Abstract

Truck platooning closely regulates gaps between heavy-duty freight trucks to exploit slipstream effects for reducing aerodynamic friction—and therefore reducing engine effort and fuel usage. Currently deployed applications of this have been classically actuated through error-correcting PID feedback loops with connectivity amongst trucks in a fleet to form a connected and adaptive cruise control law that attenuates disturbances between trucks to maintain tolerable gaps. Typically, performance of such systems is challenged by difficult, albeit not uncommon, transients when under traffic conditions and when under road grade variations. Because of this, such platooning control requires attentive and trained drivers to disengage the adaptive cruise control—which limits its potentials for reducing driver load. More advanced longitudinal motion planning under predictive optimal control can push for higher levels of autonomy under a larger range of scenarios, as well as improve fuel efficiency. Here, model predictive control for fuel-performant truck platooning is vetted in both simulation and experimentation for representative traffic and road grade routes. Several approaches are used exploiting physics-based models with and without the powertrain system, and neural network-encoded models. The fuel benefits of aerodynamic platooning are isolated from the more general eco-driving approach, which already provides fuel benefit to trucks by smartly selecting truck velocity. Results from simulation and validation in experimentation are presented—showing up to 6% benefit in fuel economy through eco-driving and an additional 3% achievable through platooning. Observed losses in fuel performance are explained by energy dissipation from braking.

1 Introduction

Efficient mobility in transportation is well enabled through automation, in which driver-assistive or driverless technologies have the potential for more optimal and robust decision making as compared to their manually driven counterparts. Whereas manual drivers can be limited in their ability to precisely command the motion of a vehicle, automation instead offers tight control that allows for motion planning and actuation aimed at optimizing particular performance categories such as fuel economy, energy economy, timeliness, comfort, and safety. Automation in particular also has the ability to consume more information about the surrounding environment to probabilistically reason about their future strategies—sourced from multiple on-board sensor measurements or connected information available from infrastructure or other vehicles. The connected exchange of information from surrounding automated vehicles ultimately reduces uncertainty in their imminent motion by broadcasting current and potentially future plans, leading to more cooperative driving strategies which enable harmony and boosted performance of transportation [1].

Fig. 1
Cooperative truck convoy in a leader–follower platoon configuration while undergoing traffic cycle performance tests at the TRC high-speed proving grounds
Fig. 1
Cooperative truck convoy in a leader–follower platoon configuration while undergoing traffic cycle performance tests at the TRC high-speed proving grounds
Close modal

Heavy-duty long-haul truck transportation has received much attention in automated longitudinal control to achieve performant driving [2]. Automation offers potent strategies when managing a convoy of long-haul trucks, whereby automation can ease the burden of long trips on trained manual drivers, and has soon-realizable potentials for reducing costs in various economic facets like more efficient usage of fuel for reduced expenses, eco-planning of the trip for predictable travel times, and end-to-end driverless trips [3]. Cooperative and adaptive cruise control (CACC) has been the classical and most common choice, typically actuated with an adaptive cruise controller with additional connected exchange of acceleration information of other trucks as a feedforward term [4,5]. Advanced planning strategies can choose to form a platoon between trucks in the convoy when under appropriate highway conditions, so that drafting effects are exploited to reduce aerodynamic drag losses and thereby improve fuel economy [6]. Platooning is demonstrated in Fig. 1. PID-based CACC has been shown to be a suitable choice of control for heavy trucks in a platooning configuration when under low-intensity disturbances, such as Ref. [7] that nominally show an 8% reduction in fuel expense when platooning trucks under test-track conditions, and more recently validated in Ref. [8] for heterogeneous trucks. However, classical CACC is of insufficient performance in all typical conditions that can arise over the course of a trip: whereas real-world highway conditions were experimented and reported on in Ref. [9] for a platooned convoy of heavy-duty trucks, which found that all fuel benefits of having platooned were negated due to poor control during uphill climbs. Furthermore, the classical CACC demonstrated poor harmonization between trucks and was susceptible to disengagements that require operator intervention. With demonstrably weak performance in certain scenarios, classical CACC ultimately requires driver attentiveness and will scale poorly as automation strategies become more commonly deployed. Recently, commercial autonomous solutions for single-truck control have been found to improve fuel economy over their human-driven counterparts by up to 20% in low-speed driving and 3% in highway speed driving [10,11].

Notably, some of these strategies neglect road grade perturbations for simplicity in experimental evaluation, and in general, there are not yet well-adopted control strategies that compensate against heavy road grade in line-haul truck convoys [8,12], though some optimally guided trucks have explicitly considered road grade disturbances in planning. In the motion planning of automated trucks for improved fuel economy, He et al. [13] analytically derive fuel-optimal trajectories to guide a heavy truck through a nominal traffic disturbance and road profile, whereas in Ref. [14], a numerical fuel-optimal strategy was implemented to assess heavy truck performance on real roads with varied altitude, and Turri et al. [15] use a hierarchal control strategy that centrally plans the velocities of each truck in the convoy through dynamic programming. Engine and transmission considerations have been recently considered in Ref. [16] to improve kinetic energy usage through optimal selection of transmission modes and engine torque. Finally, Liu et al. [17] directly model fuel consumption through a pedal-to-engine framework and optimize the motion of platooned heavy trucks in a nonlinear fashion.

More advanced control strategies exist as an opportunity to improve the independence of automated vehicles and boost overall performance in a wider variety of scenarios [18]. Look-ahead predictive control algorithms can pose a multi-stage optimization problem to select a sequence of actions to predict and better mitigate the effects of system dynamics, actuator limitations, and any disturbances that are assumed to act on the system. Such formulations allow for a system designer to impose an objective function as an explicit performance criteria for a motion planning control to meet. Improved vehicle energetics are shown in Ref. [19] by calculating coasting distances from a preceding vehicle to cut unnecessary braking, improved fuel economy in Ref. [20] to account for powertrain dynamics, and in Ref. [15] to additionally exploit drafting effects for reduced aerodynamic drag in heavy trucks. Cooperative control can additionally be introduced through look-ahead preview by sharing planned intentions of distributed and connected agents [21]. Efficient string stabilization of a system of autonomous vehicles conditioned on communications between nearest neighboring agents are shown in Ref. [22], and improved safety via coordinated braking of platooned agents is shown in Ref. [23]. Importantly, Dunbar and Caveney [24] evaluate string stability of platoons under receding horizon control and give bounds on the feasible platoon sizes, and Ard et al. [25] consider communication delay and model uncertainty effects in stable platoon performance. Cooperative motion planning has been simulated on in Ref. [26] and then verified through experimentation in Ref. [27] for a large-scale mixed-traffic scenario, nominally showing up to 30% benefit in fuel economy for passenger vehicles due to harmonizing effects and shockwave suppression.

Frameworks of motion planning naturally marry with long-term routing optimizations. The formation of truck platoons are coordinated in Ref. [28] by pairing trucks with similar route destinations, the intelligent decision of when to form or re-form platoons in the event of platoon dissipation is shown in Ref. [29], and the evaluation of the large-scale fuel and emissions performance of a transportation network is shown in Ref. [30] when enabling truck platooning. Motion planning strategies also enable disturbance compensation not easily realizable with manual drivers: prediction of upcoming traffic shockwaves is leveraged in Ref. [31] to throttle down velocity ahead of time to avoid unnecessary propulsion and braking—estimating up to 20% reduction in fuel cost of heavy trucks.

