Multiple Vehicle Driving Control for Traffic Flow Efficiency Seong-Woo Kim, Gi-Poong Gwon, Seung-Tak Choi, Seung-Nam Kang, Myoung-Ok Shin, In-Sub Yoo, Eun-Dong Lee, and Seung-Woo Seo

Abstract— The dynamics of multi-agent in nature have been largely studied for a long time to investigate how the aggregation of agents can move smoothly in complex environments without collision. The main insights can be summarized such that the aggregated dynamics of animals and particles can be explained by an individual’s simple rules. In a similar vein, we conjecture that such simple rules for vehicle maneuvering can accommodate the fluid flow of traffic and reduce car accidents in highway and urban areas. In this paper, we first show the Reynolds’ three rules are applicable to autonomous driving on a single lane. Moreover, we provide additional requirements and algorithms for multiple lanes. Based on these results, we show that the proposed nature-inspired driving maneuver can increase traffic flow by 1) mitigating shockwave at bottlenecks and 2) extending the perception range for better path planning, which requires the support of the vehicle autonomy and wireless communication, respectively. Finally, we prove the feasibility of our work with experiments using multiple UAVs.

I. I NTRODUCTION Modern transportation systems are faced with technical challenges such as traffic flow efficiency, safety enhancement and environmental conservation. To tackle these challenges, the proposed approaches are classified into two parts: a top-down approach and a bottom-up approach. In the topdown approach, a central system provides real-time traffic information to drivers, which is expected to dissipate traffic jam and guide the traffic flow rationally. In the bottom-up approach, vehicle autonomy intervenes in the driving of the vehicle, that is, a vehicle is controlled electronically. The top-down approach has contributed mainly to traffic flow efficiency. In contrast, the bottom-up approach has been used for immediate vehicle safety. As automotive electronics are beginning to be widely used, there have been several research efforts to increase traffic flow efficiency through vehicle autonomy such as platooning [1] and cooperative adaptive cruise control (CACC) [2]. In platooning, each vehicle is autonomously controlled to adopt the velocity of its predecessor by electronic braking system, electronic throttle control, and range sensors. With the support of long range sensors or wireless communication, the intermediate gap between successive vehicles in the same lane can be minimized without collision. Therefore, S. Kim is with the Singapore-MIT Alliance for Research and Technology, Massachusetts Institute of Technology, [email protected] Other authors are with the Department of Electrical Engineering and Computer Science, Seoul National University, {gpgwon, stchoi, snkang, moshin, isyoo, edlee}@cnslab.snu.ac.kr, and [email protected]. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2012-0000913) and partially Institute of New Media and Communication.

the reduced gap by platooning increases the traffic density. Each vehicle can sustain the velocity consensus such as a speed limit, which results in an increase of traffic flow [3]. CACC is one of the specific implementations of platooning. However, the existing platooning is restricted to single lane cases. In general, transportation systems include multiple lanes that have different characteristics and scenarios such as lane drop, lane split, or lane merging. For these lane changing related issues, multiple lanes are much more difficult to deal with analytically and experimentally. The approaches proposed for lane changing issues, in the literature, are too complex to be used in practice. Moreover, a human does not drive in such a complex manner. Instead, a driver abstracts the driving strategy with simple rules, e.g., keeping a safe distance to the predecessor vehicle, braking for collision avoidance, and lane changing for velocity increase. In this context, there have been many studies that have attempted to explain the aggregate dynamics of multiple agents using simple rules for quite some time [4]–[6]. In particular, animal aggregations have been known to move fast and smoothly in a distributed manner based on a number of simple rules. Reynolds introduced three fundamental laws, separation, alignment, and cohesion, for computer animation of bird flocking in his celebrated paper [7]. The distinct point of Reynolds’ work is that the proposed rules define an individual behavior with no assumption of a centralized coordination. The underlying insight of Reynolds’ work is that an independent individual behavior can achieve a common group goal by simple laws. From the perspective of an individual autonomous agent, the movement for animal aggregation is similar to traffic flow in transportation systems. The difference is whether there is free space or a lane system. These observations motivated us to apply animal aggregation dynamics to vehicle driving in order to increase the traffic flow efficiency in the multiple lane transportation systems. In this paper, we first show that Reynolds’ three rules are applicable to vehicle driving in a single lane. Since Reynolds developed his model for birds in air space, multiple lanes were not considered in his model. Therefore, we provide additional requirements and algorithms necessary for driving in multiple lanes. The next fundamental question is whether these proposed nature-inspired driving approaches can achieve any benefit in terms of traffic flow. A bottleneck, caused by several reasons such as accident, lane drop, or lane merging, has been known to be one of the major causes of traffic jams. The bottleneck causes braking-to-stop that creates a shockwave [8]. In contrast, the aggregations in

