Predictive Model-Based and Control-Aware Communication Strategies for Cooperative Adaptive Cruise Control

Utilizing Vehicle-to-everything (V2X) communication technologies, vehicle platooning systems are expected to realize a new paradigm of cooperative driving with higher levels of traffic safety and efficiency. Connected and Autonomous Vehicles (CAVs) need to have proper awareness of the traffic context. The cooperative platoon’s performance will be influenced by the communication strategy. In particular, time-triggered or event-triggered are of interest here. The expenses related to communication will increase significantly as the number of connected entities increases. Periodic communication can be relaxed to more flexible aperiodic or event-triggered implementations while maintaining desired levels of performance. This paper proposes a predictive model-based and control-aware communication solution for vehicle platoons. The method uses a fully distributed Event-Triggered Communication (ETC) strategy combined with Model-Based Communication (MBC) and aims to minimize communication resource usage while preserving desired closed-loop performance characteristics. In our method, each vehicle runs a remote vehicle state estimator based on the most recently communicated model and the event-driven communication scheme only updates the model when the performance metric error exceeds a certain threshold. Our approach achieves a significant reduction in the average communication rate (82%) while only slightly reducing control performance (e.g., less than 1% speed deviation).

SECTION I. Introduction

Cruise Control (CC) was originally created to maintain a steady speed set by the driver without any fluctuations. This approach is extended by Adaptive Cruise Control (ACC), which constantly monitors the longitudinal gap between the ego vehicle and its immediate leader and adjusts the velocity accordingly to maintain a safe distance. In contrast, ACC is incapable of providing strong string stability [1]. The exchange of information between vehicles can be leveraged to anticipate the motion of neighboring vehicles. Cooperative Adaptive Cruise Control (CACC), enabled by Vehicle-to-Vehicle (V2V) communication, promises to enhance traffic flow behavior regarding string stability while achieving short inter-vehicle gaps. When compared to ACC, this makes it more powerful in terms of preventing collisions while also maximizing traffic throughput [2], [3].

A platoon of Connected and Automated Vehicles (CAVs) can be represented by a Cyber-Physical System (CPS), which combines computation, communications, and physical processes on cyber and physical planes [4]. In these platoons, the physical plane closely relates to mobility behaviors, whereas the cyber plane describes communications behaviors among adjacent vehicles and infrastructures [5], [6], [7]. The backbone of distributed Multi-Agent Systems (MASs) is information exchange to create situational awareness. Excessive use of communication resources may lead to communication congestion, resulting in increased packet loss, high latency, and low throughput, all of which will inevitably degrade system stability, performance, and reliability [8], [9], [10]. Thus, a well-designed distributed control system in MASs must ensure not only satisfactory control performance but also preserve limited communication and computing resources.

Model-Based Communication (MBC) is a recent and innovative solution for managing communication scalability that has shown potential in reducing channel overload [11]. The primary goal of MBC is to use a more suitable data structure for transmitting packets containing the parameters of the joint vehicle dynamic/driver behavioral models than the data format of the Basic Safety Message (BSM), according to the J2735 standard [12]. Several modeling approaches may be used to represent the vehicle’s dynamics while employing the MBC approach. Gaussian Processes (GPs), which are non-parametric Bayesian inference techniques, are efficient methods for modeling joint vehicle’s dynamic/driver’s behavior.

It’s worth mentioning that most current studies on controlling vehicle platoons utilize Time-Triggered Communication, in which information is exchanged between two consecutive vehicles at a regular communication rate, as shown in Figure 1. In this case, data communications are activated on a regular basis regardless of measurement changes, even if the difference between two successively transmitted data is very small. TTC, which only schedules transmission based on time and not on the system status in real-time, frequently results in inefficient communication resource utilization, which is not desirable in CACC as previously mentioned. Hence, it is more reasonable to adopt communication methods that take into account available resources and determine transmission moments based on output measurements, in order to obtain a superior balance between effective communication and control performance. Event-Triggered Communication (ETC) provides such a resource-aware communication method, as shown in Figure 1. Another way to express the triggering mechanism in TTC is $$\begin{equation*} t_{k+1}=t_{k}+T_{s}, k \in \mathbb {N}\tag{1}\end{equation*}$$ where $t_{0} = 0$ and $T_{s}$ is the sampling time. The next communication time in ETC is governed by an event-triggering process that regularly checks if a specific condition based on the real-time state matrix becomes true. This condition often encompasses details about the state matrix $S(t)$ and its estimated value $\tilde S(t)$ at time $t_{k}$ and can be written, for instance, as $\mathcal {F}(S(t), \tilde S(t)) > 0$ . Formally, the transmission times are then decided based on $$\begin{equation*} t_{k+1}=\inf \left \{{t>t_{k} \mid \mathcal {F}\left ({S(t),\tilde S(t)}\right)>0}\right \}\tag{2}\end{equation*}$$ with $t_{0} = 0$ . Therefore, it is clear that a feedback mechanism exists in determining the next transmission time, which is dependent on the measured state matrix.

Fig. 1.

Approach change from Time-Triggered Communication (TTC) to Event-Triggered Communication (ETC). The error value increases over time, but it is revised when a new message is received. In ETC, the average communication rate can be changed by adjusting the triggering threshold.