When forming a look-ahead optimal control problem (OCP), a control horizon of N stages is used to directly form and evaluate a control sequence against a possibly uncertain dynamic model and constraints. In this, for computational reasons and due to uncertainty in reasoning about the future, terminal components can be designed to truncate the end of the control horizon via an estimated cost-to-go for stages N + 1 → ∞, or via constraining terminal sets the states must lie within [32]. These components are critical in performance and stability of the strategy and can be utilized to enable intelligent behavior of a controller such as in Refs. [15,19] which encourage coasting over wasteful braking in automated cruise control. Recently, an active area of research involves learning the terminal components via prior experience and exploration of a feedback control policy [33]. These learning methods can additionally be fused with more traditional adaptive methods for online identification of a model, constraints, and their uncertainties. These include methods such as learning terminal safe sets and a cost-to-go by repeated trials [34], learning a model through data-driven approaches and then exploiting through a look-ahead control [35], and identification and compensation against disturbances [36,37]. As another aspect of learning, model approximators, such as neural networks (NNs), can be fused into a look-ahead predictive control approach, such as Ref. [38] which learn a recursive stochastic process and uncertainty bounds for a then formal tube-based robust treatment using a model predictive control (MPC). Such stochastic control methods are more thoroughly reviewed in Refs. [33,39] and could be further explored for truck platooning in the future.

2 Motivating Control Problem and Contributions

Recently available highway test data exposed problematic control performance from a classical CACC for platooning operation of two homogeneous line-haul trucks deployed under real-world conditions [9]. In this, a gain-scheduled PID compensator was used to engage autonomous longitudinal operation of the trailing truck while maintaining safety through strict gap tracking and velocity harmonization via designer requirements such as responsive rise time, settling time, etc. Whereas the compensator successfully attenuates environmental road grade disturbances to regulate gap and velocity errors, and it aggressively requests engine torque which compromises fuel, comfort, and wear performance. Figure 2 illustrates experimentally measured operation of the autonomous trailing truck in the platoon to regulate tracking errors [9]. Overall, the measured fuel performance of the two-truck platoon under the PID compensator as compared to a non-platooned variant is summarized in Fig. 3 for varied conditions of low grade variation, medium grade variation, and high grade variation. This measures that platooning on the highway is a 3–4% fuel improvement over non-platooning when under low and medium grade conditions, but the control becomes problematic under high grade for a net 1% loss in fuel performance. In general, the platooning operation must be cost effective to justify its use.

Fig. 2
Experimental test data from a PID-controlled CACC truck in a platoon [9]. The calibration of the PID-enabled responsive gap and velocity harmonization, but led to chattering behavior in engine command. Δ(·) indicates difference in ego truck quantity from preceding truck quantity.
Fig. 2
Experimental test data from a PID-controlled CACC truck in a platoon [9]. The calibration of the PID-enabled responsive gap and velocity harmonization, but led to chattering behavior in engine command. Δ(·) indicates difference in ego truck quantity from preceding truck quantity.
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Fig. 3
Experimentally measured fuel economy improvement of a line-haul truck platoon controlled via PID-based CACC—compared against a non-platooned formation under low grade, medium grade, and high grade [9]
Fig. 3
Experimentally measured fuel economy improvement of a line-haul truck platoon controlled via PID-based CACC—compared against a non-platooned formation under low grade, medium grade, and high grade [9]
Close modal

This paper compares the design of several feedback control and predictive control strategies for the efficient guidance of a convoy of line-haul trucks under highway operation in a distributed manner. In doing so, trucks in the convoy operate under one of two modes: (1) cruising operation, designated for the leading truck that follows a pre-calculated fuel-efficient velocity profile over the route, and (2) platooning operation, designated for trailing trucks that aim to tightly track close distances from their predecessor and benefit from aerodynamic drafting. Explicit drafting models are leveraged to accurately predict the control power requirements during platooning operation. The platooning control in this case is also designed to be connected, in which acceleration information is exchanged from the preceding truck. Figure 1 depicts a line-haul truck convoy engaged in platoon operation.

To address the experimentally noted short-comings of PID-based CACC for platooning control:

  1. The rest of Sec. 2 concludes with a description of the classical CACC design used as a baseline longitudinal controller and as available in Ref. [9].

  2. Three MPC formulations of varied predictive model design are presented in Sec. 3: (1) detailed powertrain and engine mappings are modeled to directly minimize fuel consumption, (2) truck energetics are modeled and minimized as a surrogate to reduce fuel consumption, and (3) a neural network trained to predict longitudinal truck dynamics and fuel consumption given easily measurable driving data. The platooning controller performances utilizing both a first-principles model and a data-driven model are compared to a controller using a high fidelity, but difficult to obtain, powertrain model.

  3. Extensive high-fidelity platooning simulation is done in Sec. 4 to evaluate the different model predictive controllers. Results of each controller under representative traffic and road grade conditions are examined, and gained fuel efficiency in platooning due to eco-driving and aerodynamic platooning are examined. Additionally, fuel expenditure is correlated to braking losses.

  4. Experimental testing and validation are done using MPC with a real two-truck platooning system in Sec. 5.

Section 6 then concludes and summarizes the manuscript with notes for future work.

2.1 Classical CACC Through PID Compensator.

As a baseline control strategy for the platooning application, a classical controller with a feedforward acceleration available via V2V connectivity from the leading truck ar and feedback PID structure is developed to regulate distance gap tracking and relative velocity errors between the ego truck and preceding truck for safety. Quantities d and Δv, respectively, indicate the intertruck gap and the difference of ego truck to preceding truck velocities, whereas ar is the acceleration of the preceding truck as available through connected exchange. The controller commands the acceleration and deceleration of the ego truck, whereby the final PID action is given by the following governing law. Argument t is omitted for conciseness.
u=ar+KP(d,Δv)ed+KD(d,Δv)e˙Δv+KI0teddt
(1)

Here, u is the final acceleration command at a given time instant t, KP and KD are, respectively, the proportional and derivative gains that are scheduled via measurements d and Δv, KI is the constant integral gain, ed is the current distance error from a reference time headway between trucks, and eΔv is the relative velocity error between the ego truck and its predecessor. The PID is operationally similar to approaches such as Refs. [5,7].

Because the controller commands truck acceleration, the desired acceleration request is realized by a scalar conversion to an engine torque demand τ(t) with maximum torque τ¯, or an engine brake and possible wheel brake torque τb if the engine is at its braking capabilities τ. In other words, acceleration command is mapped to engine torque and brake engagement from powertrain and vehicle friction relations [40]
meu(t)σ(ı^)+τ~(t)={τ(t),τ_τ(t)τ¯τ_+τb(t),τ_>τ(t)τ¯,τ¯<τ(t)
(2)

Here, τ~ is a feedforward torque to compensate for aerodynamic and rolling frictions, me is the effective inertial mass of the truck, and σ(ı^) is a transmission mapping to engine torque with current gear ı^.