nature smoothly go through bottlenecks in a cooperative manner. However, it is difficult to expect such cooperation on the road since a driver has a short line of sight such that vehicles can only predict short-term traffics in front of them, which can also be explained with the worst-case Nash equilibrium in a non-zero sum non-cooperative game [9]. To solve the problem, we proposed two approaches: 1) vehicle autonomy support and 2) perception range extension. First, vehicle autonomy intervenes in a bottleneck situation to reduce shockwave. In this paper, we show how smoothly the proposed nature-inspired driving strategy passes the bottleneck in a cooperative manner with experimental results using multiple unmanned autonomous vehicles (UAVs). Moreover, our approach is not too complex to apply to driving strategies of UAVs thanks to the simplicity of the Reynolds’ rules. Second, we conjecture that traffic flow is increased by the proposed vehicle aggregation movement laws with the support of long range sensing or wireless communication. We also prove this conjecture experimentally. The contributions of this paper can be summarized as follows: • This paper suggests an open problem of how vehicle autonomy contributes to traffic efficiency, particularly in terms of vehicle autonomy. • We show that Reynolds’ three rules are applicable to unmanned autonomous automotive vehicle driving in a single lane. • Based on the rules for a single lane, we provide additional requirements and algorithms necessary for multiple lane scenarios. • We show the proposed nature-inspired driving strategy can increase traffic flow with the support of vehicle autonomy and wireless communication. • We provide experimental results and scientific explanations from real experiments using the solutions and 4WD autonomous automotive vehicles. The remainder of this paper examines the proposed natureinspired driving strategy in more detail. Section II and III deal with driving in single and multiple lanes, respectively. Section IV provides experimental verification of our work. Section V concludes this paper. II. D RIVING IN A S INGLE L ANE In this section, a system model for autonomous driving in a single lane is provided. Based on the model, a decision making process is provided for obtaining the proper controls.

LKS2 . Not surprisingly, if ACC and LKS are supported for a vehicle, autonomous driving is possible in a single lane. For vehicle actuation, three independent control inputs are necessary: brake, throttle valve and steering wheel. The brake and throttle valve correspond to longitudinal control. Likewise, the steering wheel corresponds to lateral control. ACC and LKS take responsibility of longitudinal and lateral controls, respectively. Reynolds’ rules are decomposed into three steps: separation, alignment, and cohesion. Separation corresponds to braking for maintaining a given safety gap. Alignment corresponds to adjusting the steering wheel toward the predecessor vehicle while staying in the current lane. Lastly, cohesion corresponds to opening the throttle valve up for maintaining the safety gap. ACC accommodates separation and cohesion, and LKS conducts alignment. ACC and LKS can achieve autonomous driving in a single lane. Consequently, driving in a single lane is explained by Reynolds’ rules. B. System Model To realize the autonomous driving, a system for longitudinal and lateral controls is described as follows: 1) Longitudinal Control: Necessary equations for longitudinal vehicle control have been derived from [14] and some changes have have been made for our model. The longitudinal control is described as follows: νk = νk−1 + τ · ak−1

(1)

where νk is the vehicle speed at time k, and τ is a unit time, e.g., 1 s. ak denotes the acceleration input at time k, which is determined by ak = min(aν , ad )

