Bayesian Methods in Automated Vehicles Car-following Uncertainties Enabling Strategic Decision Making

2025-05-06 0 0 1.81MB 22 页 10玖币

侵权投诉

Bayesian Methods in Automated Vehicle’s Car-following

Uncertainties: Enabling Strategic Decision Making

Wissam Kontara, Soyoung Ahna,∗

aCivil and Environmental Engineering, University of Wisconsin-Madison, USA

Abstract

This paper proposes a methodology to estimate uncertainty in automated vehicle (AV) dynamics

in real time via Bayesian inference. Based on the estimated uncertainty, the method aims to

continuously monitor the car-following (CF) performance of the AV to support strategic actions

to maintain a desired performance. Our methodology consists of three sequential components: (i)

the Stochastic Gradient Langevin Dynamics (SGLD) is adopted to estimate parameter uncertainty

relative to vehicular dynamics in real time, (ii) dynamic monitoring of car-following stability (local

and string-wise), and (iii) strategic actions for control adjustment if anomaly is detected. The

proposed methodology provides means to gauge AV car-following performance in real time and

preserve desired performance against real time uncertainty that are unaccounted for in the vehicle

control algorithm.

Keywords: Bayesian Inference, Stochastic Gradient, Langevin Dynamics, Linear Control, Car

Following, Autonomous Vehicle, Real time, Decision Making, Uncertainity Quantiﬁcation

1. Introduction

Skepticism toward Autonomous Vehicle’s (AVs’) ability to coexist in our transportation system

in a safe, eﬀective, and desirable manner has been a momentous barrier to the market deployment

of AVs. A critical element in the development and deployment of AVs is the design of car-following

(CF) controllers capable of producing desirable performance in real-world settings. Ideally, a CF

control system would eﬀectively and safely handle the longitudinal maneuvers of the vehicle at

every encounter it faces. However, designing and training such a controller requires enormous data,

testing, and experimentation that covers all possible driving scenarios/encounters. In other words, it

requires us to have a perfect understanding of the environment these AVs would be operating under.

Clearly, this is very challenging and, possibly, unattainable. AVs are likely to encounter unseen

scenarios and be exposed to exogenous and endogenous uncertainties in the physical world. The

sources of exogenous and endogenous uncertainties are vast and roughly classiﬁed into (Macfarlane

and Stroila, 2016; Yao et al., 2020; Katrakazas et al., 2015): (i) vehicular and system dynamics (e.g.,

vehicle condition, road gradient, aerodynamic drag force, external loads, transmission, brake, the

performance of the engine, etc.), (ii) environmental conditions (snow, dust, wind, wet conditions,

etc.), and (iii) situational detection (e.g., sensor/measurement errors, radar errors, vehicle speed

ﬂuctuations, vehicle localization, communication latency, etc.). All these types of uncertainties

can hinder desirable performance (e.g., stability). Yet, a major challenge lies in the complexity

of integrating these uncertainties into the control system and the design of the AV. For instance,

∗Corresponding author: sue.ahn@wisc.edu

arXiv:2210.13683v1 [eess.SY] 25 Oct 2022

it is often hard to formulate an analytical representation of these uncertainties and quantify their

impact on performance. Additionally, even when these uncertainties can be modeled through

parameterization, the complexity of formulation increases signiﬁcantly. The caveat, however, is that

such uncertainties are most inﬂuential on the CF control as they can alter the desired performance,

resulting in actuation lag and a mismatch between demanded acceleration and realized acceleration

of the AV. Such behavior has been shown to impact the local/string stability of the vehicle and the

traﬃc system as a whole (Yao et al., 2020; Kontar et al., 2021; Zhou et al., 2020; Zhou and Ahn,

2019).

Guided by empirical experimentation, analytical analysis, and commercial product investigation

(e.g., factory ACC vehicles and current self-driving technologies), the literature has recently given

speciﬁc interest to how vehicular dynamics impact the performance of the vehicle. A typical CF

controller consists of an upper-level and lower-level control. The upper-level functions as a planner

that receives sensor data (on distance, velocity, acceleration) and sends commands to the lower-

level to execute (i.e., braking, accelerating, etc.). Notably, there could be a discrepancy between

the commanded action (upper-level) and the executed action (lower-level). This has been shown to

be the reality in real-life driving conditions. The assumption of perfect execution of commands by

low-level controllers has been shown to be unrealistic, with signiﬁcant implications on local/string

stability and overall performance (Zhou and Ahn, 2019; Gunter et al., 2019; Li, 2020; Zhou et al.,

2019; Wang et al., 2018; Zhou et al., 2017; Yi and Do Kwon, 2001; Zhou and Ahn, 2019; Shi and Li,

2021; Yi and Do Kwon, 2001; Zhou et al., 2022). A recent paper by (Zhou et al., 2022) investigates

the signiﬁcance of low-level control for ACC vehicles on string stability. Their theoretical and

empirical investigations connect disturbances’ frequency and ampliﬁcations to low-level control

functions.