Truck platooning is a safety critical application, in which a controller must compensate for actuation and sensor noise while actively mitigating road disturbances. In doing so, the controller is tuned to softly meet strict design requirements that are otherwise not guaranteed to be met, and operationally the PID is aggressive to enforce safe platooning gaps—in which this behavior may not be efficient in powertrain operation. This motivates the need for more advanced control methodologies in platooning operation, in which explicit guarantee of constraint satisfaction can be anticipated and handled, and additionally fuel usage can be directly optimized.

3 Model Predictive Control for Platoon Strategy

To explicitly address platooning system requirements, an MPC can be formed to perform a constrained optimization for motion planning that enforces safety, road laws, and create performative driving strategies through a designable objective function. In this section, two model-based designs requiring varying system-specific knowledge (e.g., designs requiring detailed powertrain knowledge or designs requiring only fundamental knowledge of longitudinal motion) are compared, and an additional data-driven model that is trained on simulation data to predict longitudinal motion is also proposed. The fundamentals of longitudinal motion by describing force-at-the-wheel kinetics subject to aerodynamic and road losses are given here for brevity before presenting MPC designs, however more complete descriptions of longitudinal vehicle dynamics models are available in Ref. [40].

Unifying force-at-the-wheel kinetics relate rate of change of velocity v
me(ı^)v˙=FtFbFa(d,v)Fr(α)
(3)
where Ftτ/σ(ı^) is the applied tractive force at the wheel from the engine after a gearbox conversion σ through the drivetrain for the current gear ı^, and me is effective inertial mass of the truck considering rotating components. Fb is the effective braking force from the brake disc if service braking is applied.
The longitudinal aerodynamic drag force Fa when subject to no external wind is expressed as a function of vehicle speed v and possibly a function of intertruck gap d if following behind another truck:
Fa(d,v)={12ρAfCDβ(d)v2following \; a\; truck12ρAfCDv2otherwise
(4)
where ρ is the density of air, Af is the effective frontal surface area of the truck, CD is the nominal drag coefficient, and β(d) is a drag reduction function. This drag reduction is empirically available and can be expressed as in Fig. 4. Drag reduction may be decided via more complex fluid dynamics models [41], so instead an exponential model is fit here for ease of use in later optimization [15].
Fig. 4
Platooning drag reduction by inter-vehicle gaps d experimentally identified under flat-road conditions. A = 0.838, B = 0.908 × 10−3, C = −0.049, and D = −0.093
Fig. 4
Platooning drag reduction by inter-vehicle gaps d experimentally identified under flat-road conditions. A = 0.838, B = 0.908 × 10−3, C = −0.049, and D = −0.093
Close modal
Similarly, the longitudinal rolling forces Fr are expressed as a function of road grade α that varies with position s
Fr(α)=mg(Crcosα(s)+sinα(s))
(5)
where g is the gravitational constant and Cr is the rolling resistance. Upcoming α(s) is additionally available as empirical data given that the route is known during a trip-planning stage. For use in the motion planning optimization, its relationship over the upcoming horizon of the MPC can then be fit to a quadratic form α(s) ≈ a2s2 + a1s + a0 [42].

The state-space model with state x, control input u, and external disturbance w that is used to predict motion is expressed generally as x˙=f(x,u,w). How this model relates to fuel consumption is the subject to be changed within each separate MPC design for platooning.

For evaluation of the control strategy, the fuel rate consumption of the engine can be generally expressed as a polynomial in engine torque τ and engine speed ω of order m + n with coefficients c, and is well-approximated with first-order terms similar to Ref. [15]. Empirical data of this relationship are depicted in Fig. 5.
m˙f(τ,ω)=a=0nb=0mcabτaωbm˙f(τ,ω)max(c11τω+c00,0)
(6)
Importantly, engine actuation limitations are expressed in the form of a bounding constraint and an isometric power constraint, whereby engine torque is bounded by upper limitation τ¯ and lower limitation τ, and engine torque is bounded by an isometric power curve on maximum engine power P¯ and current engine speed.
τ_τ(t)τ¯τ(t)P¯/ω(t)
(7)
Fig. 5
Empirically measured fuel rate data overlaid with resulting fuel curve fit (6) (R2 = 0.99)
Fig. 5
Empirically measured fuel rate data overlaid with resulting fuel curve fit (6) (R2 = 0.99)
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Constraints on states of the control system can then be imposed to enforce gap safety and road laws.

d_d(t)d¯v_v(t)v¯
(8)
Each considered MPC then forms an OCP with varied models and appropriate control inputs and constraints, and follows as a fuel MPC, kinetic MPC, and NN MPC. Comparatively, each MPC shares common terms in their respective objective functions with scalar weightings q that regulate distance tracking error from a reference time headway T and velocity harmonization with the V2V-communicated leading truck velocity vr—similar to the baseline CACC of Eq. (1).
Je=qd(diTvi)2+qv(vivr,i)2
(9)

Here, subscript i indicates the stage of the optimization—which is evaluated for a total of N look-ahead stages. It is assumed that the current road grade α and the current gear ı^ are constant over the prediction horizon, and a prediction is made that the leading truck drives with constant acceleration until reaching the speed limit or coming to a stop.

It follows that output engine torque y(t) ≜ τ(t) is bounded by the set Y from Eq. (7), and that states x(t)[d(t)v(t)] are bounded by the set X from Eq. (8). Additional slack decision variables are used to soften the state constraints with an L1 penalty for run-time feasibility, but are omitted for brevity [43]. Here, boldface indicates a vector of decision variables, e.g., F=Fii1N.

3.1 Fuel-Efficient MPC.

An MPC based on Ref. [17] is designed to exploit full knowledge of engine and drivetrain maps for fuel-efficient platooning control. The MPC plans throttle and braking pedal deflection for each stage of the control horizon δt, δb.
minδt,δbi=1N[Je+qδ(δt,i+δb,i)2+qfm˙f(τi,ωi)]s.t.{d˙=vrvv˙=1/me(ı^)[FtFbFa(d,v)Fr(α)]Ft=ft(ω,ı^,δt)Fb=fb(ω,ı^,δb,α)xiX,yiY0δt,i10δb,i1
(10)
This OCP was found to be the most expensive to evaluate, as it directly leverages look-up tables for precise evaluation of throttle and braking dynamics: ft, fb. However, the following MPC designs utilize approximations of fuel-optimal control behavior for the benefit of improved run-time performance.

3.2 Kinetic Model Predictive Control.

To avoid control model reliance on detailed powertrain maps for pedal response, engine response, and fuel consumption—which may be unavailable to the automation designer, difficult to identify, or inaccurate due to vehicle wear and tear—an MPC based on first-principles equation (3) is designed. Force at the wheel F is commanded by the MPC, which is then actuated through a feedforward conversion in a lower-level controller to split the requested force to an engine demand and possible service braking demand similar in form to Eq. (2).
minFi=1N[Je+qFFi2]s.t.{d˙=vrvv˙=1/me(ı^)[FFa(d,v)Fr(α)]xiX,yiYF_FiF¯
(11)
Such an OCP is a relatively cheap computation compared to the other formulations for good performance.