(2)

where aν is the acceleration necessary to achieve the desired speed from the current speed. aν is described as follows: ( ( ) ) aν = α · νmax 1 − e−R − ν (3) where α is a constant-speed error factor. νmax is the maximum allowable speed and R is the curvature radius. ad is the acceleration necessary to adopt to the speed of the predecessor vehicle. If a predecessor vehicle exists, the acceleration demand ad is described as follows: ad = αa · ap + αp · (νp − ν) + αd · (r − rs )

(4)

Although Reynolds’ rules are intended to model bird flocking, the rules are applicable to automotive vehicles, specifically corresponding to the functionality of ACC1 and

where ap and νp denote the acceleration and the speed of the target predecessor vehicle, respectively; ad = ∞, otherwise. r is the distance between the ego and the predecessor vehicle. αa , αp and αd are constant factors. rs is the minimum safe distance from the target predecessor, which is described as 1) ν2 ( 1 − (5) rs = 2 dp d

1 An adaptive cruise control (ACC) maintains appropriate distance from a predecessor vehicle [10], [11]. With the support of steering, the yawrate sensor, and the range sensor input, ACC recognizes the immediate predecessor in the same lane. Accordingly, throttle valve and electric brake input messages are generated to sustain a safe distance from the predecessor vehicle. ACC deals with only longitudinal vehicle control.

2 A lane keeping system (LKS) recognizes the current lane and then calculates the amount of errors from the reference point and angle. The reference point is typically the center point of the lane. The reference angle is typically the tangential angle of the lane. The sensing method of recognizing the lane is largely classified into vision-based [12] or LIDARbased approaches [13].

A. Reynolds’ Rules for Automotive Vehicles

e2

sl

foresight sensing data. The curvature radius R is formulated as follows: ( 2R ) ( 2R ) + cos−1 =π−θ (8) cos−1 l1 l2

el

c.g.

e2

e1

lw

rw er

sr

Fig. 1. System model for lane keeping system, and measurement model. The dash-dot line indicates the desired path.

where l1 and l2 are the distances between given points on the desired path (see Fig. 2). Note that (8) is not a closed-form. Consequently, control variables are the steering angle δ and the longitudinal velocity ν in (6). The longitudinal velocity ν is determined by the acceleration input ak shown in (1). The control variables at time k are rewritten in a recursive form as follows: (δk , ak ) = (δk−1 + ∆δk , ak−1 + ∆ak ).

l

R

2

θ

The problem is redefined as finding the sequence of optimal control vector ∆uk = [∆δk , ∆ak ].

R l 1 R

Fig. 2.

C. Measurement Model

Curvature radius estimation based on foresight sensing data.

where dp and d denote the deceleration capabilities of the ego and the target vehicle, respectively. 2) Lateral Control: We derive the following equations for lateral vehicle control from [1] with some changes to apply our scenario. Figure 1 shows a system model of LKS whose desired path is the center of the lane. The system dynamics for UAV lateral control is described as follows: ˙ des x˙ = Ax + Bδ + C Ψ

(6)

where x = [e1 , e˙1 , e2 , e˙2 ]. e1 is the lateral position error from the center of the desired path. e2 is the yaw angle difference between the current heading and the tangential line of the desired path. A, B and C are described as follows:   0 1 0 0 cf +cr −cf lf +cr lr  c +c  0 − fmν r   m mν A= 0  0 0 1   2 2 −cf lf +cr lr −cf lf +cr lr cf lf −cr lr 0 Iν I Iν     0 0  cf lf −cr lr − ν   cf    mν m  B= C =    0  0   2 2 −cf lf −cr lr Iν

cf lf I

where cf and cr are front and rear cornering stiffness, respectively. I denotes the yaw moment of inertia and m is a vehicle mass. ν denotes a vehicle velocity. lf and lr are the longitudinal distance from the center of gravity to front and rear tires, respectively. ˙ des is the δ is the front wheel steering angle input, and Ψ desired yaw rate, which is defined as follows: ˙ des = ν/R Ψ

(9)

(7)

where R is the curvature radius, which can be estimated if more than three points are given on the desired path, as shown in Figure 2. The points can be provided by

