Connectivity Enhanced Safe Neural Network Planner for Lane Changing in
  Mixed Traffic
Connectivity technology has shown great potentials in improving the safety
and efficiency of transportation systems by providing information beyond the
perception and prediction capabilities of individual vehicles. However, it is
expected that human-driven and autonomous vehicles, and connected and
non-connected vehicles need to share the transportation network during the
transition period to fully connected and automated transportation systems. Such
mixed traffic scenarios significantly increase the complexity in analyzing
system behavior and quantifying uncertainty for highly interactive scenarios,
e.g., lane changing. It is even harder to ensure system safety when neural
network based planners are leveraged to further improve efficiency. In this
work, we propose a connectivity-enhanced neural network based lane changing
planner. By cooperating with surrounding connected vehicles in dynamic
environment, our proposed planner will adapt its planned trajectory according
to the analysis of a safe evasion trajectory. We demonstrate the strength of
our planner design in improving efficiency and ensuring safety in various mixed
traffic scenarios with extensive simulations. We also analyze the system
robustness when the communication or coordination is not perfect.
Xiangguo Liu, Ruochen Jiao, Bowen Zheng, Dave Liang, Qi Zhu
# Connectivity Enhanced Safe Neural Network Planner

###### Abstract.

Connectivity technology has shown great potentials in improving the safety and efficiency of transportation systems by providing information beyond the perception and prediction capabilities of individual vehicles. However, it is expected that human-driven and autonomous vehicles, and connected and non-connected vehicles need to share the transportation network during the transition period to fully connected and automated transportation systems. Such mixed traffic scenarios significantly increase the complexity in analyzing system behavior and quantifying uncertainty for highly interactive scenarios, e.g., lane changing. It is even harder to ensure system safety when neural network based planners are leveraged to further improve efficiency. In this work, we propose a connectivity-enhanced neural network based lane changing planner. By cooperating with surrounding connected vehicles in dynamic environment, our proposed planner will adapt its planned trajectory according to the analysis of a safe evasion trajectory. We demonstrate the strength of our planner design in improving efficiency and ensuring safety in various mixed traffic scenarios with extensive simulations. We also analyze the system robustness when the communication or coordination is not perfect.

Connected and Autonomous Vehicles, Safe Neural Network Planner, Mixed Traffic, Human-driven Vehicles +
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planned trajectory does not need to complete the lane changing in one go. As long as there is a safe evasion trajectory, the ego vehicle can start the attempt and interact with surrounding vehicles. We analyze the worst case for the ego vehicle in dynamical environments. For the case without a connected leading vehicle, i.e., \(N=0\), we can directly assume that in the worst case, vehicle \(L_{1}\) takes the maximum deceleration under the mechanical constraints. In other cases that \(N>0\), we can leverage the coordination from connected vehicles to prevent overly conservative planning. We evaluate the fastest evasion trajectory of the ego vehicle in emergency situations. For instance, when there is an emergency brake in the downstream, connected vehicles that first realize the event can collaboratively take a smaller deceleration, if it is safe for themselves, thus leaving more reaction time for the ego vehicle. If the evasion trajectory can prevent collisions, the ego vehicle can proceed to change lanes under the neural network based planners, otherwise it has to hesitate around the boundary of the two lanes or return back to the original lane for safety.

The contribution of our work can be summarized as:

* We propose a connectivity-enhanced neural network based lane changing planner in mixed traffic environment with human-driven and autonomous vehicles, and connected and non-connected vehicles.
* Surrounding vehicles' behaviors are modeled via connectivity or aggressiveness assessment for safety analysis. Our planner design is guaranteed to be safe if the communication is perfect, the aggressive assessment is accurate, or if we choose to always treat the following vehicle as aggressive.
* We demonstrate significant system efficiency improvements by leveraging connectivity in dynamic environment, through simulations with comprehensive experimental settings. We also analyze system robustness when coordination between connected vehicles is not perfect.

The rest of this paper is organized as follows. In Section 2, we review related works on lane changing, inter-vehicle interaction, neural network-based planning and connected vehicles. In Section 3, we present our connectivity-enhanced planning framework. Section 4 shows the experimental results and Section 5 concludes the paper.