3.3 Neural Network Model Predictive Control.

The control model of Sec. 3.1 assumes detailed and accurate models of powertrain response, however in reality when controlling real hardware, significant modeling errors may accumulate due to manufacturing defects, measurement and process noise during system identification, cumulative wear-and-tear, etc. As such, it is desirable to approximate platform-specific response from measured data to automatically synthesize models of the platooned system—as well as compare the quality of controller performance based on neural network approximators to the performance of controllers leveraging detailed but manually calibrated models.

Two networks with weightings θ are developed to predict next-stage truck speed vi+1 and instantaneous fuel consumption mf,i given current velocity, gear, and grade observations vi, ı^, α—as well as truck acceleration ai.

Each feedforward network architecture is composed of two fully connected hidden layers with four nodes and tanh activation function, and a fully connected, linear output node. Training is done with the Adam optimizer for stochastic gradient descent [44] with gradient threshold 1.0 and learn rate 2 × 10−3. The data for training can source from readily available sensor data during real-world driving, but in this case is collected from high-fidelity simulation of the platooning system. To sufficiently excite the system for all operating conditions, data are collected from multiple scenarios of different truck speeds, road grades, and acceleration aggressiveness, and represents 13 h of driving data. Eighty percent of the collected scenarios are used for training and the remaining 20% are used in predictor accuracy validation. Overall, the model trains to a RMSE of 8.1 mm/s in speed prediction accuracy and trains to a RMSE of 2.2 g/s in instantaneous fuel prediction accuracy.

The neural network models are then embedded into a model predictive controller using automatic gradient expressions between the input observables and outputs [45]. The controller commands next-stage truck acceleration ai+1, which is actuated through an engine demand and possible service braking demand (Eq. (2)). Output y is not calculated for computational simplicity, so constraining set Y is omitted in this case.
minai=1N[Je+qaai+12+qfmf,i(vi,ai,ı^,α,θ)]s.t.{d˙=vrvv˙=f(v,a,ı^,α,θ)xiXa_aia¯
(12)
Overall, this OCP achieves strong performance even with low-dimensional networks—which enables run-time feasibility on the embedded hardware.

4 Highway-Motivated Representative Simulation

The platooning operation is excited by imposing two separate major disturbances: road grade and downstream traffic. The leading truck is driven using a predictive cruise controller (PCC) that tracks a set-point velocity in a fuel-optimal manner with respect to road grade [17] and offers V2V connectivity by broadcasting its current speed and acceleration. The trailing truck is driven using the baseline and MPC controllers of Secs. 2 and 3.

The platooning system is first simulated in a high fidelity, Simulink-based software stack that includes the longitudinal vehicle and powertrain dynamics under closed-loop control to virtually realize the performance of the physical trucks. The simulator is similar to Truckmaker [46] and additionally includes platform-specific radar, IMU, DSRC, and drivetrain characterization.

4.1 Leading Truck Cycle.

A nominal traffic cycle to represent typical traffic fluctuations during line-haul operation is designated for the leading truck to follow. This 1.3 h traffic cycle is synthesized in Ref. [9] to replicate kinetic intensity of forced truck speed slow-downs due to typical downstream traffic—as found from the NREL fleet DNA database [47].

Additionally, a road elevation profile as from Columbus, IN, to Evansville, IN, USA, is imposed, where the leading truck is assigned to maintain cruising operation in a round-trip mission [9]. To assist in road grade compensation, Cummins PCC features are available as a route and engine-specific fuel-efficient velocity profile as recommended by look-ahead road grade information [48]. As mentioned previously in Ref. [9], the route is distinguished into continuous low, medium, and high grade segments that are approximately similar in length. They have, respectively, grade intensities of 0.5%, 0.9%, and 1.6% on average. Figure 6 depicts a segment of the road grade profile of the considered highway with the PCC-recommended velocity profile for the leading truck to follow, given a 28.7 m/s driver-set velocity.

Fig. 6
Leading truck cycle with cummins PCC features for the grade profile from Columbus, IN, to Evansville, IN USA
Fig. 6
Leading truck cycle with cummins PCC features for the grade profile from Columbus, IN, to Evansville, IN USA
Close modal

The PCC system on the leading truck improves fuel economy through eco-driving. When used in a platooning system with homogeneous weight class and hardware specifications—as is the case for the results of this paper—the eco-driving benefits also extend to the trailing trucks, since they are designed to drive at similar velocities during platooning operation. Table 1 measures the energy benefits of utilizing the PCC system on the leading truck. The approach is found to improve fuel economy by 1.9% in low grade driving, and up to 5.9% in high grade driving—which correlates with experimental validation from Ref. [9]. This is attributed to improved vehicle energetics, in which unnecessary braking is significantly attenuated and vehicle overspeeding is attenuated to reduce unnecessary aerodynamic friction losses.

Table 1

Road grade performance improvements of the leading truck when using PCC features as compared to no PCC

GradeFuel economyEngine workBrake workAero work
Low1.9%1.5%83.7%1.4%
Med4.1%3.2%87.4%2.3%
High5.9%5.5%33.9%1.9%
GradeFuel economyEngine workBrake workAero work
Low1.9%1.5%83.7%1.4%
Med4.1%3.2%87.4%2.3%
High5.9%5.5%33.9%1.9%

4.2 Trailing Truck Performance.

The platooning operation is then managed for the trailing truck using the CACC-enabled PID and the outlined MPC designs. For brevity, the fuel-efficient MPC is focused on due to its consistent performance in simulation, and its later usage in platooning experimentation of Sec. 5, but all MPC performed comparably well and exhibited similar trends.

The qualitative performance of the fuel-efficient MPC compared to the PID is depicted in Fig. 7 for the Columbus–Evansville representative road grade route and is depicted in Fig. 8 for the representative traffic cycle [9]. As can be seen by correlating road grade and gap tracking error, the PID had more significant tracking issues during segments of high road grade than the MPC. In addition, the MPC attenuated unnecessary engine throttle—which led to reduced fuel consumption and improved transient response.

Fig. 7
Trailing truck trajectory over high road grade simulation from the baseline PID-enabled CACC and the fuel-efficient MPC. Fuel rate scaled by a random coefficient and reported as a 1/4-km moving average
Fig. 7
Trailing truck trajectory over high road grade simulation from the baseline PID-enabled CACC and the fuel-efficient MPC. Fuel rate scaled by a random coefficient and reported as a 1/4-km moving average
Close modal
Fig. 8
Trailing truck trajectory in representative flat-road traffic cycle from the baseline PID-enabled CACC and the fuel-efficient MPC
Fig. 8
Trailing truck trajectory in representative flat-road traffic cycle from the baseline PID-enabled CACC and the fuel-efficient MPC
Close modal

To compare the platooning performance as a whole, the truck energetics for both the leading truck when driven using PCC features and the trailing truck are shown in Fig. 9. The performance over low, medium, and high grades are given, as well as the simulated performance of the representative traffic cycle. Overall, the aerodynamic energy benefits for the trailing truck reduce total work done by 12%, and, for this system, rolling work accounts for 37% and 43% of total work economy for the leading and trailing trucks, respectively (which is hardware-dependent and cannot be improved through control strategies).