The exact factors that cause a discrepancy between demanded (by upper-level) and executed

actions (by lower-level) are hard to pinpoint due to the complexity of behavior, non-linearity, and

high dimensionality of such factors (multiple exogenous and endogenous factors play a role here).

However, signiﬁcant attention has been given to uncertainties impacting vehicular dynamics. Some

limited eﬀorts to deal with such uncertainties have led to the development of robust control methods

that adjust system states for uncertain vehicular dynamics. Most notably, the General Longitu-

dinal Vehicle Dynamics (GLVD) model is considered in robust control frameworks to formalize

such uncertainties. The GLVD model parameterizes two key uncertainties in vehicular dynamics:

actuation lag and the ratio of demanded acceleration that can be realized. The basic idea is to ac-

knowledge that lower-level controllers are not perfectly able to execute the demanded acceleration.

Thus the controller adjusts its acceleration according to the GLVD equation. The GLVD param-

eters are shown to greatly inﬂuence CF performance and local/string stability (Li et al., 2018; Yi

and Do Kwon, 2001; Wang, 2018). However, a critical challenge in modeling such parameters is

that the vehicle’s kinematic/dynamic information can be lost due to non-linearity and complexity

of dynamics, particularly when a vehicle is traversing under a high speed, a large curvature, or a

unique condition (Yao et al., 2020). A recent empirical study also showed that control sensitivity

factors (i.e., control gains that regulate the behavior) could vary depending on speed and headway

settings, thus signifying highly nonlinear control mechanisms (Shi and Li, 2021). Thus, the param-

eters of the GLVD equation are highly stochastic and correlated with the traﬃc state and even

geometric and environmental conditions.

Given the profound impact on CF control performance and stability, the stochasticity of GLVD

vehicle dynamics parameters should be addressed in a real-time setting. The principal idea here

is that we cannot fully account for all exogenous/endogenous uncertainties that might aﬀect the

vehicle’s performance while traversing the physical world simply because we cannot ascertain the

nature of these uncertainties. Thus, it is beneﬁcial to allow the performance of an AV in real-time to

speak for itself. We do so by utilizing the sensor data by an AV (speed, acceleration, jerk, position,

etc.) and estimating the real-time value of the GLVD parameters to see how much uncertainty is

occurring in our system.

Note that parameter estimation techniques have been employed in some control systems to

address stochasticity in control parameters and improve control accuracy. Some notable algorithms

include the Kalman ﬁlter, least-squares error estimate, parameter identiﬁcation, reinforcement-

learning methods, and neural predictive networks. Yao et al. (2020) reviews some applications of

these algorithms and presents the respective disadvantages of each algorithm. For instance, these

algorithms often fail to scale in an online setting, can require a large amount of data, or yield

large errors when dynamics are non-linear. Nonetheless, parameter estimation techniques could

provide eﬀective means to address parameter uncertainty. Yet, their usage in vehicular dynamics,

particularly GLVD parameters, is yet to be used. Additionally, and on a more critical note, the

fundamental shortcoming of the application of such methods is the inability of users/designers to

take strategic actions on the performance of the AV in real-time if anomalies (e.g., performance loss

due to large uncertainties ) are detected. The beneﬁt of strategic-actions, is that only through it we

can connect the individual performance of an AV, to the overall performance of the traﬃc system

containing the AV. This particular challenge is what this work aims to tackle. To the extent of the

author’s knowledge, there are not yet any existing methodologies or applications in the literature

that tackles this challenge.

