Demonstration of a Time-Efficient Mobility System Using a Scaled Smart City
Logan E. Beaver, Behdad Chalaki, AM Ishtiaque Mahbub, Liuhui Zhao, Ray Zayas, Andreas A. Malikopoulos
DDemonstration of a Time-Efficient Mobility System Using a ScaledSmart City
L. E. Beaver, B. Chalaki, A. M. I. Mahbub, L. Zhao, R. Zayas, A. A. Malikopoulos
University of Delaware, Department of Mechanical Engineering, Newark, DE, USA 19716
ARTICLE HISTORY
Compiled November 22, 2019
ABSTRACT
The implementation of connected and automated vehicle (CAV) technologies en-ables a novel computational framework to deliver real-time control actions thatoptimize travel time, energy, and safety. Hardware is an integral part of any practi-cal implementation of CAVs, and as such, it should be incorporated in any val-idation method. However, high costs associated with full scale, field testing ofCAVs have proven to be a significant barrier. In this paper, we present the im-plementation of a decentralized control framework, which was developed previ-ously, in a scaled-city using robotic CAVs, and discuss the implications of CAVson travel time. Supplemental information and videos can be found at https://sites.google.com/view/ud-ids-lab/tfms . KEYWORDS
Connected and automated vehicles; optimal control; emerging mobility systems;smart city; scaled city.
1. Introduction
Connectivity and automation provide the most intriguing opportunity for enablingusers to better monitor transportation network conditions and make better operatingdecisions to reduce energy consumption, greenhouse gas emissions, travel delays, andimprove safety. In the context of a smart city, wireless connectivity provides free-flowof information among entities, while automation provides precise execution upon suchavailable information for moving goods and people safely and efficiently (Fig. 1). Theavailability of vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communi-cation has the potential to ease congestion and improve safety by enabling vehiclesto respond rapidly to changes in their mutual environment. Furthermore, vehicle au-tomation technologies can aim at developing robust vehicle control systems that canquickly respond to dynamic traffic operating conditions.With the advent of emerging information and communication technologies, we arewitnessing a massive increase in the integration of our energy, transportation, andcyber networks. These advances, coupled with human factors, are giving rise to a newlevel of complexity in transportation networks [1]. As we move to increasingly com-plex emerging transportation systems, with changing landscapes enabled by connectiv-ity and automation, future transportation networks could shift dramatically with the
CONTACT A. A. Malikopoulos. Email: [email protected] a r X i v : . [ c s . M A ] N ov igure 1. A city enabled by connectivity and automation technologies. large-scale deployment of connected and automated vehicles (CAVs). On the one hand,with the generation of massive amounts of data from vehicles and infrastructure, thereare opportunities to develop optimization methods to identify and realize a substantialenergy reduction of the transportation network, and to optimize the large-scale sys-tem behavior using the interplay among vehicles. On the other hand, evaluation andvalidation of new control approaches under different traffic scenarios is a necessity toensure successful implementation per vehicle alongside desired system-level outcomes.The overarching goal of this paper is the experimental demonstration of a decentral-ized control framework for CAVs presented in [2] using the University of Delaware’sScaled Smart City (UDSSC). UDSSC is a 1:25 scaled testbed representing an urbanenvironment with robotic CAVs that can replicate real-world traffic scenarios in acontrolled environment (Fig. 2). UDSSC can be used to explore the acquisition andprocessing of V2V and V2I communication. It can also be used to validate control al-gorithms for CAV coordination in specific transportation segments, e.g., intersections,merging roadways, and roundabouts, by mitigating the high costs and safety concernsassociated with real-world field testing of CAVs. As an intermediate scale testbed, theUDSSC is an ideal platform to gain insight into the execution of high-level planningand coordination on physical hardware with noise, disturbances, and communicationdelays. In this paper, our emphasis is on the generation of energy-optimal trajectories,and as such, we do not consider the problem of describing low-level controllers whichtrack the optimal trajectories.The structure of the paper is organized as follows. In Section 2, we discuss relatedwork on the optimal control for CAVs reported in the literature. In Section 3, wereview the decentralized control framework presented in [2] for the coordination ofCAVs in a transportation network. Then, we describe briefly the UDSSC testbed inSection 4, and present simulation and experimental results in Section 5. Finally, wedraw concluding remarks from the experiments in Section 6.2 igure 2.
The University of Delaware’s Scaled Smart City.