## 2. Related Work

Planner design in autonomous driving has been a very active research area for its potential impact in greatly improving transportation system performance and also its challenge in ensuring system safety at the same time. There is an urgent need to prevent overly conservative design while also provide safety guarantees when considering environment uncertainty and complex inter-vehicle interactions (Safet et al., 2017; Safet et al., 2018; Safet et al., 2018). The work in (Safet et al., 2018) proposes a concept of legal safety, which means that autonomous vehicles will not be the cause of accidents and there is no collision if surrounding vehicles obey traffic rules. This is realized by proving the existence of the fail-safe trajectory under the planner all the time. Similarly, the concept of responsibility-sensitive safety is proposed in (Safet et al., 2018), which assumes that other participants behave according to common-sense rules and defines appropriate responses of autonomous vehicles in near-accident scenarios. However, safety can be compromised if other vehicles' behaviors violate the assumptions. The works in (Safet et al., 2018; Safet et al., 2018) develop a non-conservatively defensive driving strategy, which leverages sampling based or optimization based methods. Planned trajectory is executed after the safety evaluation. Model Predictive Control (MPC) based approaches can address safety issues by applying constraints or designing cost functions (Safet et al., 2018; Safet et al., 2018).

Machine learning based techniques are increasingly popular in planning and decision making for autonomous driving (Safet et al., 2018; Safet et al., 2018; Safet et al., 2018), for their potential in improving average system performance under complex scenarios. The work in (Safet et al., 2018) proposes a concept of social perception, which inferences surrounding environment from other vehicles' reactions. It then leverages inverse reinforcement

Figure 1. The ego vehicle \(E\) intends to change lane. With connectivity technology, vehicle \(E\) receives planned acceleration profiles and real-time motion states from connected leading vehicles \(L_{i}\), \(1\leq i\leq N\), and then analyzes the maximum deceleration of vehicle \(L_{1}\) during the lane changing process. By identifying the behavior of following vehicle \(F\) and analyzing system safety in the worst case, vehicle \(E\) may proceed to change lane, hesitate around the current lateral position, or abort the lane changing plan. This figure shows an example with \(N=2\) and the following vehicle \(F\) is non-connected.
learning (IRL) to acquire cost function of human driving, and uses Markov Decision Process (MDP) to get probabilistically optimal solutions. (Hendle et al., 2017) formulates the lane changing planning problem as a partially observable Markov Decision Process (POMDP), in which the cooperativeness of other traffic participants is an unobservable state. It predicts future actions of human cars via logistic regression classifier, and solves the POMDP by Monta-Carlo Tree Search. The work in (Brockman et al., 2017) proposes a hierarchical reinforcement and imitation learning (H-REIL) approach specifically for near-accident scenarios, which consists of low-level policies learned by imitation learning (IL) for discrete driving modes, and a high-level policy learned by reinforcement learning (RL) that switches between different driving modes. (Hendle et al., 2017) proves the strength of a hierarchical neural network based planner regarding safety and verifiability, compared with a single neural network based planner.

Although these methods demonstrate great performance improvement, it is still quite challenging to verify the safety for learning-enabled systems (Srivastava et al., 2014; Sutskever et al., 2015). System efficiency is also restricted by uncertainties from perception (Srivastava et al., 2014) and prediction results of individual vehicles. And connectivity can enhance the transportation system by reducing such uncertainties (Brockman et al., 2017; Srivastava et al., 2014; Sutskever et al., 2015). For instance, the work in (Hendle et al., 2017) proposes an intersection management scheme, in which the central manager assigns arriving speed and arriving time to vehicles. It assumes that all vehicles are connected and autonomous. The approach in (Brockman et al., 2017) leverages Dynamic Bayesian Networks (DBNs) to model vehicle state evolution. The central manager can send out warning messages to vehicles for collision avoidance. It assumes that all vehicles are connected and human-driven, and collision rate depends on velocity and driver reaction time. The work in (Hendle et al., 2017) assumes that all vehicles are connected, and leverages deep reinforcement learning (DRL) for behavior-level decision making in lane changing. In particular, it gets performance improvement by incorporating traffic status in the downstream with vehicle-to-vehicle communication.

