 (119896) = [[[1 0 minusV0 sin12059301198790 1 V0 cos12059301198790 0 1

]]]

119861 (119896) = [[[[[[

cos1205930119879 0sin1205930119879 0(tan 1205750119879)119897 V0119879119897 cos2 1205750

]]]]]]

(11)




119869 (119896) = 119873119901sum119895=1

120594119879 (119896 + 119895 | 119896)119876120594 (119896 + 119895)

+ 119873119888sum119895=1

119879 (119896 + 119895 minus 1) 119877 (119896 + 119895 minus 1) (12)



y

x

Δu(k | k)Δu(k + 1 | k)






120594 (119896 + 1) =[[[[[[[

120594 (119896 + 1 | 119896)120594 (119896 + 2 | 119896)

sdot sdot sdot120594 (119896 + 119873119901 | 119896)

]]]]]]]

119906 (119896) = [[[[[[

(119896119896) (119896 + 1119896)


]]]]]]

(13)


119869 (119896) = 119909119879 (119896 + 1)119876119909 (119896 + 1) + 119906119879 (119896) 119877119906 (119896) (14)




d



120594 (119896 + 1) = 119860 (119896) 120594 (119896 | 119896) + 119861 (119896) 119906 (119896) (15)

where

119860 (119896) =[[[[[[[[[

119860 (119896 | 119896)119860 (119896 + 1 | 119896) 119860 (119896 | 119896)


119860 (119896 + 119894 | 119896)

]]]]]]]]]

119861 (119896)

=[[[[[[[[






]]]]]]]]

(16)


119869 (119896) = 119906119879 (119896)119867 (119896) 119906 (119896) + 119891119879 (119896) 119906 (119896) + 119871 (119896) (17)where

119867(119896) = (119861119879 (119896) 119876119861 (119896) + 119877)119891 (119896) = 2 (119861 (119896)119879119876119860 (119896) 120594 (119896 | 119896))119871 (119896) = 120594119879 (119896 | 119896) 119860119879 (119896) 119876119860 (119896) 120594 (119896 | 119896)

(18)
























(1) 899 38 062(2) 863 37 061(3) 894 41 059(4) 883 40 061(5) 902 41 058



Travel time(s)

Average speed(ms)

(1) 967 116 63(2) 991 120 61(3) 982 121 59(4) 963 136 66(5) 976 141 58(6) 948 116 62(7) 965 122 59(8) 957 126 64(9) 978 127 61(10) 980 128 61



TOR = 119873119887119873 (25)





0

5

10

15

20

25

Glo

bal Y

coor

dina

te (m

)


84 ＧＭ

36 ＧＭ

(a)


2022242628303234363840

Long

itudi

nal s

peed

(km

h)

50 15 20 2510Time (sec)


(b)

minus505

101520253035404550

Yaw

rate

(deg

s)

50 15 20 2510Time (sec)


(c)

0 5 15 20 25 3010t (s)

minus3

minus2

minus1

0

1

2


e(x)

(m)

(d)

minus3

minus2

minus1

0

1

2

3

0 5 15 20 25 3010t (s)


e(y)

(m)

(e)





5 Conclusion




0 5 10 15 20 25 30 35minus5


minus20

minus15

minus10

minus5

0

5

Glo

balY

coor

dina

te (m

)



Notations










Acknowledgments


References





































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











y

x

Δu(k | k)Δu(k + 1 | k)






120594 (119896 + 1) =[[[[[[[

120594 (119896 + 1 | 119896)120594 (119896 + 2 | 119896)

sdot sdot sdot120594 (119896 + 119873119901 | 119896)

]]]]]]]

119906 (119896) = [[[[[[

(119896119896) (119896 + 1119896)


]]]]]]

(13)


119869 (119896) = 119909119879 (119896 + 1)119876119909 (119896 + 1) + 119906119879 (119896) 119877119906 (119896) (14)




d



120594 (119896 + 1) = 119860 (119896) 120594 (119896 | 119896) + 119861 (119896) 119906 (119896) (15)

where

119860 (119896) =[[[[[[[[[

119860 (119896 | 119896)119860 (119896 + 1 | 119896) 119860 (119896 | 119896)


119860 (119896 + 119894 | 119896)

