Multiple Vehicle Diving Contol fo Taffic Flow Efficiency Seong-Woo Kim, Gi-Poong Gwon, Seung-Tak Choi, Seung-am Kang, Myoung-Ok Shin, In-Sub oo, Eun-Dong Lee, and Seung-Woo Seo Abstact The dynamics of multi-agent in natue have been lagely studied fo a long time to investigate how the aggegation of agents can move smoothly in complex envionments without collision. The main insights can be summaized such that the aggegated dynamics of animals and paticles can be explained by an individual s simple ules. In a simila vein, we conjectue that such simple ules fo vehicle maneuveing can accommodate the fluid flow of taffic and educe ca accidents in highway and uban aeas. In this pape, we fist show the Reynolds thee ules ae applicable to autonomous diving on a single lane. Moeove, we povide additional equiements and algoithms fo multiple lanes. Based on these esults, we show that the poposed natue-inspied diving maneuve can incease taffic flow by 1) mitigating shockwave at bottlenecks and ) extending the peception ange fo bette path planning, which equies the suppot of the vehicle autonomy and wieless communication, espectively. Finally, we pove the feasibility of ou wok with expeiments using multiple UAVs. I. ITRODUCTIO Moden tanspotation systems ae faced with technical challenges such as taffic flow efficiency, safety enhancement and envionmental consevation. To tackle these challenges, the poposed appoaches ae classified into two pats: a top-down appoach and a bottom-up appoach. In the topdown appoach, a cental system povides eal-time taffic infomation to dives, which is expected to dissipate taffic jam and guide the taffic flow ationally. In the bottom-up appoach, vehicle autonomy intevenes in the diving of the vehicle, that is, a vehicle is contolled electonically. The top-down appoach has contibuted mainly to taffic flow efficiency. In contast, the bottom-up appoach has been used fo immediate vehicle safety. As automotive electonics ae beginning to be widely used, thee have been seveal eseach effots to incease taffic flow efficiency though vehicle autonomy such as platooning [1] and coopeative adaptive cuise contol (CACC) []. In platooning, each vehicle is autonomously contolled to adopt the velocity of its pedecesso by electonic baking system, electonic thottle contol, and ange sensos. With the suppot of long ange sensos o wieless communication, the intemediate gap between successive vehicles in the same lane can be minimized without collision. Theefoe, S. Kim is with the Singapoe-MIT Alliance fo Reseach and Technology, Massachusetts Institute of Technology, sungwoo@smat.mit.edu Othe authos ae with the Depatment of Electical Engineeing and Compute Science, Seoul ational Univesity, {gpgwon, stchoi, snkang, moshin, isyoo, edlee}@cnslab.snu.ac.k, and sseo@snu.ac.k. This eseach was suppoted by Basic Science Reseach Pogam though the ational Reseach Foundation of Koea (RF) funded by the Ministy of Education, Science and Technology (1-913) and patially Institute of ew Media and Communication. the educed gap by platooning inceases the taffic density. Each vehicle can sustain the velocity consensus such as a speed limit, which esults in an incease of taffic flow [3]. CACC is one of the specific implementations of platooning. Howeve, the existing platooning is esticted to single lane cases. In geneal, tanspotation systems include multiple lanes that have diffeent chaacteistics and scenaios such as lane dop, lane split, o lane meging. Fo these lane changing elated issues, multiple lanes ae much moe difficult to deal with analytically and expeimentally. The appoaches poposed fo lane changing issues, in the liteatue, ae too complex to be used in pactice. Moeove, a human does not dive in such a complex manne. Instead, a dive abstacts the diving stategy with simple ules, e.g., keeping a safe distance to the pedecesso vehicle, baking fo collision avoidance, and lane changing fo velocity incease. In this context, thee have been many studies that have attempted to explain the aggegate dynamics of multiple agents using simple ules fo quite some time [4] [6]. In paticula, animal aggegations have been known to move fast and smoothly in a distibuted manne based on a numbe of simple ules. Reynolds intoduced thee fundamental laws, sepaation, alignment, and