Fig. 9
Energy consumption composition of the leading truck using PCC (left) and the trailing truck (right) when operated by fuel-efficient MPC
Fig. 9
Energy consumption composition of the leading truck using PCC (left) and the trailing truck (right) when operated by fuel-efficient MPC
Close modal

Importantly, the consequences of controller behavior appear in the total braking energy dissipated. Braking energy wastes truck momentum and chemical energy burned to propel the truck forward, and so ideal truck operation cuts unnecessary braking as much as possible. However, it is not feasible to completely eliminate braking: necessary system constraints are enforced to prevent collisions with surrounding traffic, and speed limit enforcement can require braking during downhill sections to prevent unsafe speeding. Figure 7 further shows this in the speed limit lines and engine braking lines for the high grade segment of the route, in which a majority of the braking that occurred was during downhill segments that require speed limit maintenance.

Platooned truck fuel consumption over braking energy economy is depicted in Fig. 10, which shows the holistic performance of each platooning controller during the grade and traffic scenarios. Additionally, a linear regression with confidence bounds of the regression parameters is shown to extrapolate the data. This suggests that fuel consumption scales approximately linearly with braking energy dissipated, and that the maximal possible fuel savings with respect to the worst-performing scenario is 15% when no braking is utilized. Indeed, the high grade portion of the route consumed the most fuel, and the other scenarios were close to their maximal fuel efficiency with the performant MPC designs.

Fig. 10
Controller performance of the trailing truck over representative traffic and road grade cycles of similar average velocity. Fuel consumption normalized against the worst-case cycle is plotted over braking energy dissipated per kilometer traveled. The best of fit line and its functional fit 95% confidence bound are additionally given as y(x) = (18.72 ± 1.92)x + (84.2 ± 0.78).
Fig. 10
Controller performance of the trailing truck over representative traffic and road grade cycles of similar average velocity. Fuel consumption normalized against the worst-case cycle is plotted over braking energy dissipated per kilometer traveled. The best of fit line and its functional fit 95% confidence bound are additionally given as y(x) = (18.72 ± 1.92)x + (84.2 ± 0.78).
Close modal

The simulation results for fuel consumption, gap tracking performance, and energy dissipated of all controllers are summarized in Table 2. Overall, each MPC is found to more accurately track the gap target compared to PID. Additionally, braking work was found to reduce by 90% when driving on low grade as opposed to high grade, and the traffic cycle realized between 40% and 75% reduction in braking work when utilizing MPC as compared to the PID. Small aerodynamic work differences occurred due to different operational velocities in the scenarios. Overall, choosing MPC over PID is found to improve fuel economy for the platooned truck by 1% in low and medium grade driving, 3% in high grade driving, and between 4–8% in traffic.

Table 2

Platooning controller simulation comparison over highway grade segments and representative traffic cycle

ScenarioControllerFuel use (%)Gap RMSE (m)Engine work (MJ/km)Brake work (MJ/km)Aero work (MJ/km)
Low gradePID82.80.733.110.061.62
Kinetic MPC81.90.653.080.031.62
NN MPC81.90.713.090.041.62
Fuel MPC82.30.493.110.061.62
Med. gradePID84.91.272.630.151.31
Kinetic MPC83.30.702.570.101.31
NN MPC83.30.652.580.111.31
Fuel MPC83.40.442.590.121.31
High gradePID100.06.164.100.751.66
Kinetic MPC97.22.813.980.651.65
NN MPC97.22.613.980.671.65
Fuel MPC96.82.503.970.661.65
Traffic—flat roadPID89.84.564.310.481.93
Kinetic MPC86.22.694.090.271.93
NN MPC82.70.773.920.121.92
Fuel MPC83.70.563.950.161.92
ScenarioControllerFuel use (%)Gap RMSE (m)Engine work (MJ/km)Brake work (MJ/km)Aero work (MJ/km)
Low gradePID82.80.733.110.061.62
Kinetic MPC81.90.653.080.031.62
NN MPC81.90.713.090.041.62
Fuel MPC82.30.493.110.061.62
Med. gradePID84.91.272.630.151.31
Kinetic MPC83.30.702.570.101.31
NN MPC83.30.652.580.111.31
Fuel MPC83.40.442.590.121.31
High gradePID100.06.164.100.751.66
Kinetic MPC97.22.813.980.651.65
NN MPC97.22.613.980.671.65
Fuel MPC96.82.503.970.661.65
Traffic—flat roadPID89.84.564.310.481.93
Kinetic MPC86.22.694.090.271.93
NN MPC82.70.773.920.121.92
Fuel MPC83.70.563.950.161.92

Finally, the simulation study is concluded by re-examining the platooning fuel results as compared to the non-platooning case when under high road grade (as is the motivation from CACC testing results represented in Fig. 2). Table 3 depicts fuel improvements of the platooning controllers compared to the non-platooned case. As was found previously, the simulation results suggest that the PID consumes more fuel if platooning under high road grade, however the MPC approaches indeed successfully platoon to improve fuel economy.

Table 3

Simulated platooning controller fuel improvements under high grade compared to non-platooned case

PIDKinetic MPCNN MPCFuel MPC
Fuel−1.1%1.6%1.6%2.0%
PIDKinetic MPCNN MPCFuel MPC
Fuel−1.1%1.6%1.6%2.0%

5 Traffic Cycle Experimental Performance

The platooning system control is then validated through experimentation. In this, the representative traffic cycle is used to validate the performance of a two-truck platoon at the Transportation Research Center (TRC) high-speed proving grounds—which tested the platooned system for over 80 km of driving. This flat-road testing is depicted in Fig. 1.

5.1 Hardware for Control Setup.

The trucks used in testing are of homogeneous hardware specifications. The truck makeup is summarized in Table 4. In addition, the hardware stack enabling autonomy on the testing trucks consists of a radar and service braking control system, Cummins engine controller, Cohda wireless on-board device for V2V communications, and Speedgoat prototyping microcontroller with a 1.4 GHz Intel Celeron. Bus communications are through J1939 CAN protocol.

Table 4

Truck platooning testing hardware specifications

ComponentDescription
Truck modelInternational 2020 LT625 6X4
Trailer2020 Great Dane 53′ Van with underbody skirts
Gross weight67,000 lb
EngineCummins X15 Efficiency Series
EPA 2017 430 HP
TransmissionEaton Endurant 12-Speed Fully Automated
Manual Overdrive
Steer, trailer tiresMichelin X Line Energy
Drive tiresMichelin XDA Energy
ComponentDescription
Truck modelInternational 2020 LT625 6X4
Trailer2020 Great Dane 53′ Van with underbody skirts
Gross weight67,000 lb
EngineCummins X15 Efficiency Series
EPA 2017 430 HP
TransmissionEaton Endurant 12-Speed Fully Automated
Manual Overdrive
Steer, trailer tiresMichelin X Line Energy
Drive tiresMichelin XDA Energy

The MPC designs are cast as nonlinear optimization problems subject to non-convex constraints. Real-time embedded implementation of the algorithms are solved using Forces PRO via an interior point method with L-BFGS Hessian approximation [49], which combines with CasADi for generating gradient expressions of the resulting optimization [45]. Locally optimal solutions are then found in the region local to the supplied initial guess. The continuous-time model equations are discretized with Δt = 0.5 s and explicitly integrated with a second-order Runge Kutta method with 10 integrating nodes between each optimization stage. So that the controllers have similar computation times, the fuel-efficient and neural network MPC then both use a 8 s look-ahead interval, and the kinetic MPC uses a 12 s look-ahead interval. The MPCs presented in this work are runnable at control frequencies of 10 Hz on the embedded hardware.