2. Related Work
CAVs have attracted considerable attention for the potential of improving mobilityand safety along with energy and emission reduction [3,4]. There have been two ma-jor approaches to utilizing connectivity and automation to improve transportationefficiency and safety, namely, platooning and traffic smoothing.The first approach utilizes connectivity and automation to form closely-coupled ve-hicular platoons to reduce aerodynamic drag effectively, especially at high cruisingspeeds. The concept of forming platoons of vehicles was a popular system-level ap-proach to address traffic congestion, which gained momentum in the 1980s and 1990s[5,6]. Such automated transportation system can alleviate congestion, reduce energyuse and emissions, and improve safety while increasing throughput significantly. TheJapan ITS Energy Project [7], the Safe Road Trains for the Environment program [8],and the California Partner for Advanced Transportation Technology [9] are among themostly-reported efforts in this area.The second approach is to smooth the traffic flow by centralized or decentralized ve-hicle control to reduce spatial and temporal speed variation and braking events, e.g.,automated intersection crossing [10–14], cooperative merging [2,15,16], and speed har-monization through optimal vehicle control [17]. In centralized approaches, there is atleast one task in the system that is globally decided for all vehicles by a single centralcontroller, whereas in decentralized approaches, the vehicles are treated as autonomousagents that collect traffic information to optimize their specific performance criteriawhile satisfying physical constraints. One of the very early efforts in this directionwas proposed by Athans [18] for safe and efficient coordination of merging maneuverswith the intention to avoid congestion. Since then, numerous approaches have beenproposed on coordinating CAVs to improve traffic flow [19–21], and to achieve safe andefficient control of traffic through various traffic bottlenecks where potential vehiclecollisions may happen [22–31]. In terms of energy impact, many studies have shownthat significant fuel consumption savings could be achieved through eco-driving andvehicle optimal control without sacrificing driver safety [2,12,16,32–34]. Consideringnear-future CAV deployment, recent research work has also explored both traffic andenergy implications of partial penetration of CAVs under different transportation sce-3arios, e.g., [35–37]. Several survey papers that report the research efforts in this areacan be found in [38–40].Although previous work has shown promising results emphasizing the potentialbenefits of coordination of CAVs, validation has been primarily in simulation. Someprogress has been made with constructing experimental testbeds, such as MIT’s Duck-ietown [41], which focuses primarily on local perception and autonomy, and the Cam-bridge Minicars [42], which is a testbed for cooperative driving in highway conditions.In contrast, the UDSSC focuses on traffic coordination in an urban system, where amajority of stop-and-go driving occurs. In previous work, we presented the experi-mental validation of the solution to the unconstrained merging roadway problem inUDSSC using 10 robotic CAVs [43]. In this paper, we demonstrate the impact of anoptimal decentralized framework, developed in earlier work [2], for coordinating CAVsin a transportation network with multiple conflict zones where a lateral collision mayoccur.
3. Decentralized Control Framework
We consider a network of CAVs driving in the roadway network in UDSSC, whichconsists of several conflict zones , e.g., ramps, roundabouts, and intersections, wherelateral collisions may occur (marked with red boxes in Fig. 3). For each conflict zone,there is a coordinator that communicates with all CAVs traveling within its com-munication range. In practice, the coordinator can be stationary roadside units forgeneral-purpose traffic monitoring and message dissemination or mobile roadside units(e.g., transit vehicles, drones), which can provide dynamic traffic monitoring and com-munication support at specific locations or along corridors. Each CAV is retrofittedwith a communication device necessary to interact with other vehicles and local in-frastructure within their communication range. Upstream of a conflict zone, we definea control zone in each direction, inside of which, the CAVs coordinate with each otherin order to travel through the conflict zone without any collisions (Fig. 3). The lengthof the control zone can be considered to be the maximum communication range of aV2X device. Outside the control zone, the CAVs behave as human-driven vehicles. Forsimplicity, we do not consider multi-lane trajectories or any lane changes within thecontrol zone. This is the focus of ongoing work [44], and it is not discussed here.
Let z ∈ Z be the index of a conflict zone in the corridor. Let N z ( t ) = { , , ..., N ( t ) } bea queue of CAVs to be analyzed corresponding to the conflict zone z , where N ( t ) ∈ N isthe total number of CAVs at the time t ∈ R + . The dynamics of each vehicle i ∈ N z ( t ),are represented with a state equation˙ x ( t ) = f ( t, x i , u i ) , x i ( t z, i ) = x z, i , (1)where x i ( t ) , u i ( t ) are the state of the vehicle and control input, t z, i is the initial timeof vehicle i ∈ N z ( t ) entering the control zone corresponding to the conflict zone z ,and x z, i is the value of the initial state. For simplicity, we model each vehicle as adouble integrator, i.e., ˙ p i = v i ( t ) and ˙ v i = u i ( t ), where p i ( t ) ∈ P i , v i ( t ) ∈ V i , and u i ( t ) ∈ U i denote the position, speed, and acceleration/deceleration (control input) of4 igure 3. Vehicle routes in the University of Delaware’s Scaled Smart City environment. each vehicle i . Let x i ( t ) = [ p i ( t ) v i ( t )] T denote the state of each vehicle i ∈ N z ( t ), withinitial value x z, i ( t ) = [0 v z, i ( t )] T , taking values in the state space X i = P i × V i . Thesets P i , V i , and U i , i ∈ N ( t ), are complete and totally bounded subsets of R . The statespace X i for each vehicle i is closed with respect to the induced topology on P i × V i and thus, it is compact.To ensure that the control input and vehicle speed are within a given admissiblerange, we impose the constraints u min ≤ u i ( t ) ≤ u max , and (2)0 ≤ v min ≤ v i ( t ) ≤ v max , ∀ t ∈ [ t z, i , t z,fi ] , where u min , u max are the minimum deceleration and maximum acceleration respec-tively, v min , v max are the minimum and maximum speed limits respectively, and t z, i , t z,fi are the times that each vehicle i enters and exits the conflict zone z .To avoid a rear-end collision between two consecutive vehicles traveling in the samelane, the position of the preceding vehicle should be greater than, or equal to the posi-tion of the following vehicle plus a predefined safe distance δ i ( t ), which is proportionalto the speed of vehicle i , v i ( t ). Thus, we impose the rear-end safety constraint s i ( t ) = p k ( t ) − p i ( t ) ≥ δ i ( t ) , ∀ t ∈ [ t z, i , t z,fi ] , (3)where vehicle k is immediately ahead of i on the same lane. The minimum safe distance, δ i ( t ), is a function of speed, namely δ i ( t ) = γ i + h · v i ( t ) , (4)where γ i is the standstill distance and h is the minimum safe time gap that CAV i can5aintain while following another vehicle. Definition 1.