cohesion, fo compute animation of bid flocking in his celebated pape [7]. The distinct point of Reynolds wok is that the poposed ules define an individual behavio with no assumption of a centalized coodination. The undelying insight of Reynolds wok is that an independent individual behavio can achieve a common goup goal by simple laws. Fom the pespective of an individual autonomous agent, the movement fo animal aggegation is simila to taffic flow in tanspotation systems. The diffeence is whethe thee is fee space o a lane system. These obsevations motivated us to apply animal aggegation dynamics to vehicle diving in ode to incease the taffic flow efficiency in the multiple lane tanspotation systems. In this pape, we fist show that Reynolds thee ules ae applicable to vehicle diving in a single lane. Since Reynolds developed his model fo bids in ai space, multiple lanes wee not consideed in his model. Theefoe, we povide additional equiements and algoithms necessay fo diving in multiple lanes. The next fundamental question is whethe these poposed natue-inspied diving appoaches can achieve any benefit in tems of taffic flow. A bottleneck, caused by seveal easons such as accident, lane dop, o lane meging, has been known to be one of the majo causes of taffic jams. The bottleneck causes baking-to-stop that ceates a shockwave [8]. In contast, the aggegations in
natue smoothly go though bottlenecks in a coopeative manne. Howeve, it is difficult to expect such coopeation on the oad since a dive has a shot line of sight such that vehicles can only pedict shot-tem taffics in font of them, which can also be explained with the wost-case ash equilibium in a non-zeo sum non-coopeative game [9]. To solve the poblem, we poposed two appoaches: 1) vehicle autonomy suppot and ) peception ange extension. Fist, vehicle autonomy intevenes in a bottleneck situation to educe shockwave. In this pape, we show how smoothly the poposed natue-inspied diving stategy passes the bottleneck in a coopeative manne with expeimental esults using multiple unmanned autonomous vehicles (UAVs). Moeove, ou appoach is not too complex to apply to diving stategies of UAVs thanks to the simplicity of the Reynolds ules. Second, we conjectue that taffic flow is inceased by the poposed vehicle aggegation movement laws with the suppot of long ange sensing o wieless communication. We also pove this conjectue expeimentally. The contibutions of this pape can be summaized as follows: This pape suggests an open poblem of how vehicle autonomy contibutes to taffic efficiency, paticulaly in tems of vehicle autonomy. We show that Reynolds thee ules ae applicable to unmanned autonomous automotive vehicle diving in a single lane. Based on the ules fo a single lane, we povide additional equiements and algoithms necessay fo multiple lane scenaios. We show the poposed natue-inspied diving stategy can incease taffic flow with the suppot of vehicle autonomy and wieless communication. We povide expeimental esults and scientific explanations fom eal expeiments using the solutions and 4WD autonomous automotive vehicles. The emainde of this pape examines the poposed natueinspied diving stategy in moe detail. Section II and III deal with diving in single and multiple lanes, espectively. Section IV povides expeimental veification of ou wok. Section V concludes this pape. II. DRIVIG I A SIGLE LAE In this section, a system model fo autonomous diving in a single lane is povided. Based on the model, a decision making pocess is povided fo obtaining the pope contols. A. Reynolds Rules fo Automotive Vehicles Although Reynolds ules ae intended to model bid flocking, the ules ae applicable to automotive vehicles, specifically coesponding to the functionality of ACC 1 and 1 An adaptive cuise contol (ACC) maintains appopiate distance fom a pedecesso vehicle [1], [11]. With the suppot of steeing, the yawate senso, and the ange senso input, ACC ecognizes the immediate pedecesso in the same lane. Accodingly, thottle valve and electic bake input messages ae geneated to sustain a safe distance fom the pedecesso vehicle. ACC deals with only longitudinal vehicle contol. LKS. ot supisingly, if ACC and LKS ae suppoted fo a vehicle, autonomous diving is possible in a single lane. Fo vehicle actuation, thee independent contol inputs ae