We conjecture that addressing exogenous and endogenous uncertainties in CF control should

be done both at the modeling level (e.g., robust control design) and the decision-making level (e.g.,

dynamic updating of control parameters). This paper focuses on the latter and aims to develop

a methodology to estimate uncertainties in vehicle dynamics, as modeled in GLVD, in real-time

and monitor the performance of CF control to enable strategic decisions if needed. Speciﬁcally, the

methodology comprises three elements: (i) Bayesian inference of parameter uncertainties in GLVD

that can be dynamically updated in response to diﬀerent driving scenarios and capture unobserved

stochasticity, (ii) dynamic monitoring of CF performance such as stability, and (iii) strategic ad-

justment of parameters to improve the CF control performance if an anomaly is detected. Note

that Bayesian inference is usually computationally demanding, which renders online applications

impractical. To overcome this issue, we utilize Stochastic Gradient Langevin Dynamics (SGLD) to

formulate a stochastic optimization problem that estimates uncertainties in GLVD parameters in

real-time and continuously update the estimates on the ﬂy with new sensor measurements. Build-

ing on this, we develop a monitoring methodology that continuously assesses the performance of

the CF controller, speciﬁcally local and string stability requirements. This integrated framework

allows for strategic adjustment of controller parameters to induce desired performance in a more

adaptive manner. Therefore, the main novelty of this paper lies in adaptive AV CF control enabled

by the integrated framework of real-time uncertainty quantiﬁcation and dynamic monitoring of the

CF controller performance.

The rest of the paper is organized as follows: Section 2 presents a background analysis of the

impacts of parameter uncertainties of vehicular dynamics on AV CF stability. Section 3 provides

the details of the mathematical formulation for our real-time uncertainty estimation model. Then

Section 4 describes the parameter monitoring schemes and how they are combined with strategic

parameter adjustment to preserve the desired performance of the controller. Finally, discussion and

concluding remarks are provided in Section 5.

2. Background

This section introduces the basis of linear CF controller - which will be used here to showcase our

modeling and applicability in diﬀerent scenarios - and highlights the potential impact of vehicular

dynamics on performance. Speciﬁcally, we show how the GLVD equation can be incorporated into

a typical linear controller and the underlying impacts on local and string stability.

2.1. Linear Controller Background

Linear controllers are widely adopted control algorithms, primarily due to their analytical prop-

erties and stability guarantees. They have rich theoretical and methodological literature and

have recently shown great promise in real-life applications, speciﬁcally on ACC/CACC systems

(Shladover et al., 2015; Li et al., 2021; Gunter et al., 2020; Milan´es and Shladover, 2014; Morbidi

et al., 2013). While various linear control systems exist in the literature, their underlying control

strategy is relatively consistent. In this paper, we focus mainly on robust linear controllers that

incorporate vehicular dynamics. Speciﬁcally, we focus on the state-of-the-art controller developed

by Zhou and Ahn (2019) for demonstration purposes. It provides mathematical formulations of

local/string stability requirements while incorporating vehicular dynamics and communication de-

lays. Note that the overall methodology developed in the present paper is primarily data-driven

(as will be shown in Sec.3) and thus can be adapted to diﬀerent control paradigms (e.g., MPC).

The controller developed by Zhou and Ahn (2019) follows a hierarchical design whereby the

upper-level controller regulates the CF behavior based on the widely adopted constant time gap

policy (CTP). Accordingly, the state space formulation is deﬁned as x(t) = [∆s(t),∆v(t), a(t)]T,

where ∆s(t) is the deviation from target spacing deﬁned by a constant time gap τ∗, ∆v(t) is the

speed diﬀerence with the leading vehicle, and a(t) is the actual acceleration of the vehicle.

Notably, this design assumes that acceleration is not perfectly implemented due to various

uncertainties in vehicular dynamics (e.g., vehicle condition, gear position, aerodynamic drag, road

gradient, etc.). Accordingly, a lower-level controller is added, which adopts the GLVD equation to

incorporate such uncertainties. The formulation of vehicle dynamics in GLVD is shown in Eq. 1

(Yi and Do Kwon, 2001; Wang, 2018).

˙a(t) = −1

a(t) + KL

u(t) + (t) (1)

where ˙a(t) is the vehicle’s jerk, a(t) is the actual acceleration, u(t) is the demanded acceleration

by the controller at time t.TLis the actuation time lag, and KLis the ratio of the demanded

acceleration that can be realized. u(t) is determined through the feedback control law as u(t) =

kx(t), where k= [ks, kv, ka] is a vector of feedback control gains that regulates ∆s(t), ∆v(t),

and a(t), respectively. (t) is an additive error term. (Note that a feedforward gain parameter

that considers uncertain communication delays in the presence of vehicle-to-vehicle or vehicle-to-

infrastructure communication is added in Zhou and Ahn (2019); however, for conciseness, we will

not consider such uncertainties.)