The proposed system detects the lane using vision camera. The vision camera derives sl and sr shown in Fig. 1, i.e., how distant the ego vehicle is located from the left and the right lane, respectively. The measurement vector at time k is written as yk = [sr , sl ], which is formulated by   rw /2 − e1 lw [ ] [ l ] − sl vk  e2 2  =  r cos (10) + lw  sr vkr w /2 + e1 − cos e2 2 where lw is the width of the ego vehicle and rw is the lane width. [vkl , vkr ]T is the measurement error vector. Note that the measurement model (10) is non-linear. D. Decision Making Process In (10), the control variable ∆uk is obtained in real-time by the following formulation: ∆u∗k = arg min rc ∥rk − yk ∥p + qc ∥∆uk ∥p , ∆uk

(11)

where rc , qc ∈ R+ , and ∥ · ∥p is p-norm. In our work, p = 2. The reference value rk is the desired path that is defined as [ ]T rw − lw rw − lw rk = , . (12) 2 2 Finally, longitudinal and lateral control inputs are obtained on-line by solving (11) and (12). Although this section investigated a single lane scenario, the lane width rw can be unavailable in some scenarios such as partially removed lane markings, or disturbances from sun-light or shadows. To solve this problem, we recovered removed lane markings with an interpolation method and mitigated disturbances with vision filters (see Fig. 5.) If we consider beyond a single lane, a special path planning is algorithm necessary to obtain a desired path. However, this is quite complex because of the various scenarios such as intersections, junctions, or no lane space. Path planning itself is beyond the scope of this paper. Note that we focus on single lane and multiple lanes in this paper.

III. D RIVING IN M ULTIPLE L ANES In the previous section, it was shown that ACC and LKS are sufficient conditions for autonomous driving in a single lane. In this section, lane changing3 issues are addressed in terms of the requirements and algorithms, which are necessarily incurred for driving in multiple lanes. A. Lane Changing Problem In autonomous driving in a single lane, the references for the longitudinal and lateral control are definitely always provided, as addressed in Sec. II. On the other hand, driving in multiple lanes is not straightforward. Lane changing is decomposed into two parts. First, a driver has to constantly make the decision of whether to keep the current lane or change into another lane. Second, the driver has to decide how to change lanes if lane changing is decided. 1) Lane Changing Decision Problem: The major reason for lane changing is the expectation of some benefits by moving into another lane. In this paper, vehicle velocity is considered as the benefit. The best strategy is to keep the current lane, if a certain amount of velocity increase is not expected by lane changing, or a certain amount of velocity decrease is not expected by lane keeping. The realworld examples where lane changing has to considered are typically a low-speed predecessor vehicle or obstacles in the same lane, and a bottleneck caused by accidents, lane-drop or lane-merging. If there is no obstacle in front, a vehicle can increase the velocity up to the speed limit. Figure 3 shows the sequence diagram to deal with the above mentioned scenarios. Suppose that no predecessor vehicle is in front of the ego-vehicle (S1). The vehicle is accelerated up to maximum speed keeping the current lane if there is no lane drop or merging (S2). Otherwise, the vehicle notifies a lane drop to the successor vehicles typically through wireless communications (S3). The bottleneck notification is intended to mitigate the shockwave incurred by the sudden braking of the predecessor vehicles. Likewise, the vehicle can predict the traffic flow and lane situation in front if there is any information delivered from the predecessor vehicles (S4). In this case, the ego vehicle can optimize the safety gap based on the information. If there is a predecessor vehicle, the ego-vehicle checks weather the adjacent left or right lane is lane changeable, i.e., no vehicle in the candidate lane (S5). If there is an empty adjacent lane, the ego-vehicle checks whether any velocity benefit is expected by moving into the lane (S6). The expected velocity benefit can be formulated as follows. Let ϕ be a lane that an ego vehicle wants to move to. C denotes the set of vehicles currently in the lane ϕ. V (·) is defined as the expected velocity benefit as a result of lane 3 A lane changing system (LCS) is a lateral control system along with LKS [15]. A vehicle changes the immediate lane when a speed increase is expected by lane changing. A lane changing maneuver significantly affects traffic congestion.