Large-scale involvement of agents makes centralized control and management of MASs prohibitively expensive, if not impossible [13]. To address this problem and improve the scalability of MASs, it is more advantageous to perform distributed control by sharing local information between neighboring agents over wireless communication networks. Because of the range restrictions of communication and sensing technologies, controllers only have access to data from a nearby region. Thus, controllers rely only on local data to achieve platoon-wide performance. The trigger condition suggested in this work only needs data that is locally accessible, allowing for a distributed control strategy.

More generally, the rising acceptance of networked CPS across all disciplines is likely to be a strong motivator for these topics. In particular, the strong interdependence between the physical dynamics of the vehicle (physical parts), estimation/tracking module, and communication (cyber parts) highlight the requirements for more effective implementation of such systems, treating resources such as wireless communication and computation as resources rather than taking them for granted. Due to the compromise between the efficiency of the vehicle platoon control and communication resource usage, it is essential to design an effective ETC for the platoon. In this paper, we describe the development of such networks from a CPS viewpoint and offer a novel approach for modeling the interaction between different platoon components to enhance performance. The contributions of this paper are as follows:

• We proposed a predictive model-based and control-aware communication solution that combines ETC and MBC for cooperative control of vehicle platoons, achieving a significant reduction in the average communication rate while only mildly reducing control performance.

• We describe a fully distributed Event-Triggered Communication (ETC) approach for platooning that decreases the consumption of communication while preserving the desired closed-loop control performance.

• In our approach the minimum of inter-event times is lower bounded by one communication period, meaning that Zeno behavior is completely ruled out. In addition, multiple packet losses can be tolerated by the proposed method.

SECTION II. Related Work

The collective actions of CAVs are controlled by the vehicles’ situational awareness (e.g., inter-vehicle distance and vehicles’ speed), which is achieved through sensing and communication. The efficiency of cooperative applications is directly tied to the amount of successful vehicle information delivery and the number of vehicles that receive the information. This Section will go over one of the cooperative driving applications, CACC, and V2V communication.

A. Cooperative Adaptive Cruise Control (CACC)

CACC overcomes ACC’s most significant performance limitation: the uncertainty and delay in sensing the motions of the preceding vehicles. These sensor limitations restrict ACC from functioning in gaps shorter than one second, limiting its practicality in moderate to heavy traffic where other drivers may attempt to cut into the one-second gap. CACC systems must be able to handle special maneuvers like interfering vehicles cutting into CACC platoons or leading cars hard braking [3], [14], [15]. V2V communication, with its faster and more accurate information on the preceding vehicle’s motion, allows the CACC vehicle to follow the leading vehicle with greater precision and at a much shorter gap. This not only increases acceptance by users but also has the ability to enhance traffic flow dynamics and lane throughput capacity. Researchers have shown that platooning has significant potential to tackle various transportation problems [16], [17], [18]. For example, by forming vehicle platoons out of all passenger cars, road capacity can be increased by 200% [2].

A well-designed CACC must meet two objectives: The primary objective is to reduce the spacing error, or deviation from the safe gap, minimize collision risk, and maximize the benefits of platoon formation, such as lower fuel consumption and increased traffic flow. Due to the small gap between vehicles, fuel efficiency is improved significantly since aerodynamic drag is greatly reduced. As a result of such increased fuel efficiency, CO2 emissions are also decreased [19], [20], [21].

For vehicle $n$ with position $x_{n}(t)$ , speed $v_{n}(t)$ and desired spacing $d_{n}^{\ast}$ , the spacing error should satisfy $$\begin{equation*} \lim _{t \rightarrow \infty }\left \|{x_{n}(t)- x_{n-1}(t)}\right \|=d_{n}^{\ast}, \quad \text {for } n=1,\ldots, N_{v}-1\tag{3}\end{equation*}$$ The second goal is to reduce disturbances/shock waves along vehicle platoons. In other words, the platoon vehicles should travel at the same speed: $$\begin{equation*} \lim _{t \rightarrow \infty }\left \|{v_{n}(t)-v_{0}(t)}\right \|=0, \quad \text {for } n=1,\ldots, N_{v}-1\tag{4}\end{equation*}$$ where $v_{0}(t)$ is the leader’s speed. Detecting changes in the speeds of preceding vehicles is essential for attenuating or eliminating traffic shock waves that cause “stop and go” disturbances [3].

Communication issues can greatly affect the performance of CACC systems. If communication delays are too long or transmission rates are too low, string stability and other performance characteristics for a specific time gap may no longer be assured [22]. As a result, the transmission number must be large enough and packet delays must be short enough to achieve the desired platooning behavior [23].

Remark 1:

Generally, two common policies for platoon control are the Constant Distance (CD) and the Constant Time Headway (CTH). The choice between the two policies depends on whether the desired spacing between vehicles is dependent on their speed. The CD strategy can increase traffic capacity by keeping a smaller constant space between cars compared to the CTH policy [24].

B. Vehicle-to-Vehicle (V2V) Communication

The information exchange is critical for platoon deployment because it allows control actions to be taken based on the latest information on the road and traffic status. Many studies have been conducted to determine the effect of the communication network on platoon performance [25], [26]. One of TTC’s major flaws is its lack of flexibility and scalability. This Section discusses ETC and MBC as flexible and scalable solutions. The Cellular Vehicle-to-everything (C-V2X) standard requires a positive lower bound on the Minimum Inter-Event Time (MIET), that is, the minimum amount of time to pass between two consecutive transmissions [27]. This inter-packet duration is limited to $100 ms$ in the lower bound and $600 ms$ in the upper bound. The MIET ensures that the ETC system operates in a practical and feasible manner, avoiding an excessive number of transmissions that could result in Zeno behavior, which occurs when an infinite number of events occur in a finite amount of time.