For each CAV i ∈ N z ( t ) approaching a conflict zone z ∈ Z , we definetwo subsets of N z ( t ) depending on the physical location of i inside the control zone:1) L zi ( t ) contains all CAVs traveling in the same road and lane as CAV i , which maycause rear-end collision with CAV i , and 2) C zi ( t ) contains all CAVs traveling on adifferent road from i that can cause a lateral collision inside the conflict zone z . Definition 2.
For each vehicle i ∈ N z ( t ), we define the set Γ zi that consists of thepositions along the lane where a lateral collision is possible in a conflict zone z , namelyΓ zi (cid:44) (cid:110) p i ( t ) | t ∈ [ t z,mi , t z,fi ] (cid:111) , (5)where t z,mi is the time that vehicle i exits the control zone (and enters the conflict zone z ), and t z,fi is the time that vehicle i exits the conflict zone z .Consequently, to avoid a lateral collision for any two vehicles i, j ∈ N z ( t ) on differentroads we impose the following constraintΓ zi ∩ Γ zj = ∅ , j ∈ C zi ( t ), ∀ t ∈ [ t z,mi , t z,fi ] . (6)The above constraint implies that only one vehicle at a time can be inside theconflict zone z when there is a potential for a lateral collision. If the length of theconflict zone is long, then this constraint may dissipate the capacity of the road.However, the constraint is not restrictive in the problem formulation, and it can bemodified appropriately.In the modeling framework described above, we impose the following assumptions: Assumption 1.
For each CAV i , none of the constraints is active at t z, i for conflictzone z . Assumption 2.
Each CAV i can communicate with the coordinator and other CAVsto receive local information without errors or delays.The first assumption ensures that the initial state and control input are feasible.The second assumption might be strong, but it is relatively straightforward to relaxas long as the noise in the measurements and/or delays is bounded. For example,we can determine upper bounds on the state uncertainties as a result of sensing orcommunication errors and delays, and incorporate these into more conservative safetyconstraints. When a CAV i ∈ N z ( t ) enters a control zone, it communicates with a coordinator,assigned to the corresponding conflict zone, and the other CAVs inside the controlzone. Note that the coordinator is not involved in any decision for the CAVs, andit only facilitates the communication of appropriate information among vehicles. Thecoordinator handles the information between the vehicles as follows. When a vehicleenters the control zone of the conflict zone z at time t , the coordinator assigns a uniqueidentity i = N ( t ) + 1, which is an integer representing the location of the vehicle in6 first-in-first-out queue N z ( t ). If any two, or more, vehicles enter the control zone atthe same time, then the coordinator randomly selects their positions in the queue. Definition 3.
For each CAV i ∈ N z ( t ) entering the control zone z , the informationset Y zi ( t ) , is defined as Y zi ( t ) (cid:44) (cid:110) p i ( t ) , v i ( t ) , L zi ( t ) , C zi ( t ) , t z,mi (cid:111) , ∀ t ∈ [ t z, i , t z,mi ] , (7)where p i ( t ) , v i ( t ) are the position and speed of CAV i inside the control zone z , t z, i isthe time when vehicle i enters the control zone for conflict zone z , and t z,mi is the timetargeted for vehicle i to enter the conflict zone z . The set Y zi ( t ) includes all informationthat each vehicle shares.The time t z,mi that the vehicle i will be entering the conflict zone z maximizes thethroughput while considering the maximum and minimum speed limits. Therefore, toensure that (3) and (6) are satisfied at t z,mi , we impose the following conditions whichdepend on the subset that the vehicle i − ∈ N z ( t ) belongs to.If CAV i − ∈ L zi ( t ), t z,mi = max (cid:40) min (cid:110) t z,mi − + δ ( t ) v z , L z v min (cid:111) , L z v i ( t z, i ) , L z v max (cid:41) . (8)If CAV i − ∈ C zi ( t ), t z,mi = max (cid:40) min (cid:110) t z,mi − + S z v z , L z v min (cid:111) , L z v i ( t z, i ) , L z v max (cid:41) , (9)where S z is the length of conflict zone z , L z is the length of control zone for zone z , v z is the constant imposed speed inside the conflict zone z , and v i ( t z, i ) is the initial speedof vehicle i when it enters the control zone at t z, i . The conditions (8) and (9) ensurethat the time t z,mi each vehicle i will be entering the conflict zone is feasible and canbe attained based on the imposed speed limits inside the control zone. In addition, forlow traffic flow where vehicles i − i might be located far away from each other,there is no compelling reason for vehicle i to accelerate within the control zone to havea distance δ ( t ) from vehicle i −
1, if i − ∈ L zi ( t ), or a distance S z if i − ∈ L zi ( t ), atthe time t z,mi that vehicle i enters the conflict zone z . Therefore, in such cases, vehicle i can keep cruising within the control zone with the initial speed v i ( t z, i ) that enteredthe control zone at t z, i . The recursion is initialized when the first vehicle enters the control zone z , i.e., it isassigned i = 1. In this case, t z,m can be externally assigned as the desired exit time ofthis vehicle whose behavior is unconstrained. Thus, the time t z,m is fixed and availablethrough Y ( t ). The second vehicle will access Y z ( t ) from vehicle 1 to compute the time t z,m . The third vehicle will access Y z ( t ) from vehicle 2, and the communication processwill continue with the same fashion until vehicle N ( t ) in the queue accesses Y zN ( t ) − ( t ).7 .3. Optimal Control Problem Formulation By controlling the entry time of the vehicles, the speed of queue build-up at eachconflict zone decreases. Thus, the congestion recovery time is also reduced – the lat-ter results in maximizing the throughput in the conflict zone. We now consider theproblem of deriving the optimal control input (acceleration/deceleration) of each CAVinside each control zone separately under hard safety constraints to avoid collisions.Moreover, by optimizing the acceleration/deceleration of each vehicle, we minimizetransient operation. This will have direct benefits in energy consumption since thevehicles are optimized to travel over steady state operating points (constant torqueand speed) [45].Since the coordinator for a conflict zone z is not involved in any decision on thevehicle coordination, we formulate the following optimization problem for each vehiclein the queue upstream of conflict zone z , the solution of which can be implemented inreal-time min u i (cid:90) t z,mi t z, i u i ( t ) dt, z ∈ Z , (10)Subject to : (1) , (2) , p i ( t z, i ) = p z, i , v i ( t z, i ) = v z, i , p i ( t z,mi ) = p z , and given t z, i , t z,mi , where p z is the location (i.e., entry position) of the conflict zone z , t z,mi is the time thatthe vehicle i enters the conflict zone, and p z, i , v z, i are the initial position and speedof vehicle i ∈ N z ( t ) when it enters the control zone of conflict zone z . By minimizingthe L norm of acceleration we minimize transient engine operation which results inan overall improvement in energy efficiency.For the analytical solution and real-time implementation of the control problem (10),we apply Hamiltonian analysis. The analytical solution of (10) without consideringstate and control constraints was presented in earlier work [15,16] for coordinatingCAVs in real-time at highway on-ramps. When the state and control constraints arenot active, the optimal control input (acceleration/deceleration) as a function of timeis given by u ∗ i ( t ) = a i t + b i , t z, i ≤ t ≤ t z,mi , (11)and the optimal speed and position for each vehicle are v ∗ i ( t ) = 12 a i t + b i t + c i , t z, i ≤ t ≤ t z,mi , (12) p ∗ i ( t ) = 16 a i t + 12 b i t + c i t + d i , t z, i ≤ t ≤ t z,mi , (13)where a i , b i , c i and d i are constants of integration that can be computed by usingthe initial and final conditions. Similar results to (11)-(13) can be obtained when thestate and control constraints become active within the control zone. In this case, theconstrained and unconstrained arcs need to be pieced together to satisfy the Euler-Lagrange equations and the necessary conditions of optimality. The different casesof the state and control constraint activation along with the corresponding solution8an be found in [12], whereas the complete analytical solution that includes the rear-end safety constraint is reported in [46]. In the present work, we do not consider anyconstrained optimization cases as none of the constraints in (2) become active withinthe optimal control path during the simulation, as shown in Section 5.
4. Simulation and Experimental Environment
To implement the control framework presented in the previous section, and to gen-erate the input information required for UDSSC, we first use the microscopic multi-modal simulation platform PTV VISSIM. We create a simulation setup replicating theUDSSC map and define a network consisting of four different looped routes and fivebottlenecks (one intersection, one roundabout, and three merging scenarios), as shownin Fig. 3. In order to maintain compatibility with the UDSSC experiment, we designeach of the routes to hold a finite number of vehicles (19 vehicles in total) traveling inloops for finite simulation run-time. Among the 19 vehicles, we consider 9 vehicles asthe target (ego-vehicles) to evaluate their performance metrics in different scenarios.We use the rest of the vehicles to increase the traffic volume in the urban networkand create congestion in the baseline scenario. The vehicles maintain a low desiredspeed of 7 m/s for their uncontrolled urban commute throughout the network. There-fore, the desired speed at all exits of the control zones is set to be equal to the urbanspeed. We select the maximum and minimum allowable speed of 8.33 m/s and 2 m/s,respectively. The maximum and minimum acceleration of the vehicles was taken as 3m/s and -3 m/s , respectively. To evaluate the effectiveness of the proposed optimalvehicle dynamics control, we consider two different cases: a. Baseline Scenario: We construct the baseline scenario by considering all vehiclesas human-driven and without any V2V communication capability. The vehicles sub-scribe to the Wiedemann car following model. The Wiedemann car following model isa psycho-physical model to emulate the driving behavior of real human-driven vehi-cles. The model was first presented in 1974 by Wiedemann [47] and has been adoptedby the software PTV-VISSIM as one of its in-built car following models. The completedetail of this elaborate model can be found in the literature [47]. We do not change theVISSIM default parameters of the Wiedemann model to study their impact on vehiclebehavior and traffic flow, as such exposition falls outside the scope of this paper. Webuild a fixed time signalized intersection for the four-way traffic at the center. Thefixed time signalized intersection in the simulation provides Signal Phase and Tim-ing (SPaT) messages to the leading vehicle internally through VISSIM. Based on theSPaT information, the leading vehicle stops at the desired position by adopting theWiedemann car following model. We adopt priority-based (yield/stop) movement forthe other four waypoints consisting of the roundabout and merging scenarios, wherethe secondary-road vehicles yield to the main-road vehicles. In both cases, VISSIMuses the approaching point parameter of Wiedemann car following model to detectany approaching obstacles and apply necessary braking to slow down or stop. b. Optimal Controlled Scenario:
In the optimal scenario, all 19 vehicles follow ouroptimal control framework. The vehicles are connected with each other inside thecontrol zone through V2V communication capability and are automated within thecontrol zone. Therefore, they can plan their optimal path inside the control zone,avoiding any lateral or rear-end collisions while optimizing their own travel time and9uel efficiency. In this scenario, we do not consider the fixed-time signal and movementpriorities considered in the baseline case. We consider five isolated coordinators witha control zone of 45 m for each conflict zone (see Fig. 3). For the uncontrolled pathsin-between the control zones, the vehicles adopt the Wiedemann car following model[47] to traverse their respective routes.