There are several works developed for mixed traffic (Brockman et al., 2017; Srivastava et al., 2014; Sutskever et al., 2015; Sutskever et al., 2015) of connected and non-connected vehicles. The work in (Hendle et al., 2017) presents an RL-based multi-agent longitudinal planner for connected and autonomous vehicles, which adjusts speeds in upstream traffic to mitigate traffic shock-waves downstream. The results suggest that even for a penetration rate of 10%, connected and autonomous vehicles can significantly mitigate bottlenecks in highway traffic. The approach in (Hendle et al., 2017) leverages RL for trajectory recommendation to the connected vehicles in highway merging scenarios. It assumes that not all vehicles are connected and uses camera in roadside for data fusion, in order to map all vehicles. The work in (Hendle et al., 2017) proposes an RL-based method for connected and autonomous vehicles to decide actions such as whether to change lane or keep lane based on the observation and shared information from neighbors. The system is modeled by hybrid partially observable Markov Decision Process (HPOMDP) as not all vehicles are connected. However, it does not explicitly model inter-vehicle interaction, and the safety highly depends on accurate modeling of the surrounding vehicles, especially non-connected vehicles. In this work, we propose a general lane changing planner with safety guarantee in mixed traffic, which can work safely and efficiently under any penetration rate of connected vehicles.

## 3. Design of our framework

### Overview

By leveraging the connectivity technology, our planner design can further improve system efficiency while ensuring system safety at the same time. The framework is presented in Figure 2. Based on the planned acceleration profiles in the planning horizon and the real-time motion states of surrounding vehicles, we can leverage neural networks for longitudinal and lateral trajectory planning. At the same time, we can derive the maximum deceleration of the leading vehicle \(L_{1}\) (scenario as shown in Figure 1), and then perform system analysis for the worst case and adjust trajectory to ensure safety. Here we adopt the same aggressiveness assessment method for the following vehicle \(F\) as in (Hendle et al., 2017) when vehicle \(F\) is non-connected. For the case that the following vehicle \(F\) is connected, we assume that it is collaborative.

Safety analysis and trajectory adjustment are conducted periodically. At every step during the lane changing, the ego vehicle has three behavior-level options with strictly decreasing preference: proceed changing lane, hesitate around current lateral position, or abort changing lane and return back to the original lane. It analyzes the state after executing the accelerations under neural network based planners for one time step. If it has a safe evasion trajectory in the worst case, it can go ahead and change lanes. Otherwise, it has to attempt a less preferred behavior until a safe evasion trajectory is found following that.

### Connectivity Assumptions

In this work, we assume that the connected leading vehicles \(L_{i}\), \(1\leq i\leq N\) (for example, \(N=2\) in the scenario from Figure 1) will collaboratively assist the lane changing process of the ego vehicle \(E\) and prevent collision with their own immediate leading vehicle \(L_{i+1}\). Specifically, the connected leading vehicle \(L_{i}\) will keep its acceleration within the range \([-a_{i}^{m,d},a_{i}^{m,a}]\) to execute its own driving task if that is sufficient for keeping a safe distance between \(L_{i}\) and \(L_{i+1}\). It is noted that the values of \(a_{i}^{m,d}\) and \(a_{i}^{m,a}\) will be communicated to other connected vehicles. Only in emerging scenarios, e.g., when the leading vehicle \(L_{i+1}\) decelerates suddenly, \(L_{i}\) can violate such '_promise_' and take a deceleration \(a_{x,i,d}>a_{i}^{m,d}\) to ensure safety. Note that this is considered as an _expected violation_ of the promise, and our planner framework can ensure safety in such cases (later in Section 4, we will demonstrate the impact when such promise is violated _unexpectedly_, e.g., when one surrounding vehicle is malfunctioning or influenced by other unknown obstacles).

To generalize the model, we assume that both connected human-driven vehicles and connected autonomous vehicles communicate their planned acceleration range to other vehicles in the same manner. However, human-driven vehicles could have larger acceleration range because there is typically larger uncertainty in human driver's behavior and execution process. For non-connected vehicles, we assume that it can take any acceleration value within their mechanical constraints.

### Safety Analysis

Next we will analyze the evasion trajectory given the system states. Assuming that vehicle \(L_{i}\) decelerates with \(a_{x,i,d}\), vehicle \(L_{i-1}\) needs
to decelerate with \(z_{x,i-1,d}\) to prevent collisions. By letting \(p_{m}\) denote the minimum safe distance between two vehicles, we have

\[\begin{cases}p_{x,i}+v_{x,i}t_{Li}+\frac{a_{x,i,d}t_{Li}^{2}}{2}-p_{x,i-1}-v_{x,i -1}t_{Li}-\frac{z_{x,i-1,d}t_{Li}^{2}}{2}-p_{m}=0\\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \
where \(p_{y,t_{0}}\) and \(v_{y,t_{0}}\) are the lateral position and velocity of the ego vehicle when \(t=0\). The centers of the original and target lane are \(y=0\) and \(y=w_{l}\), respectively. The width of a vehicle is \(w_{v}\).