1) Event-Triggered Communication

Event-based strategies are a popular way to ensure that communication resources are used efficiently in MASs and CPSs [28], [29]. Event-triggered control systems only send data when necessary, which reduces communication overhead and improves efficiency compared to time-triggered systems that send data at predetermined intervals regardless of actual system requirements. It is found that event-triggered systems exhibit better performance in real-time compared to time-triggered systems. The approach in [30] proposes a flexible event-triggering strategy that is based on tunable parameters for each platoon vehicle. The objective of the proposed approach is to reduce the communication burden by adjusting the trigger conditions for each vehicle based on the specific needs of the platoon. In [31], a distributed and adaptive event-triggered control mechanism is proposed using an external observer that estimates the leader’s state matrix.

In ETC, the triggering condition is an important component in determining events time instants, which is strongly associated with reducing the number of communication between neighbors. In general, the choice of such conditions should be physically interpretable. Furthermore, ETCs should be simple to implement in practice. These two points raise concerns about designing a suitable ETC for MASs. It should be noted that most of the ETCs used in the literature are categorized as follows:

• Centralized: utilizing all of the agents’ measurement data

• Decentralized: relies on the agent’s own data

• Distributed: using the information from itself and its neighbors.

Because they only use local information from individual agents rather than global information from all agents, decentralized and distributed event-triggered schemes are a more practical solution for designing event-triggered control systems in MASs.

Agents only communicate their current state to neighboring agents if either the difference from the last transmission is above a time-dependent threshold or when it reaches the upper bound of the inter-event interval. As a more practical constraint for event-triggered solutions, researchers have considered enforcing a minimum time between events [32]. Each vehicle’s event-triggered scheme can be defined as follows: $$\begin{equation*} t_{k+1} = t_{k} + \min \left ({\tau _{k}, \tau }\right),\tag{5}\end{equation*}$$ where $\tau$ is a positive constant that stands for the upper bound of the inter-event interval. $\tau _{k}$ is determined by the following equation, $$\begin{equation*} \tau _{k} = \inf _{t>t_{k}}\left \{{t-t_{k} \mid \mathcal {F}\left ({S(t) \:,\tilde S(t)}\right)>0}\right \}, \quad { \text {for }} t \geq 0. \tag{6}\end{equation*}$$ When new information is received, each agent will update its control input and use the received model for prediction. It is important to mention that these trigger moments are not synchronized among agents. In such methods, each vehicle runs a local copy of the dynamic of its neighbors. In the proposed configuration, each vehicle uses its own transmitted model to determine when to send data. Vehicles will not transmit a message if the prediction of the kinematic model from the last transmission remains accurate.

2) Model-based Communication

When designing CACC systems, we must explicitly account for the uncertainty in vehicle state, behavior, and communication [33]. Because the information from the neighboring vehicles is not continuously available, each agent must run an estimator between these instances, as shown in Figure 2. In this scheme, each agent uses a model to predict the measurements of the other agents when they do not receive a packet (either due to packet loss or because the transmission was not triggered), and the agent updates part of the state vector when new measurement data is obtained.

Fig. 2.

Each platoon member’s networking and control modules are illustrated in a block diagram. Ego vehicles will receive information from preceding vehicles if communication is successful, or they will update the information with the stochastic model estimator if data is not received (either due to packet loss or because the transmission was not triggered). The MPC will control the vehicle using the information provided by the networking module. Finally, if a triggering condition is detected, the control module will send current states and predicted velocity values to the networking module for broadcasting. Blue lines represent continuous data flow, whereas orange lines represent event-based data flow.

In this work, we look at each cooperating vehicle’s velocity time series, $v_{n}(t)$ , as a GP defined by the mean function $m_{n}(t)$ and the covariance kernel function $\kappa _{n}(t, t^{\prime })$ as $$\begin{equation*} v_{n}\left ({\mathbf {t}}\right) \sim \mathcal {G} \mathcal {P}\left ({m_{n}\left ({\mathbf {t}}\right), \kappa _{n}\left ({\mathbf {t}, \mathbf {t}^{\prime }}\right)}\right).\tag{7}\end{equation*}$$ We’re interested in bringing together the information provided by observed velocity data regarding the underlying function, $v_{n}(t)$ , and its future values. Assuming that for each cooperative vehicle, the mean of the velocity time series is zero, $m_{n}(t)=0$ , the covariance kernel is a Radial Basis Function (RBF), and the measurement noises are independent and identically distributed $(i.i.d.)$ with the Gaussian distribution $\mathcal {N}(0,\,\gamma _{n, noise}^{2})$ , the covariance matrix of the observed velocity of the $n^{th}$ cooperative vehicle is $$\begin{equation*} K_{n}\left ({\boldsymbol {t},\boldsymbol {t^{\prime }}}\right)= \kappa _{n}\left ({t,t^{\prime }}\right) + \gamma _{n,noise}^{2}I\tag{8}\end{equation*}$$ where $I$ denotes the identity matrix of dimension equal to the size of the training (measured) data and $\kappa _{n}(t,t^{\prime })$ can be calculated using the RBF definition as $$\begin{equation*} \kappa _{n}\left ({t,t^{\prime }}\right)=\exp \left ({-\frac {||t-t^{\prime }||^{2}}{2\gamma _{n}^{2}}}\right).\tag{9}\end{equation*}$$ Using the aforementioned assumptions, the joint distribution of the past observed values, $\mathcal {V}_{n}^{obs}$ , and the future values $\mathcal {V}_{n}^{\ast }$ , can be represented as $$\begin{align*} \left [{\begin{array}{l} \mathbf {\mathcal {V}_{n}^{obs}} \\ \mathbf {\mathcal {V}_{n}}^{\ast} \end{array}}\right] \sim \mathcal {N}\left ({\mathbf {0},\left [{\begin{array}{ll} K_{n}\left ({\boldsymbol {t}, \boldsymbol {t}}\right) & K_{n}\left ({\boldsymbol {t}, \boldsymbol {t^{\ast}}}\right) \\ K_{n}\left ({\boldsymbol {t^{\ast}}, \boldsymbol {t}}\right) & K_{n}\left ({\boldsymbol {t^{\ast}}, \boldsymbol {t^{\ast}}}\right) \end{array}}\right]}\right),\tag{10}\end{align*}$$ where $\boldsymbol {t}$ and $\boldsymbol {t^{\ast}}$ denote the sets of observation and future value time stamps, respectively, and $K_{n}(.,.)$ can be obtained from (8). Therefore, the predictive distribution of future velocity values, $\mathcal {V}_{n}^{\ast }$ , conditioned on having observed velocity values $\mathcal {V}_{n}^{obs}$ on time stamps $\boldsymbol {t}$ can be derived as; $$\begin{align*}&\Big (\mathbf {\mathcal {V}_{n}}^{\ast} \mid \mathbf {t^{\ast }}, \mathbf {t}, \mathbf {\mathcal {V}_{n}^{obs}}\Big) \sim \mathcal {N} \left ({\mu _{n}^{\ast },\Sigma _{n}^{\ast }}\right), \\&\;\mu _{n}^{\ast }=K_{n} \: \left [{\left ({t^{\ast }, t}\right)|\Theta _{n}}\right] \: K_{n}^{-1}\left [{\left ({t, t}\right)|\Theta _{n}}\right] \: \mathbf {\mathcal {V}_{n}^{obs}}, \\&\;\Sigma _{n}^{\ast }= -K_{n} \: \left [{\left ({t^{\ast }, t}\right)|\Theta _{n}}\right] \: K_{n}^{-1}\left [{\left ({t, t}\right)|\Theta _{n}}\right] \: K_{n}\left [{\left ({t, t^{\ast }}\right)|\Theta _{n}}\right] \\&\;\quad {}+K_{n}\left [{\left ({t^{\ast }, t^{\ast }}\right)|\Theta _{n}}\right]\tag{11}\end{align*}$$ where $\Theta _{n}$ is the set of parameters, e.g., $\Theta _{n}=\{\gamma _{n},\gamma _{n, noise}\}$ .

SECTION III. Preliminaries and Problem Formulation

It is difficult to significantly reduce V2V communication while preserving the desired efficiency of the vehicular platoon. As a result, one critical issue to address is how to design appropriate control schemes that can maintain satisfactory MAS control performance while significantly reducing the excessive use of communication and computing resources. In our control formulation, local information such as spacing error and velocity error is used in a relative sense, that is, in comparison to the agent’s own state, to revise the control input of each successive vehicle, allowing them to keep pace with the lead vehicles while maintaining a consistent headway interval between adjacent vehicles. During V2V communication outages, communication losses for CACC control were mitigated by using a GP to estimate the speed of the preceding vehicles.

A. Vehicle Model and Model Predictive Control (MPC) Design Approach

In this study, we consider a platoon of $N_{v}$ vehicles, where $n\in \{0,1,\cdots,N_{v}-1\}$ denotes the $n^{th}$ vehicle in the platoon as shown in Figure 3. $n=0$ represents the platoon leader and $d_{n}$ denotes the gap between $n^{th}$ and $(n-1)^{th}$ vehicles and is defined as $$\begin{equation*} d_{n} = x_{n-1}-x_{n}-l^{v}_{n},\tag{12}\end{equation*}$$ where $x_{n}$ and $l^{v}_{n}$ are the longitudinal location of the $n^{th}$ vehicle rear bumper and the vehicle length, respectively. The desired spacing policy can be defined as follows: $$\begin{equation*} d^{\ast}_{n}(t) = \delta _{n}\,v_{n}(t)+d^{s}_{n}.\tag{13}\end{equation*}$$ In (13), $v_{n}$ is the velocity of the $n^{th}$ vehicle, $\delta _{n}$ is the time gap, and $d^{s}_{n}$ represents the standstill distance. The difference between the gap and its desired value is defined as $\Delta d_{n}(t) = d_{n}(t)-d^{\ast}_{n}(t)$ , and the velocity difference between $n^{th}$ vehicle and its predecessor is defined as $\Delta v_{n}(t) = v_{n-1}(t)-v_{n}(t)$ . Hence, $\Delta \dot {d}_{n}$ turns into $\Delta \dot {d}_{n}(t)=\Delta v_{n}(t)-\delta _{n}\,a_{n}(t)$ and $\Delta \dot {v}_{n}=a_{n-1}-a_{n}$ , where $a_{n}$ denotes the acceleration of the $n^{th}$ vehicle. By taking the driveline dynamics $f_{n}$ into account, the derivative of the acceleration of vehicle $n$ is $\dot {a_{n}}(t) = -{f}_{n} a_{n}(t) + {f}_{n}u_{n}(t)$ , where $u_{n}(t)$ acts as vehicle input. By considering $S_{n}=[\Delta d_{n}\,\,\,\Delta v_{n}\,\,\, a_{n}]^{T}$ as the vector of states for $n^{th}$ vehicle, the state-space representation for each vehicle is $$\begin{align*} \dot {S}_{n}(t)=&A_{n}\,S_{n}(t)+B_{n}\,u_{n}(t)+D\,a_{n-1}(t) \\=&\begin{bmatrix} 0 & 1 & -\delta _{n} \\ 0& 0& -1\\ 0& 0& - {f}_{n} \end{bmatrix}S_{n}(t)+ \begin{bmatrix} 0 \\ 0\\ {f}_{n} \end{bmatrix}u_{n}(t)+ \begin{bmatrix} 0 \\ 1\\ 0 \end{bmatrix}a_{n-1}(t). \tag{14}\end{align*}$$ For $n=0$ (leader), $a_{n-1}(t)$ is replaced by zero. When the first-order forward time approximation is used, the discrete-time state-space model is described by the equation below. $$\begin{align*} S_{n}(k+1) = \left ({I+t_{s}\,A_{n}}\right)\,S_{n}(k)+t_{s}\,B_{n}\,u_{n}(k)+t_{s}\,D\,a_{n-1}(k), \tag{15}\end{align*}$$ where $t_{s}$ is the sampling time.