One can clearly notice how parameters TLand KLinﬂuence the actual acceleration of the

vehicle as compared to the demanded acceleration by the controller. Previous literature has also

highlighted the relation of parameters TLand KLto uncertainties in vehicular dynamics (Li et al.,

2018; Trudgen and Mohammadpour, 2015; Gao et al., 2016). Ideally, if no external disturbances

aﬀect the controller, a(t) = u(t), and thus TL= 0 and KL= 1. In reality, however, TLand KL

are highly stochastic parameters and carry signiﬁcant impact on the local/string stability of the

vehicle as highlighted below.

2.2. Impact of Vehicular Dynamics on Local and String Stability

Local stability (dissipation of disturbances over time) and string stability (attenuation of distur-

bances over a vehicular string) are two critical attributes in developing safe and eﬀective automated

traﬃc. In Zhou and Ahn (2019), suﬃcient and necessary local and string stability conditions are

mathematically derived as shown below (readers are referred to the cited paper for the proof and

details, we only show here some formulation for the sake of illustration):

•Suﬃcient and necessary conditions for local stability:











1−Ku

Lka>0

ksτ∗+kv>0

ks>0

1

−kaks∗τ∗+kv>Tu

1

L−kaks∗τ∗+kv>Tl

(2)

•Conditions for string stability:











Ku

Lka−12−2Tu

LKu

Lτ∗ks+kv>0

Kl

Lka−12−2Tu

LKu

Lτ∗ks+kv>0

Lh2kska+ (τ∗ks+kv)2−k2

vi−2ks>0

(3)

In a typical controller, the control gains k= [ks, kv, ka], time gap setting τ∗, and parameters

TLand KLare preset for each vehicle. However, parameters TLand KLare stochastic in nature,

and there is no guarantee that they remain consistent in real-life conditions. For instance, the

recent empirical analysis on commercial ACC-enabled vehicles by Gunter et al. (2020) estimated

systematic delays in system sensors to be 0.1−1 seconds. Note that these delays are related to

second-order lags (i.e., pertaining to speed and location), whereas TLand KLare related to third-

order lags. While the estimates of second-order lags are not strictly equivalent to TLor KL, they

suggest the signiﬁcant impact of these parameters and variation in experienced delays by real-life

vehicles. (Wang et al., 2018) shows the impact of diﬀerent actuation lag values on the acceleration

proﬁle of the vehicle controller and its overall stability.

In the formulation above TLand KLare assumed to be random but bounded: i.e., 0 < T l

L≤

TL≤Tu

Land 0 < Kl

L≤KL≤Ku

L. In essence, the vehicle is stable given that TLand KL

remain within the bounded regions. If these parameters vary beyond these limits due to uncertain

conditions in real life, stability will be impacted. Further, even within the desired bounds, variability

in these parameters may hamper the eﬀectiveness of resolving disturbances. To visualize the extent

of the impact, we simulate the stability regions in diﬀerent scenarios. Speciﬁcally, we highlight the

impact of the actuation lag TLand time gap setting τ∗as a function of control gain settings. Note

that these ﬁgures are only intended to showcase general patterns rather than deep quantitative

analysis. In a previous work by the authors, we showcase how stability regions are impacted by

controller gains (Kontar et al., 2021), and (Zhou and Ahn, 2019) provides deeper insights into

theoretical stability region. Fig. 1 shows that when TLincreases, the stability regions shrink

signiﬁcantly. This is expected as with a large actuation lag, the actual acceleration of the vehicle

is far oﬀ the demanded acceleration by the controller, which leads to undesired performance. This

further suggests that the misspeciﬁcation of this parameter can yield unstable behavior. Notably,

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

BayesianMethodsinAutomatedVehicle'sCar-followingUncertainties:EnablingStrategicDecisionMakingWissamKontara,SoyoungAhna,aCivilandEnvironmentalEngineering,UniversityofWisconsin-Madison,USAAbstractThispaperproposesamethodologytoestimateuncertaintyinautomatedvehicle(AV)dynamicsinrealtimeviaBayesianinfe...

展开>> 收起<<

Bayesian Methods in Automated Vehicles Car-following Uncertainties Enabling Strategic Decision Making.pdf

共22页,预览5页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Bayesian Methods in Automated Vehicles Car-following Uncertainties Enabling Strategic Decision Making

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: