Energy-efficient Reactive and Predictive Connected Cruise Control_2

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Energy-eﬃcient Reactive and Predictive Connected Cruise Control

Minghao Shena,∗, R. Austin Dollarb, Tamas G. Molnarc, Chaozhe R. Hed, Ardalan Vahidie, G´

abor Orosza,f

aDepartment of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA

bGeneral Motors, Concorde, NC 28027, USA

cDepartment of Mechanical and Civil Engineering, California Institute of Technology, Pasadena, CA 91125, USA

dPlusAI, Inc., Cupertino, CA 95014, USA

eDepartment of Mechanical Engineering, Clemson University, Clemson, SC 29634, USA

fDepartment of Civil and Environmental Engineering, University of Michigan, Ann Arbor, MI 48109, USA

Abstract

In this paper, we propose a framework for the longitudinal control of connected and automated vehicles traveling in

mixed traﬃc consisting of connected and non-connected human-driven vehicles. Reactive and predictive controllers

are proposed. Reactive controllers are given by explicit feedback control laws. In predictive controllers, the control

input is optimized in a receding-horizon fashion, which depends on the predictions of motions of preceding vehicles.

Beyond-line-of-sight information is obtained via vehicle-to-vehicle (V2V) communication, and is utilized in the pro-

posed reactive and predictive controllers. Simulations utilizing real traﬃc data are used to show that connectivity can

bring signiﬁcant energy savings.

Keywords: connected automated vehicles, V2X connectivity, MPC, traﬃc ﬂow models

1. Introduction

Energy eﬃciency of vehicles is an everlasting topic in the auto industry, since improving energy eﬃciency can

bring great ﬁnancial and societal beneﬁts [1]. As such, driving proﬁles play an important role in the energy consump-

tion: with the same vehicle traveling on the same route, diﬀerent drivers may have diﬀerent driving proﬁles, which

results in great diﬀerence in the energy consumption [2]. This shows great potential for improving energy eﬃciency

by optimizing driving proﬁles.

While human drivers have large variations in their driving behavior [3], which may undermine the energy eﬃ-

ciency, vehicle automation eliminates such variation and provides a more accurate and consistent way to improve

energy eﬃciency. SAE categorizes automated vehicles into 6 levels (0-5); see Table. 1. Since energy consumption is

mainly related to longitudinal motion, level 1-2 automation can already provide signiﬁcant energy savings. On one

hand, automated vehicles (AV) may optimize their speed proﬁle in advance, taking into consideration the engine and

transmission dynamics, and the road elevation along the route [4, 5]. On the other hand, extensive research has focused

on optimizing the control input (pedal, brake and gear shift) to follow some optimal driving cycles [6]. However, these

two methods do not take traﬃc into consideration. In real traﬃc, vehicles may not be able to follow pre-deﬁned ideal

trajectories.

With level 1 or 2 automation, AVs rely on adaptive cruise control (ACC) algorithm to react to motion of preceding

vehicles in traﬃc. ACC has a long history tracing back to the 1990s. The controller design usually falls into one of

the two categories: reactive controller or predictive controller. Reactive ACC (RACC) has explicit feedback control

laws that are usually parameterized, so that the controller parameters can be optimized for the energy eﬃciency while

ensuring other speciﬁcations such as stability. On the other hand, predictive ACC (PACC) can directly optimize

the future trajectory based on the prediction of the future motions of neighboring vehicles. While predictions may

∗Corresponding author.

Email addresses: mhshen@umich.edu (Minghao Shen), rdollar@clemson.edu (R. Austin Dollar), tmolnar@caltech.edu (Tamas G.

Molnar), hchaozhe@umich.edu (Chaozhe R. He), avahidi@clemson.edu (Ardalan Vahidi), orosz@umich.edu (G´

abor Orosz)

Preprint submitted to Transportation Research Part C: Emerging Technologies October 11, 2022

arXiv:2210.04397v1 [eess.SY] 10 Oct 2022

SAE Level Execution of steering,

acceleration/deceleration

Monitoring of

driving environment

Fallback performance

of dynamic driving task

System capability

(driving modes)

0 (No automation) Human Human Human N/A

1 (Driver assistance) Human & system Human Human Some driving modes

2 (Partial automation) System Human Human Some driving modes

3 (Conditional automation) System System Human Some driving modes

4 (High automation) System System System Some driving modes

5 (Full automation) System System System All driving modes

Table 1: SAE Levels of Vehicle Automation

Motion Prediction

of Remote Vehicle

Motion Planning

of Ego Vehicle

Control of

Ego Vehicle

Status Sharing Ego Vehicle Ego Vehicle Ego Vehicle

Intent Sharing Remote Vehicle Ego Vehicle Ego Vehicle

Agreement Seeking Remote Vehicle Remote Vehicle Ego Vehicle

Prescriptive Cooperation Remote Vehicle Remote Vehicle Remote Vehicle

Table 2: SAE Levels of Cooperative Driving Automation (CDA)

signiﬁcantly improve energy eﬃciency, an accurate prediction is very hard to make without additional information,

since the motions of neighboring vehicles can be highly correlated or completely stochastic.