Fig. 3.

A graphical representation of the communication network structure. The information flow between vehicles is depicted using dashed lines. The distance between $n^{th}$ vehicle and its predecessor is shown by $d_{i}$ .

Some constraints on system states and input are also considered, such as acceleration and input ranges, road speed limit, and distance between vehicles (note that a negative distance implies collision and therefore should not occur). The following inequalities (hard constraints) should always hold true $$\begin{align*}&a_{n}^{min}\leq a_{n}(k)\leq a_{n}^{max},\tag{16a}\\&u_{n}^{min}\leq u_{n}(k)\leq u_{n}^{max},\tag{16b}\\&v_{n}(k)\leq v^{max},\tag{16c}\\&d_{n}(k)>0.\tag{16d}\end{align*}$$ Furthermore, system input changes are restricted for passenger comfort as $$\begin{equation*} t_{s}\,u_{n}^{min} \leq u_{n}(k+1)-u_{n}(k) \leq t_{s}\,u_{n}^{max}. \tag{17}\end{equation*}$$ The MPC design problem for each vehicle is $$\begin{align*} \min _{\textbf {u}_{n}}&\sum _{k=0}^{N-1}\Big [\left ({\mathbf {S}_{n}(k)-R_{n}}\right)^{T}\, Q_{n} \,\left ({\mathbf {S}_{n}(k)-R_{n}}\right)\Big] \\ {\mathrm{ subject\ to}}:\ &{\mathrm{ System\ Constrains}},\tag{18}\end{align*}$$ where $\textbf {u}_{n}$ is the system inputs from $k=0$ to $k=N-1$ .

Remark 2:

The given MPC problem formulation uses a one-look-ahead topology. By modifying the cost function in (18), the $r$ -look-ahead topology may be considered as follows. $$\begin{align*}&\sum _{k=0}^{N-1}\left [{\vphantom {\sum _{j=i+1}^{n}}\left ({\mathbf {S}_{n}(k)-R_{n}}\right)^{T}\, Q_{n} \,\left ({\mathbf {S}_{n}(k)-R_{n}}\right)}\right. \\&\;\qquad {} +\sum _{i=n-r}^{n-1}\left [{ c^{d}_{i}\,\left ({x_{i}(k)-x_{n}(k)-\sum _{j=i+1}^{n}\left ({d^{\ast}_{j}(k)+l^{v}_{j}}\right)}\right)^{2}}\right. \\&\;\left.{\left.{ \vphantom {\left ({\sum _{j=i+1}^{n}\left ({d^{\ast}_{j}(k)+l^{v}_{j}}\right)^{2}}\right)} \qquad \qquad \qquad \qquad {} +c^{v}_{i} \left ({v_{i}(k)-v_{n}(k)}\right)^{2}\vphantom {\sum _{j=i+1}^{n}}}\right]}\right],\tag{19}\end{align*}$$ where $c^{d}_{i}$ and $c^{v}_{i}$ are positive coefficients, and $r$ is the number of predecessors who shared data with the $n^{th}$ vehicle. In (19), each vehicle tends to reach the desired distances from its $r$ predecessors while changing its velocity dependent on the velocity of the predecessors. It is noted that when $r>n$ (the number of predecessors is less than $r$ ), the $n^{th}$ vehicle replaces $r$ with $n$ in (19).

B. Event-triggering conditions

Transmission instants in ETC schemes are determined online by a “smart” triggering criterion that is conditional on, for example, system output measurements so that transmission is only scheduled when necessary to guarantee some performance properties, as illustrated in Figure 1. It simply needs that the event-triggered condition be verified at each communication time instant on a regular basis. As a result, ETC may offer a better balance of communication resource use and control performance than TTC. It is important to note that if the condition in (6) is always violated at every communication instance, the ETC is reduced to the TTC. As a core component of the ETC, the Event Detector module in Figure 2 is responsible for determining when agent $n$ ’s measurement should be triggered for transmission.