]]]]]]]]]

119861 (119896)

=[[[[[[[[






]]]]]]]]

(16)


119869 (119896) = 119906119879 (119896)119867 (119896) 119906 (119896) + 119891119879 (119896) 119906 (119896) + 119871 (119896) (17)where

119867(119896) = (119861119879 (119896) 119876119861 (119896) + 119877)119891 (119896) = 2 (119861 (119896)119879119876119860 (119896) 120594 (119896 | 119896))119871 (119896) = 120594119879 (119896 | 119896) 119860119879 (119896) 119876119860 (119896) 120594 (119896 | 119896)

(18)
























(1) 899 38 062(2) 863 37 061(3) 894 41 059(4) 883 40 061(5) 902 41 058



Travel time(s)

Average speed(ms)

(1) 967 116 63(2) 991 120 61(3) 982 121 59(4) 963 136 66(5) 976 141 58(6) 948 116 62(7) 965 122 59(8) 957 126 64(9) 978 127 61(10) 980 128 61



TOR = 119873119887119873 (25)





0

5

10

15

20

25

Glo

bal Y

coor

dina

te (m

)


84 ＧＭ

36 ＧＭ

(a)


2022242628303234363840

Long

itudi

nal s

peed

(km

h)

50 15 20 2510Time (sec)


(b)

minus505

101520253035404550

Yaw

rate

(deg

s)

50 15 20 2510Time (sec)


(c)

0 5 15 20 25 3010t (s)

minus3

minus2

minus1

0

1

2


e(x)

(m)

(d)

minus3

minus2

minus1

0

1

2

3

0 5 15 20 25 3010t (s)


e(y)

(m)

(e)





5 Conclusion




0 5 10 15 20 25 30 35minus5


minus20

minus15

minus10

minus5

0

5

Glo

balY

coor

dina

te (m

)



Notations










Acknowledgments


References





































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



























(1) 899 38 062(2) 863 37 061(3) 894 41 059(4) 883 40 061(5) 902 41 058



Travel time(s)

Average speed(ms)

(1) 967 116 63(2) 991 120 61(3) 982 121 59(4) 963 136 66(5) 976 141 58(6) 948 116 62(7) 965 122 59(8) 957 126 64(9) 978 127 61(10) 980 128 61



TOR = 119873119887119873 (25)





0

5

10

15

20

25

Glo

bal Y

coor

dina

te (m

)


84 ＧＭ

36 ＧＭ

(a)


2022242628303234363840

Long

itudi

nal s

peed

(km

h)

50 15 20 2510Time (sec)


(b)

minus505

101520253035404550

Yaw

rate

(deg

s)

50 15 20 2510Time (sec)


(c)

0 5 15 20 25 3010t (s)

minus3

minus2

minus1

0

1

2


e(x)

(m)

(d)

minus3

minus2

minus1

0

1

2

3

0 5 15 20 25 3010t (s)


e(y)

(m)

(e)





5 Conclusion




0 5 10 15 20 25 30 35minus5


minus20

minus15

minus10

minus5

0

5

Glo

balY

coor

dina

te (m

)



Notations










Acknowledgments


References





































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

5

10

15

20

25

Glo

bal Y

coor

dina

te (m

)


84 ＧＭ

36 ＧＭ

(a)


2022242628303234363840

Long

itudi

nal s

peed

(km

h)

50 15 20 2510Time (sec)


(b)

minus505

101520253035404550

Yaw

rate

(deg

s)

50 15 20 2510Time (sec)


(c)

0 5 15 20 25 3010t (s)

minus3

minus2

minus1

0

1

2


e(x)

(m)

(d)

minus3

minus2

minus1

0

1

2

3

0 5 15 20 25 3010t (s)


e(y)

(m)

(e)





5 Conclusion




0 5 10 15 20 25 30 35minus5


minus20

minus15

minus10

minus5

0

5

Glo

balY

coor

dina

te (m

)



Notations










Acknowledgments


References





































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












5 Conclusion




0 5 10 15 20 25 30 35minus5


minus20

minus15

minus10

minus5

0

5

Glo

balY

coor

dina

te (m

)



Notations










Acknowledgments


References





































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















Acknowledgments


References





































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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