necessay: bake, thottle valve and steeing wheel. The bake and thottle valve coespond to longitudinal contol. Likewise, the steeing wheel coesponds to lateal contol. ACC and LKS take esponsibility of longitudinal and lateal contols, espectively. Reynolds ules ae decomposed into thee steps: sepaation, alignment, and cohesion. Sepaation coesponds to baking fo maintaining a given safety gap. Alignment coesponds to adjusting the steeing wheel towad the pedecesso vehicle while staying in the cuent lane. Lastly, cohesion coesponds to opening the thottle valve up fo maintaining the safety gap. ACC accommodates sepaation and cohesion, and LKS conducts alignment. ACC and LKS can achieve autonomous diving in a single lane. Consequently, diving in a single lane is explained by Reynolds ules. B. System Model To ealize the autonomous diving, a system fo longitudinal and lateal contols is descibed as follows: 1) Longitudinal Contol: ecessay equations fo longitudinal vehicle contol have been deived fom [14] and some changes have have been made fo ou model. The longitudinal contol is descibed as follows: ν k = ν k 1 + τ a k 1 (1) whee ν k is the vehicle speed at time k, and τ is a unit time, e.g., 1 s. a k denotes the acceleation input at time k, which is detemined by a k = min(a ν, a d ) () whee a ν is the acceleation necessay to achieve the desied speed fom the cuent speed. a ν is descibed as follows: a ν = α (ν max ( 1 e R ) ν ) (3) whee α is a constant-speed eo facto. ν max is the maximum allowable speed and R is the cuvatue adius. a d is the acceleation necessay to adopt to the speed of the pedecesso vehicle. If a pedecesso vehicle exists, the acceleation demand a d is descibed as follows: a d = α a a p + α p (ν p ν) + α d ( s ) (4) whee a p and ν p denote the acceleation and the speed of the taget pedecesso vehicle, espectively; a d =, othewise. is the distance between the ego and the pedecesso vehicle. α a, α p and α d ae constant factos. s is the minimum safe distance fom the taget pedecesso, which is descibed as s = ν ( 1 d p 1 d) A lane keeping system (LKS) ecognizes the cuent lane and then calculates the amount of eos fom the efeence point and angle. The efeence point is typically the cente point of the lane. The efeence angle is typically the tangential angle of the lane. The sensing method of ecognizing the lane is lagely classified into vision-based [1] o LIDARbased appoaches [13]. (5)
l w c.g. s l e 1 s Fig. 1. System model fo lane keeping system, and measuement model. The dash-dot line indicates the desied path. Fig.. R R R e l Cuvatue adius estimation based on foesight sensing data. whee d p and d denote the deceleation capabilities of the ego and the taget vehicle, espectively. ) Lateal Contol: We deive the following equations fo lateal vehicle contol fom [1] with some changes to apply ou scenaio. Figue 1 shows a system model of LKS whose desied path is the cente of the lane. The system dynamics fo UAV lateal contol is descibed as follows: e θ l 1 ẋ = Ax + Bδ + C Ψ des (6) whee x = [e 1, e 1, e, e ]. e 1 is the lateal position eo fom the cente of the desied path. e is the yaw angle diffeence between the cuent heading and the tangential line of the desied path. A, B and C ae descibed as follows: 1 c f +c c f +c c f l f +c l mν m mν A = 1 c f l f +c l c f l f c l c f l f +c l Iν I Iν c f l f c l B = C = mν ν c f m c f l f I e l e w c f l f c l Iν whee c f and c ae font and ea coneing stiffness, espectively. I denotes the yaw moment of inetia and m is a vehicle mass. ν denotes a vehicle velocity. l f and l ae the longitudinal distance fom the cente of gavity to font and ea ties, espectively. δ is the font wheel steeing angle input, and Ψ des is the desied yaw ate, which is defined as follows: Ψ des = ν/r (7) whee R is the cuvatue adius, which can be estimated if moe than thee points ae given on the desied path, as shown in Figue. The points can be povided by foesight sensing data. The cuvatue adius R is fomulated as follows: ( cos 1 R ) ( + cos 1 R ) = π θ (8) l 1 l whee l 1 and l ae the distances between given points on the desied path (see Fig. ). ote that (8) is not a closed-fom. Consequently, contol vaiables ae the steeing angle δ and the longitudinal velocity ν in (6). The longitudinal velocity ν is detemined by the acceleation input a