Start/Iteration

N

S1:Predecessor?

N

S2:Lane drop?

ACC/ Lane keeping

Y Y S3:Lane drop warning to successors

Y

S5:Other vehicle on new lane? N

N

S6:Benefit from lane change? Y

S4:Lane drop from predecessor?

Y

Lane merging

N

Lane changing

Fig. 3.

Procedure of cooperative vehicle controller.

changing by the ego vehicle, which is represented as follows: ∫ 1 ∑ V (C, Ts , ϕ) = at (i, ϕ) dt, (13) |Ts | Ts i∈C

where Ts (∈ R ) is the time duration for measuring the acceleration increase, and at (i, ϕ) is the acceleration of vehicle i in a lane ϕ at time t. In summary, V (C, Ts , ϕ) is the total velocity increase caused by the ego vehicle’s lane changing. Given C and Ts , let V (ϕ) = V (C, Ts , ϕ). Using this, the changeable lane can be formulated as follows: +

ϕ = arg max {V (ϕl ), V (ϕc ) − η, V (ϕr )} , ϕl ,ϕc ,ϕr

(14)

where ϕl , ϕc , and ϕr represent a left, current and right lane, respectively. η is the threshold for mitigating oscillation, i.e., frequent lane changing. 2) Execution of Lane Changing: A lane changing controller includes a lateral and longitudinal controller. In this paper, no special lateral controller is newly proposed. For our experiments, we used a Fuzzy logic controller proposed in [16]. The longitudinal controller has a role in avoiding collisions between vehicles during lane changing. For vehicle collision avoidance, the lane changing maneuver has to control its speed to maintain a minimum spatial safety gap and safety level proposed in [17], [18]. We implemented all these considerations for the real experiments. B. Long-term Perspective Driving One thing not explained in Fig. 3 is the part about the information from predecessors. Before we propose our schemes, we will introduce the concept of short and long term perspective driving first. Let us see (13) from the view point of Ts . Tsl and Tss represent a long-term and short-term perspective, respectively, i.e., Tsl > Tss . With Tsl and Tss , a lane changing decision can be formulated as follows. The

d3

4

d2

2

3

4

TABLE I

d1

UAV S PECIFICATION 1

2 3

Fig. 4.

1

Concept of smooth lane merging; zig-zag formation.

Length × width

492 mm × 216 mm

Wheel

94 mm diameter lug pattern tire

Processor

Intel D510MO

Main board

Intel X25-V SATA (Solid State Disk)

Vision camera

MS LifeCam VX-5000 (30 fps)×1

LIDAR

Hokuyo URG-04LX-UG01×2 (front, rear)

Wireless protocol

IEEE 802.11n, ipTIME N100UA

Steering Torque

72.0 oz-in (5.18 kg-cm)

Steering Speed

0.22 sec/60◦

vehicle moves from the current lane ϕc to ϕ if V (C, Tsc , ϕ) > V (C, Tse , ϕc ) + ∆ωth ,

(15)

where ∆ωth is used to avoid oscillation and reflect opportunity costs. Since Tsl > Tss , the vehicle makes a decision for a long-term benefit rather than a short-term one. The next question is how to make Tsl ≫ Tss . Perception range extension, e.g., multi-hop sensing or wireless communications, is one of the major methods to achieve a large Tsl . In this paper, we conducted experiments with wireless communications. We will show the results in the next section. C. Lane Drop and Smooth Merging A bottleneck is known as one of the major causes of a traffic jam. If the successor vehicles can predict a lane drop or merging, they can prepare in advance for the bottleneck point. Arem et al. showed that bottleneck notification through communication could increase traffic flow in the case of a high CACC penetration rate [3]. However, the authors mentioned no specific algorithm for a lane changing strategy to cope with bottlenecks. Figure 4 shows the proposed lane merging method in the case where four vehicles are in two lanes. Concisely, two cars in the left lane can join the right lane smoothly without braking like in the bottom of Fig. 4, if d1 , d2 , d3 are positive and v1 = v2 = v3 = v4 . v1···4 denotes the velocity of the vehicles from right to left in Fig. 4, respectively. For such smooth merging, vehicles have to know not only the fact that a lane drop will appear but its position as well. One typical solution is to rely on GPS and navigational maps. One of the other solutions is that a predecessor vehicle perceiving a coming lane drop delivers the lane drop and its position to the successors through wireless communications. The advantage of this method is that it works even if GPS is unavailable or a navigational map is incorrect. Before the lane drop notification is given, an individual vehicle maintains a certain sized safety gap with the predecessor vehicle in the same lane. Note that the vehicle has to conduct ACC with the predecessor in the adjacent lane shown in the upper road of Fig. 4. We call this as a zigzag formation. If all vehicles achieve a speed consensus and zig-zag formation, the vehicle platoon can merge smoothly shown in the bottom of of Fig. 4. We also implemented this smooth lane merging successfully, which is provided in detail in the following section.