As for the longitudinal motion, the optimal trajectory is analyzed intuitively when the immediate leading vehicle \(L_{1}\) decelerates with \(a_{x,d}\)[19]. It is that the ego vehicle first accelerates with \(a_{x,d}\) and then decelerates with \(a_{x,d}\), and keeps the distance gap no smaller than \(p_{m}\) when \(t\in[0,t_{y,f}]\). It is the fastest longitudinal motion to get closer to the leading vehicle, thus obtaining more time for the lateral evasion before the following vehicle catches up.

However, in this work, it is a more general situation that the leading vehicle \(L_{1}\) can have deceleration \(a_{x,1,d}\leq a_{x,d}\). Thus when the ego vehicle \(E\) decelerates to the same velocity with the leading vehicle \(L_{1}\), its deceleration should change from \(a_{x,d}\) to \(a_{x,1,d}\). Otherwise the headway of the ego vehicle will increase when its velocity is smaller than that of the vehicle \(L_{1}\). In that way, the ego vehicle is overreacting for collision avoidance, which cannot lead to an optimal trajectory.

There are three phases in the optimal longitudinal motion. The ego vehicle first accelerates with \(a_{x}=a_{x,a}\) when \(t\in[0,t_{x,1}]\), and then decelerates with \(a_{x}=-a_{x,d}\) when \(t\in[t_{x,1},t_{x,2}]\), and then decelerates with \(a_{x}=-a_{x,1,d}\) until it stops when \(t\in[t_{x,2},t_{y,f}]\). The position of the ego vehicle when \(t=t_{y,f}\) is formulated as

\[p_{x,t_{y,f}}=\begin{cases}p_{x,t_{0}}+p_{x,t_{0}}t_{x,1}+\frac{a_{x,d}t_{x,1} ^{2}}{2}+(p_{x,t_{0}}+a_{x,d}t_{x,1})(t_{y,f}-t_{x,1})\\ -\frac{a_{x,d}(t_{x,f}-t_{x,1})^{2}}{2}\\ \hskip 28.452756pt\text{if }\frac{a_{x,t_{0}}}{x,t_{0}}+a_{x,d}t_{x,1}-a_{x,d}(t_{ y,f}-t_{x,1})\\ \hskip 28.452756pt\text{}\geq max(0,x_{0,x_{1}}-a_{x,1,d}t_{y,f}),\\ p_{x,t_{0}}+p_{x,t_{0}}t_{x,1}+\frac{a_{x,d}t_{x,1}^{2}}{2}+(\frac{a_{x,t_{0}} +a_{x,d}t_{x,1})^{2}}{2a_{x,d}}\\ \hskip 28.452756pt\text{else if }\frac{a_{x,1}}{a_{x,1,d}}\leq\frac{a_{x,d}t_{x,1} ^{2}}{2}+(p_{x,t_{0}}+a_{x,d}t_{x,1})(t_{x,2}-t_{x,1})\\ -\frac{a_{x,d}(t_{x,2}-t_{x,1})^{2}}{2}-\frac{a_{x,1,d}(t_{x,f}-t_{x,2})^{2}}{ 2}\\ +(p_{x,t_{0}}+a_{x,d}t_{x,1}-a_{x,d}(t_{x,2}-t_{x,1}))(t_{y,f}-t_{x,2})\\ \hskip 28.452756pt\text{else if }\frac{b_{x,1}}{a_{x,1,d}}\geq t_{y,f},\\ p_{x,t_{0}}+p_{x,t_{0}}t_{x,1}+\frac{a_{x,d}t_{x,1}^{2}}{2}+(p_{x,t_{0}}+a_{ x,d}t_{x,1})(t_{x,2}-t_{x,1})\\ -\frac{a_{x,d}(t_{x,2}-t_{x,1})^{2}}{2}+\frac{(a_{x,t_{0}}+a_{x,d}t_{x,1}-a_{ x,d}(t_{x,2}-t_{x,1}))^{2}}{2a_{x,1,d}}\\ \hskip 28.452756pt\text{otherwise,}\end{cases} \tag{6}\]

where \(p_{x,t_{0}}\) and \(p_{x,t_{0}}\) are the longitudinal position and the velocity of the ego vehicle when \(t=0\), respectively.