k shown in (1). The contol vaiables at time k ae ewitten in a ecusive fom as follows: (δ k, a k ) = (δ k 1 + δ k, a k 1 + a k ). (9) The poblem is edefined as finding the sequence of optimal contol vecto u k = [ δ k, a k ]. C. Measuement Model The poposed system detects the lane using vision camea. The vision camea deives s l and s shown in Fig. 1, i.e., how distant the ego vehicle is located fom the left and the ight lane, espectively. The measuement vecto at time k is witten as y k = [s, s l ], which is fomulated by [ ] sl = s w / e 1 cos e w / + e 1 cos e l w l w + [ v l k v k ] (1) whee l w is the width of the ego vehicle and w is the lane width. [vk l, v k ]T is the measuement eo vecto. ote that the measuement model (1) is non-linea. D. Decision Making Pocess In (1), the contol vaiable u k is obtained in eal-time by the following fomulation: u k = ag min u k c k y k p + q c u k p, (11) whee c, q c R +, and p is p-nom. In ou wok, p =. The efeence value k is the desied path that is defined as [ w l w k =, ] T w l w. (1) Finally, longitudinal and lateal contol inputs ae obtained on-line by solving (11) and (1). Although this section investigated a single lane scenaio, the lane width w can be unavailable in some scenaios such as patially emoved lane makings, o distubances fom sun-light o shadows. To solve this poblem, we ecoveed emoved lane makings with an intepolation method and mitigated distubances with vision filtes (see Fig. 5.) If we conside beyond a single lane, a special path planning is algoithm necessay to obtain a desied path. Howeve, this is quite complex because of the vaious scenaios such as intesections, junctions, o no lane space. Path planning itself is beyond the scope of this pape. ote that we focus on single lane and multiple lanes in this pape.
III. DRIVIG I MULTIPLE LAES In the pevious section, it was shown that ACC and LKS ae sufficient conditions fo autonomous diving in a single lane. In this section, lane changing 3 issues ae addessed in tems of the equiements and algoithms, which ae necessaily incued fo diving in multiple lanes. A. Lane Changing Poblem In autonomous diving in a single lane, the efeences fo the longitudinal and lateal contol ae definitely always povided, as addessed in Sec. II. On the othe hand, diving in multiple lanes is not staightfowad. Lane changing is decomposed into two pats. Fist, a dive has to constantly make the decision of whethe to keep the cuent lane o change into anothe lane. Second, the dive has to decide how to change lanes if lane changing is decided. 1) Lane Changing Decision Poblem: The majo eason fo lane changing is the expectation of some benefits by moving into anothe lane. In this pape, vehicle velocity is consideed as the benefit. The best stategy is to keep the cuent lane, if a cetain amount of velocity incease is not expected by lane changing, o a cetain amount of velocity decease is not expected by lane keeping. The ealwold examples whee lane changing has to consideed ae typically a low-speed pedecesso vehicle o obstacles in the same lane, and a bottleneck caused by accidents, lane-dop o lane-meging. If thee is no obstacle in font, a vehicle can incease the velocity up to the speed limit. Figue 3 shows the sequence diagam to deal with the above mentioned scenaios. Suppose that no pedecesso vehicle is in font of the ego-vehicle (S1). The vehicle is acceleated up to maximum speed keeping the cuent lane if thee is no lane dop o meging (S). Othewise, the vehicle notifies a lane dop to the successo vehicles typically though wieless communications (S3). The bottleneck notification is intended to mitigate the shockwave incued by the sudden baking of the pedecesso vehicles. Likewise, the vehicle can pedict the taffic flow and lane situation in font if thee is any infomation deliveed fom the pedecesso vehicles (S4). In this case, the ego vehicle can optimize the safety gap based on the infomation. If thee is a pedecesso vehicle, the ego-vehicle checks weathe the adjacent left o ight lane is lane changeable, i.e., no vehicle in the candidate lane (S5). If thee is an empty adjacent lane, the ego-vehicle checks whethe any velocity benefit is expected by moving into the lane (S6). The expected velocity benefit can be fomulated as follows. Let ϕ be a lane that an ego vehicle wants