5.2 Platooning Results.

For experimental evaluation, the two-truck platoon is driven similarly to the testing methodology of the simulation from Sec. 4—in that the leading truck is assigned to track a desired velocity profile using a speed-tracking predictive controller, and the platooned trailing truck is driven using both the baseline PID and fuel-efficient MPC. The experimental study focuses on the representative traffic cycle for repeatability in measuring multiple controllers and as a necessary first stage of control verification before driving on real highways with road grade.

The engine duty cycle is measured in Fig. 11, depicting a heat map of the frequency content of engine torque-speed pairs. It can be seen that the MPC maintains the engine at more fuel-favorable operating conditions than the PID, and reduced the amount of engine braking conducted. Such results are consistent with the simulation study.

Fig. 11
Measured engine duty cycle of platooned trailing truck controlled via PID (a) and via fuel-efficient MPC (b). Heatmap shows frequency content of the engine cycle with the bottom 2% of the heatmap clipped. Additionally, dashed line contours show fuel rate scaled by a random coefficient (a) PID for platooning and (b) MPC for platooning.
Fig. 11
Measured engine duty cycle of platooned trailing truck controlled via PID (a) and via fuel-efficient MPC (b). Heatmap shows frequency content of the engine cycle with the bottom 2% of the heatmap clipped. Additionally, dashed line contours show fuel rate scaled by a random coefficient (a) PID for platooning and (b) MPC for platooning.
Close modal

Figure 12 then depicts the realized trajectories of the PID and MPC platooning controllers. Contrary to the simulation model provided by the brake-split control system which did not predict engagement of the wheel brake as in Fig. 8, the experimentation realized sometimes significant wheel brake engagement for both controllers. Overall, wheel braking is less accurate in controlling speed of the truck compared to engine-assisted torque braking, and is best-suited for assisting in emergency collision avoidance or bringing the truck to a stop. Experimental testing of the platooning system saw a significantly increased need to apply braking to maintain safe distances from the leading truck and avoid gap constraint violation, thereby dissipating more propulsive energy from fuel. As established in Sec. 4, the increased use of braking likely reduced potential fuel benefits in the chosen control strategies, but offers opportunity for later research to improve the control to maximize fuel savings potentials. Table 5 measures the fuel and energy usage between the PID and fuel-efficient MPC when platooning the trailing truck and reports fuel usage of the truck compared to non-platooned operation (gaps greater than 200 m). It was found that platooning PID improved fuel economy by 6.2%, and MPC improved fuel economy by 9.1%. Additionally, the MPC was found to improve fuel economy by 3.0% over the PID under this representative traffic cycle.

Fig. 12
Experimentally measured performance over representative traffic cycle of the baseline PID and the fuel-efficient MPC. Distance from the constraint d − d is shown for the MPC case.
Fig. 12
Experimentally measured performance over representative traffic cycle of the baseline PID and the fuel-efficient MPC. Distance from the constraint d − d is shown for the MPC case.
Close modal
Table 5

Experimental platooned truck performance of PID and fuel-efficient MPC

Ctrl.Fuel useGap RMSEBrake workAero work
PID93.8 (%)1.28 (m)1.58 (MJ/km)2.39 (MJ/km)
MPC90.9 (%)2.33 (m)1.43 (MJ/km)2.39 (MJ/km)
Ctrl.Fuel useGap RMSEBrake workAero work
PID93.8 (%)1.28 (m)1.58 (MJ/km)2.39 (MJ/km)
MPC90.9 (%)2.33 (m)1.43 (MJ/km)2.39 (MJ/km)

Note: Fuel use normalized against non-platooned case.

During experimentation, unmodelled exogeneous disturbances possibly changed the acceleration response and polluted the performance of the designed controllers. More significantly, the system is challenged by the model uncertainty, which increases the magnitude of corrective actions from feedback control. Comparing the measured braking work in Table 5 to the simulation-predicted braking work in Table 2, experimentation realized threefold higher amounts of braking and is present in both PID and MPC performance. Braking can be engaged necessarily to avoid system constraint violation and, as in the case of the measured results, occurred to avoid collisions with the leading truck. Such corrective actions to maintain constraint satisfaction were shown to reduce the aerodynamic energy benefits of having platooned as in Sec. 4. MPC was found to perform better in fuel economy than the gain-scheduled PID for platooning operation, and exists as a framework to even better compensate for such uncertainties in future designs.

6 Conclusion

Truck platooning of heavy-duty line-haul trucks offers potentials in improving fuel economy of trucks by exploiting drafting effects from predecessor trucks, thereby reducing operational costs and reducing harmful emissions. The model predictive platooning controller designs presented in this paper exploit knowledge of these drafting effects to optimize energy consumption during operation and harmonize with the preceding truck while enforcing gap, speed, and powertrain capability constraints to enable safe operation.

Overall, it was found that direct minimization of fuel consumption during platooning operation had a mild 1–2% benefit in fuel economy as compared to first-principles approaches when dealing with grade variations, but lead to greater benefits of 3–4% in fuel economy when dealing with the nominal traffic scenario. Additionally, a model predictive control embedded with trained neural network model approximators was found to perform comparably well to the control approach that exploited fully detailed, manually calibrated powertrain maps.

Common to any performative control approach, eco-driving aspects can attenuate unnecessary braking and reduce overspeeding. Here, the effects of eco-driving in control are independently accounted for by considering the single-truck case without platooning: in low grade environments eco-driving improved fuel economy by 1.9%, and in high grade environments eco-driving improved fuel economy by 5.9%.

These eco-driving effects are then further improved by introducing aerodynamic benefit with platooning. Test-track testing measured a 3.0% additional fuel benefit when using fuel-efficient model predictive control over gain-scheduled PID for platooning control under representative traffic conditions. Additional simulation of real highway conditions with high road grade found a further 3.0% fuel benefit in using the MPC over PID. In total, up to 9.1% fuel savings is measured by enabling eco-driving and platooning control features.

During both simulation and experimentation, it was shown that enforcing necessary gap and speed constraints required braking input for the platooned trucks, which did degrade energy performance by up to 15%. Such necessary braking was found to occur when the system was subjected to high road grade to maintain road speed limits, as well as corrective braking required to enforce gap safety constraints.

We emphasize that platooning control strategies should predictively mitigate the use of braking systems—which will tend to become more active due to maintaining strict gap tracking for safety—which has otherwise been shown here to increase energy losses that limit platooning fuel and safety performance.

Acknowledgment

This material is based upon work supported by the Department of Energy, Office of Energy Efficiency and Renewable Energy (EERE), under Award Number DE-EE0008469. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Conflict of Interest

There are no conflicts of interest.

Data Availability Statement

The authors attest that all data for this study are included in the paper.