UDSSC is a 1:25 scaled testbed spanning over 400 square feet (see Fig. 2) and is capableof accommodating scaled robotic CAVs. It is equipped with a VICON motion capturesystem that uses eight cameras to track the position of each vehicle with sub-millimeteraccuracy. Each road in the UDSSC is built up from arc or line segments. In order totrack the desired vector position of each CAV, all road segments are parameterizedin terms of their total length. This formulation allows each vehicle to calculate itsdesired position in UDSSC based only on the scalar distance along its current path,which is achieved by numerically integrating the speed profile in real-time on boththe mainframe computer and each CAV. This decoupling of speed and position allowssignificant flexibility in UDSSC, especially in dynamic-routing scenarios.
The CAVs of UDSSC (see Fig. 4) have been designed using off the shelf electricalcomponents and 3D printed parts created at the University of Delaware. The primarymicrocontroller on the CAV is a Raspberry Pi 3B running Ubuntu Mate and ROSKinetic. An Arduino Nano is used as a slave processor for the Pi to do low-levelmotor control and ad-hoc analog to digital conversion for the state of charge (SOC)measurements. The CAV’s rear-wheel drive train is powered by a Pololu 75 . r = 1 . . Coordination of the CAVs within the UDSSC is achieved using a multi-level controlframework spanning a central mainframe computer (Processor: Intel Core i7-6950XCPU @ 3 .
00 GHz x 20, Memory: 125 . igure 4. A picture of the connected and automated vehicle’s electronics (left) and outer shell with VICONmarkers, ultrasonic sensors, and camera visible (right). of the experiment, each CAV sets its temporal baseline from which it measures alllater times; this avoids the problem of synchronizing CAV clocks, as all information iscalculated relative to the experiment start time. During the experiment, the mainframepasses a message to each CAV containing its current position and two seconds oftrajectory data using the UDP/IP protocol at 50 Hz. The CAV receives trajectoryinformation from the mainframe and uses a modified Stanley [48] controller to handlelane tracking, while a feedforward-feedback [49] PID controller tracks the desired speedprofile.Medium and low-level control is accomplished onboard each CAV in a purely dis-tributed manner. Using information from the mainframe, each CAV updates at 50 Hzto calculate a lateral, heading, and distance error. The lateral and heading errors arethen passed to the Stanley controller to calculate an output steering angle. Meanwhile,the position error and desired speed are used in a feedforward-feedback controller tocalculate the desired motor speed. The desired speed and steering angle are then passedto the Arduino Nano, which runs a low-level PID controller to precisely control thegearmotor and steering servo.
In order to replicate the simulation results in the UDSSC, speed profiles for the 9ego vehicles are exported from VISSIM to the mainframe. The path information andspeed profile are dispersed to each CAV for the duration of the experiment. Then, theCAVs at UDSSC numerically integrate the speed profile data in real-time to calculatetheir desired position, allowing them to track the desired speed and position in adecentralized manner. Simultaneously, the mainframe computer integrates the speedprofile in order to send current and future path information to the CAVs.11 . Results
The speed profiles of the CAVs, making multiple passes through each loop of theUDSSC map, for the baseline and optimal control scenario are shown in Fig. 5a - 5d.The baseline speed profiles show significant stop-and-go driving behavior. The effectof congestion in these cases can induce artificial congestion or phantom traffic jams outside the corridor, as can be seen in Fig. 5d between 60 and 120 s.Compared to the baseline speed profiles, we note that the optimal controller hascompletely eliminated stop-and-go driving, and the optimal quadratic profile speed isrealized within the control zones. The congestion observed in the baseline scenario inFig. 5d has also been mitigated, rendering an overall smooth traffic flow throughoutthe network.Note that the speed profiles are kept within the maximum and minimum limit insidethe control zone as described in Section 4.1. Therefore, none of the state and controlconstraints of (2) became active in the unconstrained arc, and our relaxation of (2)holds. However, we see a few cases of constraint violation of the acceleration profileoutside the control zone in Fig. 5a - 5d, where the Wiedemann car-following model[47] is applied instead of the optimal control. Note that optimal control is applied onlyinside the designated control zones.