to move to. C denotes the set of vehicles cuently in the lane ϕ. V ( ) is defined as the expected velocity benefit as a esult of lane 3 A lane changing system (LCS) is a lateal contol system along with LKS [15]. A vehicle changes the immediate lane when a speed incease is expected by lane changing. A lane changing maneuve significantly affects taffic congestion. Stat/Iteation S1:Pedecesso? S5:Othe vehicle on new lane? S6:Benefit fom lane change? Lane changing Fig. 3. S:Lane dop? S4:Lane dop fom pedecesso? S3:Lane dop waning to successos ACC/ Lane keeping Lane meging Pocedue of coopeative vehicle contolle. changing by the ego vehicle, which is epesented as follows: V (C, T s, ϕ) = 1 a t (i, ϕ) dt, (13) T s T s i C whee T s ( R + ) is the time duation fo measuing the acceleation incease, and a t (i, ϕ) is the acceleation of vehicle i in a lane ϕ at time t. In summay, V (C, T s, ϕ) is the total velocity incease caused by the ego vehicle s lane changing. Given C and T s, let V (ϕ) = V (C, T s, ϕ). Using this, the changeable lane can be fomulated as follows: ϕ = ag max ϕ l,ϕ c,ϕ {V (ϕ l ), V (ϕ c ) η, V (ϕ )}, (14) whee ϕ l, ϕ c, and ϕ epesent a left, cuent and ight lane, espectively. η is the theshold fo mitigating oscillation, i.e., fequent lane changing. ) Execution of Lane Changing: A lane changing contolle includes a lateal and longitudinal contolle. In this pape, no special lateal contolle is newly poposed. Fo ou expeiments, we used a Fuzzy logic contolle poposed in [16]. The longitudinal contolle has a ole in avoiding collisions between vehicles duing lane changing. Fo vehicle collision avoidance, the lane changing maneuve has to contol its speed to maintain a minimum spatial safety gap and safety level poposed in [17], [18]. We implemented all these consideations fo the eal expeiments. B. Long-tem Pespective Diving One thing not explained in Fig. 3 is the pat about the infomation fom pedecessos. Befoe we popose ou schemes, we will intoduce the concept of shot and long tem pespective diving fist. Let us see (13) fom the view point of T s. T l s and T s s epesent a long-tem and shot-tem pespective, espectively, i.e., T l s > T s s. With T l s and T s s, a lane changing decision can be fomulated as follows. The
4 d 3 d d 1 TABLE I UAV SPECIFICATIO 3 1 4 3 1 Fig. 4. Concept of smooth lane meging; zig-zag fomation. vehicle moves fom the cuent lane ϕ c to ϕ if Length width Wheel Pocesso Main boad Vision camea LIDAR Wieless potocol Steeing Toque Steeing Speed 49 mm 16 mm 94 mm diamete lug patten tie Intel D51MO Intel X5-V SATA (Solid State Disk) MS LifeCam VX-5 (3 fps) 1 Hokuyo URG-4LX-UG1 (font, ea) IEEE 8.11n, iptime 1UA 7. oz-in (5.18 kg-cm). sec/6 V (C, T c s, ϕ) > V (C, T e s, ϕ c ) + ω th, (15) whee ω th is used to avoid oscillation and eflect oppotunity costs. Since T l s > T s s, the vehicle makes a decision fo a long-tem benefit athe than a shot-tem one. The next question is how to make T l s T s s. Peception ange extension, e.g., multi-hop sensing o wieless communications, is one of the majo methods to achieve a lage T l s. In this pape, we conducted expeiments with wieless communications. We will show the esults in the next section. C. Lane Dop and Smooth Meging A bottleneck is known as one of the majo causes of a taffic jam. If the successo vehicles can pedict a lane dop o meging, they can pepae in advance fo the bottleneck point. Aem et al. showed that bottleneck notification though communication could incease taffic flow in the case of a high CACC penetation ate [3]. Howeve, the authos mentioned no specific algoithm fo a lane changing stategy to cope with bottlenecks. Figue 4 shows the poposed lane meging method in the case whee fou vehicles ae in two lanes. Concisely, two cas in the left lane can join the ight lane smoothly without baking like in the bottom of Fig. 4, if d 1, d, d 3 ae positive and v 1 = v = v 3 = v 4. v 1 4 denotes the velocity of the vehicles fom ight to left in Fig. 4, espectively. Fo such smooth meging, vehicles have to know not only the fact that a lane dop will appea but its position as well. One typical solution is to ely on GPS and navigational maps. One of the othe solutions is that a pedecesso vehicle peceiving a coming lane dop delives the lane dop and its position to the successos though wieless