References

1.
Vahidi
,
A.
, and
Sciarretta
,
A.
,
2018
, “
Energy Saving Potentials of Connected and Automated Vehicles
,”
Trans. Res. Part C: Emerg. Technol.
,
95
(
Apr.
), pp.
822
843
.
2.
Lammert
,
M. P.
,
Duran
,
A.
,
Diez
,
J.
,
Burton
,
K.
, and
Nicholson
,
A.
,
2014
, “
Effect of Platooning on Fuel Consumption of Class 8 Vehicles Over a Range of Speeds, Following Distances, and Mass
,”
SAE Int. J. Commer. Veh.
,
7
(
2
), pp.
7
9
.
3.
Besselink
,
B.
,
Turri
,
V.
,
Van De Hoef
,
S. H.
,
Liang
,
K. Y.
,
Alam
,
A.
,
Mårtensson
,
J.
, and
Johansson
,
K. H.
,
2016
, “
Cyber-Physical Control of Road Freight Transport
,”
Proc. IEEE
,
104
(
5
), pp.
1128
1141
.
4.
Tsugawa
,
S.
,
Jeschke
,
S.
, and
Shladover
,
S. E.
,
2016
, “
A Review of Truck Platooning Projects for Energy Savings
,”
IEEE Trans. Intell. Veh.
,
1
(
1
), pp.
68
77
.
5.
Ploeg
,
J.
,
Scheepers
,
B. T.
,
Van Nunen
,
E.
,
Van De Wouw
,
N.
, and
Nijmeijer
,
H.
,
2011
, “
Design and Experimental Evaluation of Cooperative Adaptive Cruise Control
,”
2011 14th International IEEE Conference on Intelligent Transportation Systems (ITSC)
,
Washington, DC
, pp.
260
265
.
6.
McAuliffe
,
B.
,
Croken
,
M.
, and
Ahmadi-Baloutaki
,
M.
,
2017
, “
Fuel-Economy Testing of a Three-Vehicle Truck Platooning System
,”
National Research Council of Canada Aerodynamics Laboratory
.
7.
McAuliffe
,
B.
,
Lammert
,
M.
,
Lu
,
X. Y.
,
Shladover
,
S.
,
Surcel
,
M. D.
, and
Kailas
,
A.
,
2018
, “
Influences on Energy Savings of Heavy Trucks Using Cooperative Adaptive Cruise Control
,”
SAE Technical Papers
,
2018 April
, pp.
10
12
.
8.
Stegner
,
E.
,
Ward
,
J.
,
Siefert
,
J.
,
Hoffman
,
M.
, and
Bevly
,
D. M.
,
2021
, “
Experimental Fuel Consumption Results From a Heterogeneous Four-Truck Platoon
,”
SAE Technical Papers
, pp.
1
11
.
9.
Borhan
,
H.
,
Lammert
,
M.
,
Kelly
,
K.
,
Zhang
,
C.
,
Brady
,
N.
,
Yu
,
C. S.
, and
Liu
,
J.
,
2021
, “
Advancing Platooning With ADAS Control Integration and Assessment Test Results
,”
SAE Technical Papers
, pp.
1969
1975
.
10.
Online
,
2022
, “
Autonomous Trucking Benefits — Fuel Efficiency
.”
11.
Online
,
2022
, “
Tusimple — Environmental, Social, and Governance Report
.”
12.
Alam
,
A.
,
Mårtensson
,
J.
, and
Johansson
,
K. H.
,
2015
, “
Experimental Evaluation of Decentralized Cooperative Cruise Control for Heavy-Duty Vehicle Platooning
,”
Control Eng. Pract.
,
38
(
1
), pp.
11
25
.
13.
He
,
C. R.
,
Maurer
,
H.
, and
Orosz
,
G.
,
2016
, “
Fuel Consumption Optimization of Heavy-Duty Vehicles With Grade, Wind, and Traffic Information
,”
ASME J. Comput. Nonlinear Dyn.
,
11
(
6
), p.
061011
.
14.
Hellström
,
E.
,
Ivarsson
,
M.
,
Åslund
,
J.
, and
Nielsen
,
L.
,
2009
, “
Look-Ahead Control for Heavy Trucks to Minimize Trip Time and Fuel Consumption
,”
Control Eng. Pract.
,
17
(
2
), pp.
245
254
.
15.
Turri
,
V.
,
Besselink
,
B.
, and
Johansson
,
K. H.
,
2017
, “
Cooperative Look-Ahead Control for Fuel-Efficient and Safe Heavy-Duty Vehicle Platooning
,”
IEEE Trans. Control Syst. Technol.
,
25
(
1
), pp.
12
28
.
16.
Held
,
M.
,
Flärdh
,
O.
,
Roos
,
F.
, and
Mårtensson
,
J.
,
2020
, “
Optimal Freewheeling Control of a Heavy-Duty Vehicle Using Mixed Integer Quadratic Programming
,”
IFAC-PapersOnLine
,
53
(
2
), pp.
13809
13815
.
17.
Liu
,
J.
,
Pattel
,
B.
,
Desai
,
A. S.
,
Hodzen
,
E.
, and
Borhan
,
H.
,
2019
, “
Fuel Efficient Control Algorithms for Connected and Automated Line-Haul Trucks
,”
2019 IEEE Conference on Control Technology and Applications (CCTA)
,
Hong Kong, China
, pp.
730
737
.
18.
Guanetti
,
J.
,
Kim
,
Y.
, and
Borrelli
,
F.
,
2018
, “
Control of Connected and Automated Vehicles: State of the Art and Future Challenges
,”
Ann. Rev. Control
,
45
(
May
), pp.
18
40
.
19.
Turri
,
V.
,
Kim
,
Y.
,
Guanetti
,
J.
,
Johansson
,
K. H.
, and
Borrelli
,
F.
,
2017
, “
A Model Predictive Controller for Non-cooperative Eco-platooning
,”
2017 American Control Conference (ACC)
,
Seattle, WA
, Vol. 3, pp.
2309
2314
.
20.
Borek
,
J.
,
Groelke
,
B.
,
Earnhardt
,
C.
, and
Vermillion
,
C.
,
2020
, “
Economic Optimal Control for Minimizing Fuel Consumption of Heavy-Duty Trucks in a Highway Environment
,”
IEEE Trans. Control Syst. Technol.
,
28
(
5
), pp.
1652
1664
.
21.
Wang
,
Z.
,
Bian
,
Y.
,
Shladover
,
S. E.
,
Wu
,
G.
,
Li
,
S. E.
, and
Barth
,
M. J.
,
2020
, “
A Survey on Cooperative Longitudinal Motion Control of Multiple Connected and Automated Vehicles
,”
IEEE Intell. Trans. Syst. Mag.
,
12
(
1
), pp.
4
24
.
22.
Dunbar
,
W. B.
, and
Murray
,
R. M.
,
2006
, “
Distributed Receding Horizon Control for Multi-vehicle Formation Stabilization
,”
Automatica
,
42
(
4
), pp.
549
558
.
23.
Wang
,
J. Q.
,
Li
,
S. E.
,
Zheng
,
Y.
, and
Lu
,
X. Y.
,
2015
, “
Longitudinal Collision Mitigation Via Coordinated Braking of Multiple Vehicles Using Model Predictive Control
,”