Vehicle-to-vehicle (V2V) communication can potentially resolve this problem. Peer-to-peer communication en-

ables connected vehicles to share information for prediction and control, as well as facilitates cooperation among

vehicles in the traﬃc. SAE categorized cooperative driving automation (CDA) into status-sharing, intent-sharing,

agreement-seeking and prescriptive cooperation [7]; see Table 2. Many of the existing research works assume high

level of cooperation, e.g., prescriptive cooperation. Assuming that an entire platoon of vehicles are connected and

automated, the high level of cooperation enables centralized control over all these vehicles. Such controllers are often

referred to as cooperative adaptive cruise control (CACC). Similar to ACC, CACC design can also be categorized

into reactive and predictive control [8, 9]. Reactive control tries to synchronize the speed of the platoon, guaranteeing

string stability and maintaining desirable headway [10, 11]. On the other hand, predictive controllers have access

to the future motion plans of leading vehicles, therefore coordinated and even global optimization becomes possi-

ble [12, 13, 14, 15, 16]. To make the system more scalable, distributed control protocol has also been studied [17].

Research has shown that CACC and platooning bring signiﬁcant energy beneﬁts under diﬀerent scenarios [18, 19, 20].

However, currently the V2V technology is far from being widely deployed. The assumption of high penetration of

connectivity and high level of cooperation is hard to realize in practice in the near future.

The near future of transportation is more likely to evolve into mixed traﬃc. Controllers that operate under mixed

traﬃc consisting of connected and non-connected vehicles are referred to as connected cruise control (CCC). Only

low-level cooperation as status-sharing is assumed and centralized control is not possible. Potentially four kinds of

vehicles may paticipate in the mixed traﬃc: human-driven vehicle (HV), connected human-driven vehicle (CHV), au-

tomated vehicle (AV) and connected and automated vehicle (CAV). Without connectivity, the longitudinal controllers

for AVs execute adaptive cruise control. While with connectivity, CAVs may execute more performant controllers,

even with low level of cooperation such as status-sharing protocol. In CCC, CAVs have access to beyond-line-of-sight

information of CHVs and CAVs in the distance, which is incorporated into the controller design. Similar to ACC and

CACC, CCC can also be categorized into reactive control and predictive control. Reactive CCC (RCCC) takes the

V2V information from leading vehicles as reference signals, the objective is still to synchronize the speed in the traﬃc

for string stability and smooth driving [21, 22, 23]. Meanwhile, predictive CCC (PCCC) can incorporate the informa-

tion of preceding vehicles to make predictions on the motion of the vehicle immediately in the front [24]. This may

signiﬁcantly improve predictions, and enable optimized planning of motions in advance, which may reduce speed

variations and save energy. In Fig. 1 the concepts of RACC, PACC, RCCC, and PCCC are illustrated graphically for

mixed traﬃc scenarios containing HVs, AVs, CHVs, and CAVs.

With all these distinctions made, this paper presents contributions to improve energy eﬃciency in mixed traﬃc as

AVHV HV HV HV

CAVHV HV CHV HV

Reactive Connected Cruise Control (RCCC)

Reactive Adaptive Cruise Control (RACC)

(c)

(a)

AVHV HV HV HV

Predictive Adaptive Cruise Control (PACC)(b)

CAVHV HV CHV HV

Predictive Connected Cruise Control (PCCC)(d)

Figure 1: Illustration of longitudinal control strategies for automated vehicles (AVs) and connected automated vehicles (CAVs) traveling in mixed

traﬃc that involves human-driven vehicles (HVs) and connected human-driven vehicles (CHVs). Predictive controllers rely on the predictions on

the future motions of preceding vehicles, as is shown in shadowed vehicles.

CAVHV HV CHV HV

0 1 L

Hidden

Vehicles

Figure 2: Connected cruise control in mixed traﬃc consisting of connected and non-connected vehicles.

follows:

•We provide design framework on reactive and predictive control of connected automated vehicles driving in

mixed traﬃc consisting of connected and non-connected vehicles.

•Under both reactive and predictive controller framework, we show the signiﬁcant energy beneﬁts provided by

V2V connectivity. We provide explanations to the energy savings by comparing simulated trajectories.