IV. E XPERIMENTAL R ESULTS In this section, we investigated the proposed schemes with real experiments on our UAV test platform. A. UAV Testbed We implemented an unmanned vehicle controlled fully autonomously. Table I shows the specifications of the vehicle. We used two kinds of range sensors: vision and LIDAR. First, the vision sensor has the major responsibility for ACC and LKS. Specifically, the vision camera is used for lane detection and identification of other vehicles. OpenCV was used as our basic computer vision-processing library. Based on the OpenCV, we implemented our own vision algorithms capable of processing lane detection, obstacle detection and vehicle identification in real-time. Based on these postprocessing results, the distance from the predecessor vehicle, i.e., r in (4), can be derived by using the perspective of the camera [19]. In particular, we installed an additional fisheye lens onto the vision camera, which is useful not merely for lane detection on a curve but also for far-sighted obstacle detection. Figure 5 shows a snapshot of on-line post-processing for current and predecessor vehicle detection in Fig. 5(a), and multiple lane detection in Fig. 5(b). It took, on average, 73 ms to post-process the vision data. Two LIDARs were used to maintain the safety gap from other vehicles. We conducted the experiments with three UAVs shown in Fig. 6. The 802.11n protocol was used for vehicle-to-vehicle communication. The 802.11p protocol is not commercially available currently. Based on this platform, our proposed schemes were implemented in a vehicle that mainly consisted of four systems: ACC, LKS, LCS, and wireless communication equipment. Since cooperation between ACC and wireless communication equipment is largely overlapped with CACC, we can also restate our UAV consisted of CACC, LKS, and LCS, although there were some major differences such as the adoption of a rear range sensor for the zig-zag formation. Figure 7 depicts the test road track consisting of four onroad scenarios: multiple lanes, lane drop, single lane, and lane split (counter-clockwise from left), which was installed at the IVIT research center at Seoul National University. In Fig. 7, the lane drop can also be considered as lane merging or some accident on the road.

(a)

(b)

Fig. 5. On-line post-processing results of (a) current lane and vehicle detection, and (b) multiple lanes detection. The green line depicts the center of the lane, i.e., the desired path rk .

Fig. 8.

Fig. 6.

Test-bed for multiple unmanned autonomous ground vehicles.

B. Evaluation First of all, we experimentally proved that Reynolds’ three laws were sufficient conditions for autonomous ground vehicle driving in a single lane. In Sec. II.A, we explained that multiple vehicles embedded with ACC and LKS can achieve fast and smooth driving in a single lane. In the case of a single lane, the lane and predecessor vehicles always give references such as a desired path and minimum safety gap. Therefore, a single lane can be somewhat straightforward. However, the case of multiple lanes is much more complicated. Our experiments were also conducted on multiple lanes with three UAVs. To evaluate our works, we measured traffic flow at the end of a lane drop, i.e., the flag in bottom right of Fig. 7. More specifically, traffic flow was defined as the inverse of the arrival time gap between the first and third vehicles at the flag point in Fig. 7. Hence, the unit of traffic flow is s−1 . The arrival time was independently measured outside of the UAVs. To mitigate the effect of the initial conditions, three UAVs started at the flag and turned counterclockwise. Then, we measured the arrival time after driving 410