To validate the effectiveness and efficiency of our optimal control observed in thesimulation, we compare the travel time of 9 CAVs between the baseline and optimalscenarios. The travel time is calculated as the time taken for each vehicle to completea single loop by sampling the raw VICON data over the 80 s experiment. In particular,returning to the initial position was defined as the first time the vehicle came within 10cm of its initial position after a 5 s initial window. These values are presented in Table 1and Fig. 6 alongside the route each CAV took (as annotated in Fig. 3); a value of greaterthan 80 s corresponds to a vehicle not fully completing its loop during the experiment,which occurred 3 times in the baseline scenario. Videos of the experiment can be foundat the supplemental site, https://sites.google.com/view/ud-ids-lab/tfms . Table 1.
Travel time for each vehicle to complete a single loop.
Vehicle Baseline time [s] Optimal time [s] Loop Time saved [s] % Decrease8 >
80 54 .
10 North > . >
80 48 .
00 North > . .
25 45 .
55 East 20 .
70 31.214 65 .
95 49 .
90 East 16 .
05 24.34 57 .
80 53 .
25 South 4 .
55 7.913 60 .
30 59 .
75 South 0 .
55 0.92 46 .
61 37 .
40 West 9 .
21 19.85 43 .
90 44 .
20 West − .
30 -0.717 >
80 41 .
50 West > . .
35 s (25%) over the baselinetravel time was observed in the UDSSC. The marginal improvement was in the South-12
Optimal Range Optimal Avg. (a) North Loop
Optimal Range Optimal Avg. (b) East Loop
Optimal Range Optimal Avg. (c) South Loop
Optimal Range Optimal Avg. (d) West Loop
Figure 5.
Instantaneous maximum, minimum, and average speed of each vehicle by route. Each data set istaken from the first 160s of simulation. ern loop, where the traffic was effectively free-flowing in the baseline scenario. In theloops with conflict zones, i.e., north, east, and west, the impact of the coordinator andoptimal control is clear and significant.The speed profiles of CAVs 2 , ,
17, and 13 are shown in Fig. 7. These profileswere taken by numerically deriving the VICON position data taken at 100 Hz to getvelocity components. Then, any speeds above 0 . .
45 s.We conclude from the above results that 1) almost the entire reduction in transittime can be attributed to optimal control in the conflict zones, and 2) the optimalcontrol framework almost entirely eliminates stop-and-go driving.13 igure 6.
Histogram for the arrival time of each vehicle in Table 1 with 6 bins per experiment.
6. Conclusion
In this paper, we presented an experimental demonstration of a decentralized optimalcontrol framework for CAVs, presented in [2]. We used a 1:25 scaled testbed repre-senting an urban environment with robotic CAVs that can replicate real-world trafficscenarios in a controlled environment. We showed that the optimal control frame-work could contribute a 25% reduction in travel time compared to a baseline scenarioconsisting of human-driven vehicles without connectivity. We should note that underheavy congested traffic conditions, the control framework might not be as effective asit is under light to medium traffic conditions in improving traffic flow without tuningsome control parameters (e.g., minimum time gap, length of the control zone, etc.)[50]. In recent work [51], the effectiveness of the proposed optimal control frameworkhas been investigated under different traffic conditions to confirm its robustness.Ongoing research includes the formulation of an upper-level optimization problem,the solution of which yields, for each CAV, the optimal entry time and lane changesrequired to cross the intersection [44] and explores the associated tradeoffs betweenthroughput and energy consumption of each vehicle.An important direction for future research is to consider different penetrations ofCAVs, which can significantly alter the efficiency of the entire system. For example,an important question that needs to be addressed is, “what is the minimum numberof CAVs in order to realize potential benefits?” Future work should also considerthe robustness of the control framework and its applicability under various trafficconditions. The impact of communication errors and delays on safety and optimalityare also areas of future research. 14 igure 7.
Speed vs time profiles for vehicles (clockwise from top left) 2 (west), 14 (east), 17 (west), 13(south.).
Acknowledgement(s)
The authors would like to acknowledge Michael Lashner, Kunzheng Li, Haley Lloyd,Thomas Patterson, and the rest of the UDSSC Senior Design team for their effort indesigning, building, and testing the newest generation of CAVs used in this paper. Theauthors would also like to thank Ioannis Vasileios Chremos for his valuable commentsand feedback on the manuscript.
Funding
This research was supported in part by ARPAEs NEXTCAR program under the awardnumber DE- AR0000796 and by the Delaware Energy Institute (DEI). This supportis gratefully acknowledged.
References [1] Malikopoulos AA. A duality framework for stochastic optimal control of complex systems.IEEE Transactions on Automatic Control. 2016;61(10):2756–2765.[2] Zhao L, Malikopoulos AA. Decentralized optimal control of connected and automatedvehicles in a corridor. In: 2018 21st International Conference on Intelligent TransportationSystems (ITSC); IEEE; 2018. p. 1252–1257.[3] Spieser K, Treleaven K, Zhang R, et al. Toward a systematic approach to the design nd evaluation of automated mobility-on-demand systems: A case study in singapore. In:Road vehicle automation. Springer; 2014. p. 229–245.[4] Fagnant DJ, Kockelman KM. The travel and environmental implications of shared au-tonomous vehicles, using agent-based model scenarios. Transportation Research Part C:Emerging Technologies. 2014;40:1–13.[5] Shladover SE, Desoer CA, Hedrick JK, et al. Automated vehicle control developments inthe PATH program. IEEE Transactions on Vehicular Technology. 1991;40(1):114–130.[6] Rajamani R, Tan HS, Law BK, et al. Demonstration of integrated longitudinal and lateralcontrol for the operation of automated vehicles in platoons. IEEE Transactions on ControlSystems Technology. 2000;8(4):695–708.[7] Tsugawa S. An overview on an automated truck platoon within the energy its project.IFAC Proceedings Volumes. 2013;46(21):41–46.[8] D´avila A, Nombela M. Sartre: Safe road trains for the environment. In: Conference onPersonal Rapid Transit PRT@ LHR; Vol. 3; 2010. p. 2–3.[9] Shladover SE. PATH at 20–History and major milestones. IEEE Transactions on intelli-gent transportation systems. 2007;8(4):584–592.[10] Lee J, Park B. Development and Evaluation of a Cooperative Vehicle Intersection ControlAlgorithm Under the Connected Vehicles Environment. IEEE Transactions on IntelligentTransportation Systems. 2012;13(1):81–90.[11] Rakha H, Kamalanathsharma RK. Eco-driving at signalized intersections using V2I com-munication. In: Intelligent Transportation Systems (ITSC), 2011 14th International IEEEConference on; IEEE; 2011. p. 341–346.[12] Malikopoulos AA, Cassandras CG, Zhang YJ. A decentralized energy-optimal controlframework for connected automated vehicles at signal-free intersections. Automatica.2018;93:244 – 256.[13] Mahbub AMI, Zhao L, Assanis D, et al. Energy-Optimal Coordination of Connected andAutomated Vehicles at Multiple Intersections. In: Proceedings of 2019 American ControlConference; 2019. p. 2664–2669.[14] Chalaki B, Malikopoulos AA. An optimal coordination framework for connected andautomated vehicles in two interconnected intersections. In: Proceedings of 2019 IEEEConference on Control Technology and Applications, 2019; 2019. p. 888–893.[15] Rios-Torres J, Malikopoulos AA. Automated and Cooperative Vehicle Merging atHighway On-Ramps. IEEE Transactions on Intelligent Transportation Systems. 2017;18(4):780–789.[16] Ntousakis IA, Nikolos IK, Papageorgiou M. Optimal vehicle trajectory planning in thecontext of cooperative merging on highways. Transportation Research Part C: EmergingTechnologies. 2016;71:464–488.[17] Malikopoulos AA, Hong S, Park B, et al. Optimal control for speed harmonization ofautomated vehicles. IEEE Transactions on Intelligent Transportation Systems. 2018;.[18] Athans M. A unified approach to the vehicle-merging problem. Transportation Research.1969;3(1):123–133.[19] Kachroo P, Li Z. Vehicle merging control design for an automated highway system. In:Proceedings of Conference on Intelligent Transportation Systems; 1997. p. 224–229.[20] Antoniotti M, Deshpande A, Girault A. Microsimulation analysis of automated vehicleson multiple merge junction highways. In: IEEE International Conference in Systems, Man,and Cybernetics; 1997. p. 839–844.[21] Ran B, Leight S, Chang B. A microscopic simulation model for merging control on adedicated-lane automated highway system. Transportation Research Part C: EmergingTechnologies. 1999;7(6):369–388.[22] Dresner K, Stone P. Multiagent traffic management: a reservation-based intersectioncontrol mechanism. In: Proceedings of the Third International Joint Conference on Au-tonomous Agents and Multiagents Systems; 2004. p. 530–537.[23] Dresner K, Stone P. A multiagent approach to autonomous intersection management.Journal of artificial intelligence research. 2008;31:591–656.
24] de La Fortelle A. Analysis of reservation algorithms for cooperative planning at inter-sections. In: 13th International IEEE Conference on Intelligent Transportation Systems;2010. p. 445–449.[25] Huang S, Sadek A, Zhao Y. Assessing the Mobility and Environmental Benefits ofReservation-Based Intelligent Intersections Using an Integrated Simulator. IEEE Trans-actions on Intelligent Transportation Systems. 2012;13(3):1201–1214.[26] Zohdy IH, Kamalanathsharma RK, Rakha H. Intersection management for autonomousvehicles using iCACC; 2012. p. 1109–1114.[27] Yan F, Dridi M, El Moudni A. Autonomous vehicle sequencing algorithm at isolated inter-sections. 2009 12th International IEEE Conference on Intelligent Transportation Systems.2009;:1–6.[28] Li L, Wang FY. Cooperative Driving at Blind Crossings Using Intervehicle Communica-tion. IEEE Transactions in Vehicular Technology. 2006;55(6):1712,1724.[29] Zhu F, Ukkusuri SV. A linear programming formulation for autonomous intersectioncontrol within a dynamic traffic assignment and connected vehicle environment. Trans-portation Research Part C: Emerging Technologies. 2015;55.[30] Wu J, Perronnet F, Abbas-Turki A. Cooperative vehicle-actuator system: a sequence-based framework of cooperative intersections management. Intelligent Transport Systems,IET. 2014;8(4):352–360.[31] Kim KD, Kumar P. An MPC-Based Approach to Provable System-Wide Safety andLiveness of Autonomous Ground Traffic. IEEE Transactions on Automatic Control. 2014;59(12):3341–3356.[32] Barth M, Boriboonsomsin K. Energy and emissions impacts of a freeway-based dynamiceco-driving system. Transportation Research Part D: Transport and Environment. 2009;14(6):400–410.[33] Berry IM. The effects of driving style and vehicle performance on the real-world fuel con-sumption of us light-duty vehicles [dissertation]. Massachusetts Institute of Technology;2010.[34] Wu C, Zhao G, Ou B. A fuel economy optimization system with applications in vehicleswith human drivers and autonomous vehicles. Transportation Research Part D: Transportand Environment. 2011;16(7):515–524.[35] Zhao L, Malikopoulos AA, Rios-Torres J. Optimal control of connected and automatedvehicles at roundabouts: An investigation in a mixed-traffic environment. In: 15th IFACSymposium on Control in Transportation Systems; 2018. p. 73–78.[36] Rios-Torres J, Malikopoulos AA. Impact of partial penetrations of connected and auto-mated vehicles on fuel consumption and traffic flow. IEEE Transactions on IntelligentVehicles. 2018;3(4):453–462.[37] Zhong Z, Joyoung L, Zhao L. Evaluations of Managed Lane Strategies for Arterial De-ployment of Cooperative Adaptive Cruise Control . In: TRB Annual Meeting; WashingtonDC, USA; 2017.[38] Rios-Torres J, Malikopoulos AA. A Survey on Coordination of Connected and AutomatedVehicles at Intersections and Merging at Highway On-Ramps. IEEE Transactions onIntelligent Transportation Systems. 2017;18(5):1066–1077.[39] Guanetti J, Kim Y, Borrelli F. Control of connected and automated vehicles: State of theart and future challenges. Annual Reviews in Control. 2018;45:18–40.[40] Wang Y, Li X, Yao H. Review of trajectory optimisation for connected automated vehicles.IET Intelligent Transport Systems. 2018;13:580–586.[41] Paull L, Tani J, Ahn H, et al. Duckietown: An open, inexpensive and flexible platform forautonomy education and research. In: Proceedings of the IEEE International Conferenceon Robotics and Automation; 2017. p. 1497–1504.[42] Hyaldmar N, He Y, Porok A. A fleet of miniature cars for experiments in cooperative driv-ing. In: Proceedings of the IEEE International Conference on Robotics and Automation;2019.[43] Stager A, Bhan L, Malikopoulos A, et al. A Scaled Smart City for Experimental Validation f Connected and Automated Vehicles. IFAC-PapersOnLine. 2018;51(9):130–135.[44] Malikopoulos AA, Zhao L. Optimal path planning for connected and automated vehiclesat urban intersections. In: Proceedings of the 58th IEEE Conference on Decision andControl; 2019 (to appear).[45] Malikopoulos AA, Assanis DN, Papalambros PY. Optimal engine calibration for individ-ual driving styles. In: SAE Proceedings, Technical Paper 2008-01-1367; 2008.[46] Malikopoulos AA, Zhao L. A closed-form analytical solution for optimal coordination ofconnected and automated vehicles. In: Proceedings of 2019 American Control Conference;2019. p. 3599–3604.[47] Wiedemann R. Simulation des strassenverkehrsflusses [dissertation]. Universit¨at Karl-sruhe; 1974.[48] Thrun S, Montemerlo M, Dahlkamp H, et al. Stanley: The robot that won the DARPAGrand Challenge. Springer Tracts in Advanced Robotics. 2007;.[49] Spong MW, Hutchinson S, Vidyasagar M. Robot Dynamics and Control Second Edition;2004.[50] Zhao L, Malikopoulos AA, Rios-Torres J. On the traffic impacts of optimally controlledconnected and automated vehicles. In: Proceedings of 2019 IEEE Conference on ControlTechnology and Applications; 2019. p. 882–887.[51] Zhao L, Mahbub AMI, Malikopoulos A. Optimal vehicle dynamics and powertrain controlfor connected and automated vehicle. In: Proceedings of IEEE Conference on ControlTechnology and Applications; 2019. p. 33–38.f Connected and Automated Vehicles. IFAC-PapersOnLine. 2018;51(9):130–135.[44] Malikopoulos AA, Zhao L. Optimal path planning for connected and automated vehiclesat urban intersections. In: Proceedings of the 58th IEEE Conference on Decision andControl; 2019 (to appear).[45] Malikopoulos AA, Assanis DN, Papalambros PY. Optimal engine calibration for individ-ual driving styles. In: SAE Proceedings, Technical Paper 2008-01-1367; 2008.[46] Malikopoulos AA, Zhao L. A closed-form analytical solution for optimal coordination ofconnected and automated vehicles. In: Proceedings of 2019 American Control Conference;2019. p. 3599–3604.[47] Wiedemann R. Simulation des strassenverkehrsflusses [dissertation]. Universit¨at Karl-sruhe; 1974.[48] Thrun S, Montemerlo M, Dahlkamp H, et al. Stanley: The robot that won the DARPAGrand Challenge. Springer Tracts in Advanced Robotics. 2007;.[49] Spong MW, Hutchinson S, Vidyasagar M. Robot Dynamics and Control Second Edition;2004.[50] Zhao L, Malikopoulos AA, Rios-Torres J. On the traffic impacts of optimally controlledconnected and automated vehicles. In: Proceedings of 2019 IEEE Conference on ControlTechnology and Applications; 2019. p. 882–887.[51] Zhao L, Mahbub AMI, Malikopoulos A. Optimal vehicle dynamics and powertrain controlfor connected and automated vehicle. In: Proceedings of IEEE Conference on ControlTechnology and Applications; 2019. p. 33–38.