•We compare the reactive and predictive controllers in three typical scenarios and show the beneﬁt of predictive

controllers while utilizing real traﬃc data.

The remainder of this paper is organized as follows. Section 2 introduces the problem setting and longitudinal

dynamics of vehicles. Section 3 discusses the design of energy-eﬃcient reactive controllers including RACC and

RCCC. Section 4 discusses predictive controller designs including PACC and PCCC. Section 5 shows the energy

beneﬁts of diﬀerent controller designs with lean penetration of connected vehicles. Section 6 concludes this paper and

points out future research directions.

2. Vehicle Dynamics

In this section, we introduce the problem setup, and derive the state space model for longitudinal controller design.

Consider the connected cruise control scenario in Fig. 2, in which a connected and automated vehicle (CAV) is driving

on a ﬂat road without elevation change, with the intention to follow human-driven traﬃc. The longitudinal dynamics

of the CAV with respect to its position sand velocity vcan be modeled as in [25]:

˙s=v,

˙v=−1

meﬀmgξ+kv2+Tw

meﬀR.(1)

Here the eﬀective mass meﬀ=m+I/R2incorporates the mass m, mass moment of inertia Iand the radius Rof the

wheels. Moreover, gis the gravitational constant, ξdenotes the rolling resistance coeﬃcient and kdenotes the air resis-

tance coeﬃcient. We can control the vehicle speed by applying diﬀerent torque on wheels Twusing the engine/electric

motors and the brakes. To highlight how control actions inﬂuence the system, we consider the commanded accelera-

tion as control input u, and rewrite (1) as

˙s(t)=v(t),

˙v(t)=−fv(t)+satu(t−σ),(2)

where

f(v)=−1

meﬀmgξ+kv2,satu(t−σ)=Tw(t)

meﬀR.(3)

The model incorporates the delay σin powertrain system, and the saturation sat(·) arising from limitations of en-

gine/motor power, engine/motor torque and braking capability. More speciﬁcally, the saturation is modeled as

sat(u)=min n˜umax,max{umin,u}o,(4)

˜umax =min {umax,m1v+b1,m2v+b2},(5)

as is shown in Fig. 3(a) and (b). Here umin is the minimum acceleration (maximum deceleration) due to the braking

capability, and m1,m2,b1,b2are determined by engine torque limit and power limit.

In order to follow the desired acceleration, ad, the control action

u(t)=˜

fv(t)+ad(t),(6)

is applied, where the term ˜

ftries to compensate the nonlinear physical eﬀects fin (3). In this article, we assume that

perfect compensation is possible and focus on the choice of desired acceleration ad, which simpliﬁes (1) to

˙s(t)=v(t),

˙v(t)=satad(t−σ),(7)

Energy consumption is the main interest in this article. It is evaluated with energy consumption per unit mass

w=Ztf

v(t)g˙v(t)+f(v(t))dt,(8)

where g(x)=max{x,0}implies that braking does not consume or recover energy. We remark that the eﬀects of energy

recovering systems can be included by choosing diﬀerent gfunctions, but this is beyond the scope of this article.

In what follows, we investigate the energy eﬃciency of four types of controllers: RACC, RCCC, PACC and

PCCC; as summarized by Table 3. These four controllers are detailed in the next two sections and in Algorithms 1-4.

3. Reactive Controllers

In this section, we design control algorithms for reactive adaptive cruise control (RACC) and reactive connected

cruise control (RCCC). We start with the simple RACC case, where an automated vehicle is controlled and there is

no connected vehicle in the traﬃc, as is shown in Fig. 1(a). With on-board sensors such as camera, lidar or radar, the

ego vehicle can only react to the vehicle immediately in the front. RACC determines the desired acceleration adas a

function of headway h, its speed v, as well as the speed v1of the vehicle immediately in the front:

ad=F(h,v,v1),(9)

where h=s1−s−lis related to the positions sand s1of the vehicles and the length lof the ego vehicle, as is shown

in Fig. 2. For example, optimal velocity model (OVM) yields the control algorithm

FOVM(h,v,v1)=αV(h)−v+βW(v1)−v,(10)

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Energy-ecientReactiveandPredictiveConnectedCruiseControlMinghaoShena,,R.AustinDollarb,TamasG.Molnarc,ChaozheR.Hed,ArdalanVahidie,G´aborOrosza,faDepartmentofMechanicalEngineering,UniversityofMichigan,AnnArbor,MI48109,USAbGeneralMotors,Concorde,NC28027,USAcDepartmentofMechanicalandCivilEngineering,C...

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