ETC strategies can be used to control MASs cooperatively. The local control actions taken by individual agents in MASs should lead to the desired behavior of the entire system as a whole. The decentralization of ETC is another important extension of the previously mentioned ETCs, particularly in large-scale networked systems. The event-triggered condition is considered “fully distributed” because it does not require global information about the communication topology. In these systems, if each agent decides when to broadcast its state information on its own, not only a reduction in control effort, but also a decrease in network load. In [34] a distributed control law is developed based on the estimated state. The following conditions can be used to make such a decision.

1) Absolute Triggering

Exceeding a certain threshold in vehicle acceleration appears to be a reasonable choice to trigger an event. As a result, $\tau _{k}$ in (6) for absolute triggering may take the form of $$\begin{equation*} \tau _{k} = \inf _{t>t_{k}}\left \{{t-t_{k} \mid \|a(t)\| \geq \beta }\right \}, \quad { \text {for }} t \geq 0.\tag{20}\end{equation*}$$ Absolute triggering is used as a baseline in this paper.

2) Control-aware Triggering

Making explicit decisions based on current control system states results in a control-aware approach [35]. In desirable states, control systems perform modestly, whereas, in undesirable states, systems change their states and are given higher priority for data transmission. Transmission thresholds are set so that each vehicle can meet stability goals and make transmission decisions to meet performance targets while reducing the total transmission rate. As a result, $\tau _{k}$ in (6) for control-aware triggering will take the form of $$\begin{equation*} \tau _{k}=\inf _{t>t_{k}}\left \{{t - t_{k} \mid \|\mathcal {C}_{i}\| \geq \beta }\right \}, \quad { \text {for }} t \geq 0\tag{21}\end{equation*}$$ where $\mathcal {C}_{i}$ is the cost function in (19).

3) Model-based Triggering

In the previously mentioned triggering conditions, the estimated state value mainly relies on the hold value of the state variable. But, if there is sufficient information about the plant based on accurate models, improved predictions of the necessary signal can be obtained using such models. A model-based event-triggered predictive communication for networked control systems is built using the periodic event trigger scheme and takes into account the effect of packet loss in [36], [37], [38].

Between update intervals, a prediction of system states is made based on a shared model. In this section, we estimate the speed time series using MBC with GP. A triggering condition can be defined based on the estimated errors to determine when the next packet should be transmitted. For the prediction error, a constant threshold logic is used, that is, the difference between the measurement and its prediction average. The $\tau _{k}$ in (6) for the model-based event-triggering condition is given by $$\begin{equation*} \tau _{k}=\inf _{t>t_{k}}\left \{{t-t_{k} \mid \left \|{\hat {\mathcal {V}}(t)-\mathcal {V}(t)}\right \| \geq \beta }\right \}, \quad { \text {for }} t \geq 0\tag{22}\end{equation*}$$ where $\hat {\mathcal {V}}(t)$ denotes the mean of speed prediction.

As a result, when the predicted state deviates too much from the current state, the next event is triggered, and the next packet is sent. With this estimation, we can now design the event-triggering rule that operates locally in each vehicle to determine the times at which the updated state information should be transmitted. The use of model-based knowledge in the triggering schemes can result in a decrease in the number of transmission events and increased communication efficiency.

SECTION IV. Experimental Results

In our experiments, we treated Packet Error Rate (PER) as a random variable that is independently and identically distributed and increasingly changed it from 0 (representing perfect communication) to 0.6 (representing losing 60% of packets randomly), to investigate the effect of communication failure on the CACC system’s performance. The first vehicle in the platoon $(V_{0})$ serves as the speed reference for the rest of the vehicles in the platoon. The leader’s target velocity trajectory is specified as $$\begin{align*} v^{\ast}_{0}(t)= \begin{cases} 27 & t< 15\,s, \\ 0 & 15\,s\leq t < 30\,s, \\ 25 & t \geq 30\,s. \end{cases}\tag{23}\end{align*}$$ Acceleration or deceleration of the leader is seen as a disturbance in a platoon. In our simulations, the communication period is set to $100 ms$ , which is also the simulation step. The proposed strategy has been tested through simulation on a platoon of $N_{v} = 10$ vehicles to prove its viability and demonstrate its technical capabilities. The optimization problem is implemented using the CVXPY package in Python, and it is solved using the Gurobi optimization package [39], [40].

In our ETC scheme, each agent decides when to transmit its data to its neighbors based on real-time measurements and each vehicle’s event detection is independent. To check the event-triggering condition, each vehicle only needs to maintain the information of its most recent event-triggered moment and constantly keep an eye on its own state. The platoon’s information flow topology is tied to how vehicles get information about their surroundings [41]. Due to the range constraints of sensing and communication systems, each controller has access to information limited to the neighboring region. Therefore, controllers rely solely on local data to achieve platoon-wide performance. We used an All-Predecessor-Leader-Following (APLF) topology [22]. This paper considers V2V communication and local sensor measurements. The radar system measures the real-time positions of the preceding vehicle for collision avoidance, while other data, such as the leader’s position and speed, is transmitted via V2V communication.

Our approach links communication behavior with platoon performance, which depends on the amount of vehicle information successfully delivered and the number of nodes receiving the information [9]. The proposed triggering conditions are varied over a selected range to study their impact on the behavior of a platoon in terms of efficiency and safety.

A. Implementation Details

Table 1 contains the parameters utilized in the simulations. Each scenario takes $60s$ , in which the platoon’s goal is to keep the desired gap time of $0.6s$ with the preceding vehicle. Figure 2 illustrates the overall communication/control architecture. Each cooperative vehicle at each transmission opportunity utilizes its 5 most recent velocity observations, measured at equally-distanced $100 ms$ time intervals, to train a GP model and obtain the set of parameters $\Theta _{n}=\{\gamma _{n},\gamma _{n, noise}\}$ .

TABLE 1 The value of the parameters used in the model and optimization in the simulations.

After learning the GP parameters, the transmitting vehicle shares the model parameters as well as a history of the 5 most recent velocity measurements and the current position and acceleration with their time stamps. It should be noted that the Preceding Vehicles information module is used to predict data for the preceding vehicles and to immediately update its information when new data from the $n^{th}$ preceding vehicle is received. In addition, the 10 future velocity values (parameter $N$ in Table 1) predicted by the vehicle’s MPC are included in the transmitting packet. Every $100ms$ , the cooperative vehicles update the information of the preceding vehicles, either based on freshly received information from them or based on the GP prediction model. This information is fed into the MPC for updating the control action. Furthermore, the control module provides the ego vehicle’s optimal predicted state values. Finally, if a triggering condition is detected, the control module will broadcast current states as well as predicted future velocity trajectory values to the networking module. It should be noted that each agent’s Event Detector module only uses local information. As a result, our proposed ETC is decentralized. Time delays in networks can be treated similarly to packet loss in this structure and are thus not discussed in this paper.

B. Analysis and Results

We use the experimental results from a TTC scheme, which determines transmission instants based on a fixed transmission rate of $10 Hz$ , as a benchmark to assess the performance and communication resource usage of the suggested ETC techniques. To evaluate the performance of ETC against various other methods, the average transmission rate is used as a function of the network resource usage pattern. The distance error is defined as the absolute difference in meters between the actual and desired distance gaps. Also, the difference between the maximum and minimum speed and acceleration among all platoon members at each time step is a useful metric for evaluating traffic flow and CACC performance. We define these metrics as speed difference and acceleration difference. The mean of the absolute value of spacing error, speed difference, and acceleration difference for an ideal $10\,Hz$ TTC scheme are $\mathbf {0.302}\,m$ , $\mathbf {4.693}\,m/s$ , and $\mathbf {1.257}\,m/s^{2}$ , respectively (see Figure 4). These are the smallest errors achieved using our method.

Fig. 4.

Performance of the CACC with TTC, PER $=$ 0, and fixed communication rate of 10 Hz.

In Figures 4–​11 the first subplot (first row) shows the distance of each vehicle from its predecessor $(d_{n}(t))$ while the second subplot shows the velocity of each vehicle $(v_{n}(t))$ . The third subplot depicts the acceleration information for each vehicle, and in the last subplot, every time instance $(\xi _{n}(t))$ when a vehicle triggers a transmission is marked. It should be mentioned that $d_{0}(t)$ cannot be defined for the leader because there is no platoon member in front of it, therefore, $d_{0}(t)$ is not included in the first subplots of the mentioned figures.

Fig. 5.

Performance of the CACC with TTC, and PER $=$ 0.6, and fixed communication rate of 10 Hz.

Fig. 6.

Performance of the CACC with absolute triggering ETC, PER $=$ 0, level 6 threshold, and average communication rate of 4.75 Hz.

Fig. 7.

Performance of the CACC with absolute triggering ETC, PER $=$ 0.6, level 6 threshold, and average communication rate of 4.75 Hz.

Fig. 8.

Performance of the CACC with control-aware triggering ETC, PER $=$ 0, level 6 threshold, and average communication rate of 5.28 Hz.

Fig. 9.

Performance of the CACC with control-aware triggering ETC, PER $=$ 0.6, level 6 threshold, and average communication rate of 5.28 Hz.

Fig. 10.

Performance of the CACC with model-based triggering ETC, PER $=$ 0, level 6 threshold, and average communication rate of 1.80 Hz.

Fig. 11.

Performance of the CACC with model-based triggering ETC, PER $=$ 0.6, level 6 threshold, and average communication rate of 1.80 Hz.

Despite the smooth acceleration shown in Figure 4, the acceleration profile in all other figures fluctuates due to a lack of precise information (either because the packets were lost or because the transmissions were not triggered). Vehicles using the proposed communication paradigm can safely follow the vehicle in front of them. The threshold level for absolute triggering, control-aware triggering, and model-based triggering are six equally spaced steps of $0.1 \, m/s^{2}$ to $1.1 \, m/s^{2}$ , 200 to 700, and $0.1 \, m/s$ to $1.1 \, m/s$ , accordingly.

Despite the fact that the ETC scheme greatly decreases communication usage, its responses are similar to those of the TTC scheme (Figures 4, 6, 8 and 10). These findings demonstrate that the frequency of communication can be significantly reduced while maintaining the desired control performance. Because we use an ideal communication $(PER=0)$ for these figures, we only considered the effect of the ETC scheme. These figures represent the simulation’s best-case scenario for the level 6 threshold. It is important to note that the only difference between Figures 6, 8, and 10 is the ETC scheme. To see the combined effect of ETC and PER refer to Figures 5, 7, 9 and 11. We considered the combined effect of the ETC and PER because we use non-ideal communication $(PER=0.6)$ for these figures. These figures represent the worst-case scenario of the simulation under consideration in this paper (the highest level of threshold and the highest level of PER). It is important to note that the only difference between Figures 7, 9 and 11 is the ETC scheme.