Integr. Comput. Aided Eng.
,
22
(
2
), pp.
171
185
.
24.
Dunbar
,
W. B.
, and
Caveney
,
D. S.
,
2012
, “
Distributed Receding Horizon Control of Vehicle Platoons: Stability and String Stability
,”
IEEE Trans. Automat. Control
,
57
(
3
), pp.
620
633
.
25.
Gao
,
F.
,
Li
,
S. E.
,
Zheng
,
Y.
, and
Kum
,
D.
,
2016
, “
Robust Control of Heterogeneous Vehicular Platoon With Uncertain Dynamics and Communication Delay
,”
IET Intell. Transp. Syst.
,
10
(
7
), pp.
503
513
.
26.
Ard
,
T.
,
Dollar
,
R. A.
,
Vahidi
,
A.
,
Zhang
,
Y.
, and
Karbowski
,
D.
,
2020
, “
Microsimulation of Energy and Flow Effects From Optimal Automated Driving in Mixed Traffic
,”
Trans. Res. Part C: Emerg. Technol.
,
120
(
1
), p.
102806
.
27.
Ard
,
T.
,
Guo
,
L.
,
Dollar
,
R. A.
,
Fayazi
,
A.
,
Goulet
,
N.
,
Jia
,
Y.
,
Ayalew
,
B.
, and
Vahidi
,
A.
,
2021
, “
Energy and Flow Effects of Optimal Automated Driving in Mixed Traffic: Vehicle-in-the-Loop Experimental Results
,”
Trans. Res. Part C: Emerg. Technol.
,
130
(
1
), p.
103168
.
28.
Alam
,
A.
,
Besselink
,
B.
,
Turri
,
V.
,
Martensson
,
J.
, and
Johansson
,
J. H.
,
2015
, “
Heavy-Duty Vehicle Platooning for Sustainable Freight Transportation
,”
IEEE Control Syst. Mag.
,
35
(
6
), pp.
34
56
.
29.
Liang
,
K. Y.
,
Martensson
,
J.
, and
Johansson
,
K. H.
,
2013
, “
When Is It Fuel Efficient for a Heavy Duty Vehicle to Catch Up With a Platoon?
,”
IFAC Proc.
,
46
(
21
), pp.
738
743
.
30.
Larson
,
J.
,
Liang
,
K. Y.
, and
Johansson
,
K. H.
,
2015
, “
A Distributed Framework for Coordinated Heavy-Duty Vehicle Platooning
,”
IEEE Trans. Intell. Trans. Syst.
,
16
(
1
), pp.
419
429
.
31.
Ibrahim
,
A.
,
Cicic
,
M.
,
Goswami
,
D.
,
Basten
,
T.
, and
Johansson
,
K. H.
,
2019
, “
Control of Platooned Vehicles in Presence of Traffic Shock Waves
,”
2019 IEEE Intelligent Transportation Systems Conference (ITSC)
,
Auckland, New Zealand
, ITSC 2019, pp.
1727
1734
.
32.
Borrelli
,
F.
,
Bemporad
,
A.
, and
Morari
,
M.
,
2015
, “Predictive Control for Linear and Hybrid Systems.” Available Online.
33.
Hewing
,
L.
,
Wabersich
,
K. P.
,
Menner
,
M.
, and
Zeilinger
,
M. N.
,
2020
, “
Learning-Based Model Predictive Control: Toward Safe Learning in Control
,”
Ann. Rev. Control Robot. Auton. Syst.
,
3
(
1
), pp.
269
296
.
34.
Rosolia
,
U.
, and
Borrelli
,
F.
,
2018
, “
Learning Model Predictive Control for Iterative Tasks. A Data-Driven Control Framework
,”
IEEE Trans. Automat. Control
,
63
(
7
), pp.
1883
1896
.
35.
Limon
,
D.
,
Calliess
,
J.
, and
Maciejowski
,
J. M.
,
2017
, “
Learning-Based Nonlinear Model Predictive Control
,”
IFAC-PapersOnLine
,
50
(
1
), pp.
7769
7776
.
36.
Cairano
,
S. D.
,
Bernardini
,
D.
,
Bemporad
,
A.
, and
Kolmanovsky
,
I. V.
,
2014
, “
Stochastic MPC With Learning for Driver-Predictive Vehicle Control and Its Application to HEV Energy Management
,”
IEEE Trans. Control Syst. Technol.
,
22
(
3
), pp.
1018
1031
.
37.
Zhang
,
C.
, and
Vahidi
,
A.
,
2011
, “
Predictive Cruise Control With Probabilistic Constraints for Eco Driving
,”
ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control
,
Arlington, VA
, pp.
233
238
.
38.
Fan
,
D.
,
Agha
,
A.
, and
Theodorou
,
E.
,
2020
, “
Deep Learning Tubes for Tube MPC
,”
Robotics: Science and Systems
,
Virtual
.
39.
Mesbah
,
A.
,
2018
, “
Stochastic Model Predictive Control With Active Uncertainty Learning: A Survey on Dual Control
,”
Ann. Rev. Control
,
45
(
1
), pp.
107
117
.
40.
Guzzella
,
L.
, and
Sciarretta
,
A.
,
2013
,
Vehicle Propulsion Systems
, 3rd ed.,
Springer Berlin, Heidelberg
.
41.
Davila
,
A.
,
Aramburu
,
E.
, and
Freixas
,
A.
,
2013
, “
Making the Best Out of Aerodynamics: Platoons
,”
SAE Technical Papers
,
2
.
42.
Vahidi
,
A.
, and
Eskandarian
,
A.
,
2002
, “
Influence of Preview Uncertainties in the Preview Control of Vehicle Suspensions
,”
Proc. Inst. Mech. Eng. Part K: J Multi-body Dyn
,
216
(
4
), pp.
295
301
.
43.
Maciejowski
,
J. M.
,
2002
,
Predictive Control With Constraints
,
Pearson
,
London, UK
.
44.
Kingma
,
D. P.
, and
Ba
,
J.
,
2015
, “
Adam: A Method for Stochastic Optimization
,”
3rd International Conference on Learning Representations, {ICLR}
,
San Diego, CA
.
45.
Andersson
,
J. A. E.
,
Gillis
,
J.
,
Horn
,
G.
,
Rawlings
,
J. B.
, and
Diehl
,
M.
,
2019
, “
CasADi—A Software Framework for Nonlinear Optimization and Optimal Control
,”
Math. Program Comput.
,
11
(
1
), pp.
1
36
.
46.
Online
,
2022
, “Software IPG Automotive.”
47.
National Renewable Energy Laboratory
,
2022
, “
Fleet DNA Project Data
.”
48.
Online
,
2022
, “
ADEPT (Advanced Dynamic Efficient Powertrain Technology)
,”
Cummins Inc.
49.
Zanelli
,
A.
,
Domahidi
,
A.
,
Jerez
,
J.
, and
Morari
,
M.
,
2017
, “
FORCES NLP: An Efficient Implementation of Interior-Point Methods for Multistage Nonlinear Nonconvex Programs
,”
Int. J. Control
,
93
(
1
), pp.
13
29
.