communications. The advantage of this method is that it woks even if GPS is unavailable o a navigational map is incoect. Befoe the lane dop notification is given, an individual vehicle maintains a cetain sized safety gap with the pedecesso vehicle in the same lane. ote that the vehicle has to conduct ACC with the pedecesso in the adjacent lane shown in the uppe oad of Fig. 4. We call this as a zigzag fomation. If all vehicles achieve a speed consensus and zig-zag fomation, the vehicle platoon can mege smoothly shown in the bottom of of Fig. 4. We also implemented this smooth lane meging successfully, which is povided in detail in the following section. IV. EXPERIMETAL RESULTS In this section, we investigated the poposed schemes with eal expeiments on ou UAV test platfom. A. UAV Testbed We implemented an unmanned vehicle contolled fully autonomously. Table I shows the specifications of the vehicle. We used two kinds of ange sensos: vision and LIDAR. Fist, the vision senso has the majo esponsibility fo ACC and LKS. Specifically, the vision camea is used fo lane detection and identification of othe vehicles. OpenCV was used as ou basic compute vision-pocessing libay. Based on the OpenCV, we implemented ou own vision algoithms capable of pocessing lane detection, obstacle detection and vehicle identification in eal-time. Based on these postpocessing esults, the distance fom the pedecesso vehicle, i.e., in (4), can be deived by using the pespective of the camea [19]. In paticula, we installed an additional fisheye lens onto the vision camea, which is useful not meely fo lane detection on a cuve but also fo fa-sighted obstacle detection. Figue 5 shows a snapshot of on-line post-pocessing fo cuent and pedecesso vehicle detection in Fig. 5(a), and multiple lane detection in Fig. 5(b). It took, on aveage, 73 ms to post-pocess the vision data. Two LIDARs wee used to maintain the safety gap fom othe vehicles. We conducted the expeiments with thee UAVs shown in Fig. 6. The 8.11n potocol was used fo vehicle-to-vehicle communication. The 8.11p potocol is not commecially available cuently. Based on this platfom, ou poposed schemes wee implemented in a vehicle that mainly consisted of fou systems: ACC, LKS, LCS, and wieless communication equipment. Since coopeation between ACC and wieless communication equipment is lagely ovelapped with CACC, we can also estate ou UAV consisted of CACC, LKS, and LCS, although thee wee some majo diffeences such as the adoption of a ea ange senso fo the zig-zag fomation. Figue 7 depicts the test oad tack consisting of fou onoad scenaios: multiple lanes, lane dop, single lane, and lane split (counte-clockwise fom left), which was installed at the IVIT eseach cente at Seoul ational Univesity. In Fig. 7, the lane dop can also be consideed as lane meging o some accident on the oad.
(a) (b) Fig. 5. On-line post-pocessing esults of (a) cuent lane and vehicle detection, and (b) multiple lanes detection. The geen line depicts the cente of the lane, i.e., the desied path k. Fig. 8. Taffic flow accoding to vehicle speed and safety gap. Fig. 6. B. Evaluation Test-bed fo multiple unmanned autonomous gound vehicles. Fist of all, we expeimentally poved that Reynolds thee laws wee sufficient conditions fo autonomous gound vehicle diving in a single lane. In Sec. II.A, we explained that multiple vehicles embedded with ACC and LKS can achieve fast and smooth diving in a single lane. In the case of a single lane, the lane and pedecesso vehicles always give efeences such as a desied path and minimum safety gap. Theefoe, a single lane can be somewhat staightfowad. Howeve, the case of multiple lanes is much moe complicated. Ou expeiments wee also conducted on multiple lanes with thee UAVs. To evaluate ou woks, we measued taffic flow at the end of a lane dop, i.e., the flag in bottom ight of Fig. 7. Moe specifically, taffic flow was defined as the invese of the aival time gap between the fist and thid vehicles at the flag point in Fig. 7. Hence, the unit of taffic flow is s 1. The aival time was independently measued outside of the UAVs. To mitigate the effect of the initial conditions, thee UAVs stated at the flag and tuned counteclockwise. Then, we measued the aival time afte diving 35 19.5 439 41 19.5 Fig. 7. Test oad tack. The tack consists