In Figure 6 (absolute triggering), if a vehicle accelerates/decelerates rapidly, all vehicles respond by sending out messages. For example, as shown in the last subplot, all of the vehicles are transmitting packets between times $0\,s$ to $10\,s$ , $20\,s$ to $25\,s$ , and $35\,s$ to $40\,s$ . In Figure 8 (control-aware triggering), communication triggering is based on the real-time state of the control system. Because the platoon’s last members will have a relatively worst control situation (they must compensate for the errors of preceding vehicles in order to provide a string stable platoon), they will transmit more frequently. For instance, communication events for $\xi _{8}(t)$ and $\xi _{9}(t)$ are always one. In Figure 10 (model-based triggering), the model-based ETC generates inter-event times that are only small when the desired speed has changed significantly and otherwise equal to the enforced upper bound of the inter-event time (demonstrating that “communication is only used when truly necessary”).

Figure 12 presents the results for different PER values for level 1 and level 6 thresholds. The figure shows the mean of the spacing error, the mean of the speed difference, and the mean of the acceleration difference for TTC, absolute triggering ETC, control-aware triggering ETC, and model-based triggering ETC. It should be noted that TTC outperforms other approaches in terms of spacing error and speed difference. As expected, as the PER rises, we can see that the performance degrades; however, the proposed approaches perform similarly to TTC. Each data point is an average of 10 simulation rounds. It is important to highlight the contrast between the various methods, given the scale is not huge, for example, for spacing error, it is just under $5\,cm$ , and for speed difference, it is just under $0.06\,m/s$ , and for acceleration difference, it is just under $0.1\,m/s^{2}$ .

Fig. 12.

The mean of the spacing error, the mean of the speed difference, and the mean of the acceleration difference for TTC (fixed communication rate of 10 Hz), absolute triggering ETC (average communication rate of 4.75 Hz), control-aware triggering ETC (average communication rate of 5.28 Hz), and model-based triggering ETC (average communication rate of 1.80 Hz) based on different PER values.

Table 2 illustrates the approaches with a numerical example and demonstrates how the trigger level can be selected to compare performance against the average communication rate. Each data point is an average of 70 simulation rounds to provide a better sense of performance (10 rounds of simulation for each PER value). The numbers in the Error column show the mean of spacing error $(m)$ , speed difference $(m/s)$ , and acceleration difference $(m/s^{2})$ , respectively. The simulation outcomes indicate that an ETC, i.e., model-based triggering, can achieve high performance and reduce network load by 82% in comparison to a TTC. In other words, for model-based triggering, the average communication rate is $1.80\,Hz$ while we used a $10\,Hz$ fixed rate for TTC. Additionally, the implementation of ETC results in a negligible decrease in control performance, with speed deviation being less than 1% for model-based triggering and TTC $(4.704\,m/s$ and $4.693\,m/s$ , respectively).

TABLE 2 Statistics for various ETC approaches with varying threshold levels.

A trade-off between control effectiveness and communication frequency is induced by the ETC strategy. As can be seen, lowering the trigger level leads to a greater data transmission rate yet with a reduced error. Long inter-event time results in significant performance errors. As a result, raising the threshold will degrade the control performance. The error of different approaches does not differ significantly depending on the scale. Intuitively, the networked control system with the periodically evaluated event-triggering conditions will behave in a similar fashion as the TTC system as long as the communication rate is sufficient.

SECTION V. Conclusion

The use of event-triggered cooperation in large-scale networks is becoming popular as the number of interconnected CPS increases. Time-triggered coordination strategies are not efficient for large networks with many interconnected devices, as they do not perform well when the number of devices surpasses previous considerations. Such constraints necessitate a shift away from periodic communication toward opportunistic approaches, such as those covered in this paper, which effectively manages resources using the agents’, the environment’s, and the task’s knowledge. V2V is a crucial element in CACC systems, allowing for overcoming the limitations of sensors and establishing string-stable platoons with close inter-vehicle gaps. In MPC controllers, an optimization problem is solved using the communicated predicted state of the leading vehicles to obtain the ego vehicle’s control input. As a result of anticipatory behavior modeling in this approach, driving efficiency is increased by dynamically altering spacing and speed. Excessive use of communication resources, on the other hand, can have an adverse effect on the reliability of the wireless channel. As a result, in this article, a resource-sensitive CACC communication method is suggested, with the goal of reducing the utilization of communication resources compared to conventional TTC methods while maintaining system performance. Alternatively, the performance of the system can be improved given a fixed communication rate. Additionally, the minimum interval between events has a guaranteed lower bound to prevent Zeno behavior.

In addition, we combined MBC with ETC to propose a communication strategy for distributed multi-agent coordination. Agents choose the transmission instances for new measurements based on local data, primarily the difference between the current state/model and the latest broadcast state/model. Only the event-triggered condition needs to be regularly evaluated and performed at each communication time. Simulation results demonstrate that an ETC can be implemented with good performance, reducing network load by 82% compared to a TTC, with only a small reduction in control performance (less than 1% speed deviation). We achieve similar performance improvements using both control-aware and MBC methods. For future work, we plan to investigate the combination of these methods, which requires addressing the challenge of embedding control dynamics in MBC models.