35

219.5

219.5 439

Fig. 7. Test road track. The track consists of four different scenarios: multiple lane, lane drop, single lane, and lane split. (Unit: cm)

Traffic flow according to vehicle speed and safety gap.

the whole track once. The starting point was the flag point in the bottom right of Fig. 7. At that point, the vehicles form a single lane platoon. At a lane split point, the second vehicle changed to the right lane according to S1-S5-S6-Lane changing in Fig. 3. Right before the lane drop, the first and second vehicle recognized the lane drop and then sent this lane drop detection to the successor vehicle, i.e., the third vehicle. All vehicles formed the zig-zag formation in a distributed manner. Figure 8 shows the traffic flow according to the target vehicle speed and safety gap that correspond to νmax in (3) and rs in (5), respectively. Note that we can see that there is an optimal control point to maximize the traffic flow in Fig. 8. Figure 9 shows the traffic flow according to the target speed at the end point of the lane drop. As the average speed is increased, the total traffic flow also increased. At relatively low speed, i.e., up to 0.8 m/s, traffic flow increased roughly linearly. From 0.8 m/s, the second derivative of the traffic flow was negative. The major reason is that the high speed makes vehicle control difficult. Each UAV has collision avoidance mechanisms whose priority is the highest. If an UAV recognizes the high probability of collision, the UAV immediately slows down. Therefore, under high speed, a frequent shockwave is incurred by sudden braking for vehicle collision avoidance. Note that given the vehicle speed, traffic flow is not increased according to the growth of the safety gap. Let us investigate the impact of the safety gap. Figure 10 shows the traffic flow from the perspective of the safety gap. In Fig. 10, there is an optimal safety gap to maximize the traffic flow. Intuitively, the traffic flow decreased according to the growth of the safety gap from 0.6 m to 1.0 m. However, the traffic flow also decreased in situations with a safety gap that was too small from 0.4 m to 0.6 m. Similar to high speed in Fig. 9, an insufficient safety gap can incur sudden braking for collision avoidance. Smooth lane merging without shockwave requires a certain sized safety gap. A marginal safety gap from the sufficient safety gap, e.g., 0.6 m in Fig. 10, contributed to the decrease in traffic density. For a given safety gap, the traffic flow did not increase according to the growth of the vehicle speed.

Fig. 9.

Traffic flow w.r.t. target vehicle speed along with the safety gap.

Consequently, the proposed smooth lane merging method minimizes the shockwave at a bottleneck, which can achieve fluid traffic flow. We also discovered that there is an optimal consensus for vehicle speed and the safety gap to maximize the traffic flow at a lane drop point. One could say that the speed of our UAVs was not fast enough to compare to road traffic. However, the size of our vehicle was less than ten times a real vehicle. Considering the size of the vehicle, the authors think that the speed was fast enough and the results are scalable to road traffic. In addition, a longer platoon is known to be more susceptible to the propagation of shockwave. We will further investigate the relationship between upstream shockwave propagation and platoon size theoretically and experimentally based on this work. V. C ONCLUSION In this paper, we investigated how vehicle autonomy can contribute to traffic flow efficiency. To answer the question, ACC and LKS were derived from Reynolds’ three laws as minimum requirements for autonomous single lane driving. To cope with autonomous driving in multiple lanes, we derived LCS as a required component and proposed algorithms for multiple vehicles in multiple lanes. In addition, we proposed the concept of smooth lane merging and longterm perspective driving. Long-term perspective driving is expected to encourage voluntary cooperation on road. One of the major methods to provide such long-term perspective is to let the following vehicles know in-front traffic and road situations through wireless communications. In this context, the role of wireless communication was investigated. We verified all these proposal and deduction with UAVs on a test track including various scenarios on the road. The experimental results show the proposed requirements and algorithms works well in multiple lanes as well as a single lane. In particular, the proposed smooth lane changing explicitly contributes to traffic flow increase by shockwave mitigation due to an optimal safety gap and velocity consensus. R EFERENCES [1] R. Rajamani, H.-S. Tan, B. K. Law, and W.-B. Zhang, “Demonstration of integrated longitudinal and lateral control for the operation of automated vehicles in platoons,” IEEE Transactions on Control Systems Technology, vol. 8, pp. 695–708, July 2000.