of fou diffeent scenaios: multiple lane, lane dop, single lane, and lane split. (Unit: cm) the whole tack once. The stating point was the flag point in the bottom ight of Fig. 7. At that point, the vehicles fom a single lane platoon. At a lane split point, the second vehicle changed to the ight lane accoding to S1-S5-S6-Lane changing in Fig. 3. Right befoe the lane dop, the fist and second vehicle ecognized the lane dop and then sent this lane dop detection to the successo vehicle, i.e., the thid vehicle. All vehicles fomed the zig-zag fomation in a distibuted manne. Figue 8 shows the taffic flow accoding to the taget vehicle speed and safety gap that coespond to ν max in (3) and s in (5), espectively. ote that we can see that thee is an optimal contol point to maximize the taffic flow in Fig. 8. Figue 9 shows the taffic flow accoding to the taget speed at the end point of the lane dop. As the aveage speed is inceased, the total taffic flow also inceased. At elatively low speed, i.e., up to.8 m/s, taffic flow inceased oughly linealy. Fom.8 m/s, the second deivative of the taffic flow was negative. The majo eason is that the high speed makes vehicle contol difficult. Each UAV has collision avoidance mechanisms whose pioity is the highest. If an UAV ecognizes the high pobability of collision, the UAV immediately slows down. Theefoe, unde high speed, a fequent shockwave is incued by sudden baking fo vehicle collision avoidance. ote that given the vehicle speed, taffic flow is not inceased accoding to the gowth of the safety gap. Let us investigate the impact of the safety gap. Figue 1 shows the taffic flow fom the pespective of the safety gap. In Fig. 1, thee is an optimal safety gap to maximize the taffic flow. Intuitively, the taffic flow deceased accoding to the gowth of the safety gap fom.6 m to 1. m. Howeve, the taffic flow also deceased in situations with a safety gap that was too small fom.4 m to.6 m. Simila to high speed in Fig. 9, an insufficient safety gap can incu sudden baking fo collision avoidance. Smooth lane meging without shockwave equies a cetain sized safety gap. A maginal safety gap fom the sufficient safety gap, e.g.,.6 m in Fig. 1, contibuted to the decease in taffic density. Fo a given safety gap, the taffic flow did not incease accoding to the gowth of the vehicle speed.
Fig. 9. Taffic flow w..t. taget vehicle speed along with the safety gap. Fig. 1. Taffic flow w..t. safety gap along with the taget vehicle speed. Consequently, the poposed smooth lane meging method minimizes the shockwave at a bottleneck, which can achieve fluid taffic flow. We also discoveed that thee is an optimal consensus fo vehicle speed and the safety gap to maximize the taffic flow at a lane dop point. One could say that the speed of ou UAVs was not fast enough to compae to oad taffic. Howeve, the size of ou vehicle was less than ten times a eal vehicle. Consideing the size of the vehicle, the authos think that the speed was fast enough and the esults ae scalable to oad taffic. In addition, a longe platoon is known to be moe susceptible to the popagation of shockwave. We will futhe investigate the elationship between upsteam shockwave popagation and platoon size theoetically and expeimentally based on this wok. V. COCLUSIO In this pape, we investigated how vehicle autonomy can contibute to taffic flow efficiency. To answe the question, ACC and LKS wee deived fom Reynolds thee laws as minimum equiements fo autonomous single lane diving. To cope with autonomous diving in multiple lanes, we deived LCS as a equied component and poposed algoithms fo multiple vehicles in multiple lanes. In addition, we poposed the concept of smooth lane meging and longtem pespective diving. Long-tem pespective diving is expected to encouage voluntay coopeation on oad. One of the majo methods to povide such long-tem pespective is to let the following vehicles know in-font taffic and oad situations though wieless communications. In this context, the ole of wieless communication was investigated. We veified all these poposal and deduction with UAVs on a test tack including vaious scenaios on the oad. The expeimental esults show the poposed equiements and algoithms woks well in multiple lanes as well as a single lane. 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