Fig. 10.

Traffic flow w.r.t. safety gap along with the target vehicle speed.

[2] D. de Bruin, J. Kroon, R. van Klaveren, and M. Nelisse, “Design and test of a cooperative adaptive cruise control system,” in IEEE Intelligent Vehicles Symposium, June 2004. [3] B. van Arem, C. J. G. van Driel, and R. Visser, “The impact of cooperative adaptive cruise control on traffic-flow characteristics,” IEEE Transactions on Intelligent Transportation Systems, vol. 7, no. 4, pp. 429–436, Dec. 2006. [4] D. J. T. Sumpter, “The principles of collective animal behaviour,” Philosophical transactions of the royal society, biological sciences, vol. 361, pp. 5–22, 2006. [5] J. K. Parrish and L. Edelstein-Keshet, “Complexity, pattern, and evolutionary trade-offs in animal aggregation,” Sceince, vol. 284, pp. 99–101, April 1999. [6] L. Conradt and T. J. Roper, “Group decision-making in animals,” Nature, vol. 421, pp. 155–158, January 2003. [7] C. Reynolds, “Flocks, herds, and schools: A distributed behavioral model,” Computer Graphics, vol. 21, no. 4, July 1987. [8] Y. Sugiyama, M. Fukui, M. Kikuchi, K. Hasebe, A. Nakayama, K. Nishinari, S. Tadaki, and S. Yukawa, “Traffic jams without bottlenecks - experimental evidence for the physical mechanism of the formation of a jam,” New Journal of Physics, vol. 10, 2008. [9] J. Nash, “Non-cooperative games,” Annals of Mathematics, vol. 54, no. 2, pp. 286–295, 1951. [10] G. Marsden, M. McDonald, and M. Brackstone, “Towards an understanding of adaptive cruise control,” Transportation Research Part C: Emerging Technologies, vol. 9, pp. 33–51, Feb. 2001. [11] P. Ioannou, “Guest editorial adaptive cruise control systems special issue,” IEEE Transactions on Intelligent Transportation Systems, vol. 4, pp. 113–114, Sep. 2003. [12] J. McCall and M. Trivedi, “Video-based lane estimation and tracking for driver assistance: survey, system, and evaluation,” IEEE Transactions on Intelligent Transportation Systems, vol. 7, pp. 20–37, March 2006. [13] T. Ogawa and K. Takagi, “Lane recognition using on-vehicle lidar,” in IEEE Intelligent Vehicles Symposium, June 2006, pp. 540–545. [14] J. VanderWerf, S. Shladover, N. Kourjanskaia, M. Miller, and H. Krishnan, “Modeling effects of driver control assistance systems on traffic,” Journal Transportation Research Record: Journal of the Transportation Research Board, vol. 1748, pp. 167–174, 2001. [15] J. A. Laval and C. F. Daganzo, “Lane-changing in traffic streams,” Transportation Research Part B, vol. 40, pp. 251–264, March 2006. [16] J. Naranjo, C. Gonzalez, R. Garcia, and T. de Pedro, “Lane-change fuzzy control in autonomous vehicles for the overtaking maneuver,” IEEE Transactions on Intelligent Transportation Systems, vol. 9, pp. 438–450, Sep. 2008. [17] L. Jin, W. Fang, Y. Zhang, S. Yang, and H. Hou, “Research on safety lane change model of driver assistant system on highway,” in IEEE Intelligent Vehicles Symposium, June 2009, pp. 1051–1056. [18] M. Roelfsen, J. Bie, L. Jin, and B. van Arem, “Assessment of safety levels and an innovative design for the lane change assistant,” in IEEE Intelligent Vehicles Symposium, June 2010, pp. 83–88. [19] G. Stein, O. Mano, and A. Shashua, “Vision-based acc with a single camera: bounds on range and range rate accuracy,” in IEEE Intelligent Vehicles Symposium, June 2003, pp. 120 – 125.