Depending on the initial states and \(t_{y,f}\), there are four cases in Equation (6), which correspond to the four velocity curves in Figure 3. The black solid line and yellow dot dash line represent velocity curves of the ego vehicle \(E\) and the leading vehicle \(L_{1}\), respectively. The first case represents that the ego vehicle has already finished its lateral motion before it decelerates to the same velocity with vehicle \(L_{1}\) and changes its deceleration. The second case is that the ego vehicle decelerates with \(a_{x,d}\) until it stops, and then keeps \(v_{x}=0\) until \(t=t_{y,f}\). The third case is that the ego vehicle has already finished its lateral motion before it reaches \(v_{x}=0\) with deceleration \(a_{x,1,d}\). The fourth case represents that the ego vehicle decelerates with \(a_{x,1,d}\) until it stops, and then keeps \(v_{x}=0\) until \(t=t_{y,f}\).

Given that the two vehicles reach the same velocity when \(t=t_{x,2}\), we have \(v_{x,t_{0}}+a_{x,d}t_{x,1}-a_{x,d}(t_{x,2}-t_{x,1})=v_{x,1}-a_{x,1,d}t_{x,2}\). In all four cases, the distance gap between the ego vehicle \(E\) and the leading vehicle \(L_{1}\) reaches the minimum when \(t=t_{y,f}\). By letting \(p_{x,1,t_{y,f}}-p_{x,t_{y,f}}-p_{m}=0\), we can compute the value of \(t_{x,1}\) as

\[t_{x,1}=\begin{cases}t_{y,f}-\sqrt{t_{y,f}^{2}+\frac{2v_{x,t_{0}}t_{y,f}-a_{x, d}t_{y,f}^{2}+2p_{x,t_{0}}+2p_{m}-2p_{x,1,t_{y,f}}}{a_{x,d}+a_{x,d}}}\\ \hskip 28.452756pt\text{if }\frac{a_{x,t_{0}}}{a_{x,d}}+a_{x,d}t_{x,1}-a_{x,d}(t_{y,f}-t_{x,1})\\ \hskip 28.452756pt\text{}\geq max(0,v_{x,1}-a_{x,1,d}t_{y,f}),\\ -\frac{a_{x,t_{0}}}{a_{x,d}}+\sqrt{(\frac{a_{x,t_{0}}}{a_{x,d}})^{2}-\frac{2p_{ x,t_{0}}a_{x,d}+a_{x,d}^{2}+2p_{m}a_{x,d}-2p_{x,1,t_{y,f}}a_{x,d}}{(a_{x,d}+a_{x,d})a_{x,d}}}\\ \hskip 28.452756pt\text{else if }\frac{a_{x,1}}{a_{x,1,d}}\leq\frac{a_{x,t_{0}}a_{x,d}}{a_{x,d}}+t_{x,1} \leq t_{y,f},\\ -((a_{x,t_{0}}-a_{x,1})+\sqrt{(a_{x,t_{0}}-a_{x,1})^{2}-(2a_{x,d}+a_{x,1,d})C_{ 2}}\\ \hskip 28.452756pt\text{else if }\frac{a_{x,1}}{a_{x,1,d}}\geq t_{y,f},\\ -((a_{x,t_{0}}-a_{x,1})+\sqrt{(a_{x,t_{0}}-a_{x,1})^{2}-(2a_{x,d}+a_{x,1,d})C_{ 2}}\\ \hskip 28.452756pt\text{otherwise,}\end{cases} \tag{7}\]

where \(C_{2}=\frac{(b_{x,t_{0}}-b_{x,1})^{2}+(2p_{x,t_{0}}+2p_{m}-2p_{x,1})(a_{x,d}- a_{x,1,d})}{2(a_{x,d}+a_{x,d})}\).

It is noted that if \(t_{y,f}^{2}+\frac{2v_{x,t_{0}}t_{y,f}-a_{x,d}t_{x,f}^{2}+2p_{x,t_{0}}+2p_{m}-2p _{x,1,t_{y,f}}}{a_{x,d}+a_{x,d}}\leq 0\), the ego vehicle can keep accelerating until \(t=t_{y,f}\), i.e., \(t_{x,1}=t_{y,f}\), and remain safe. If \(2v_{x,t_{0}}t_{y,f}-a_{x,d}t_{y,f}^{2}+2p_{x,t_{0}}+2p_{m}-2p_{x,1,t_{y,f}}>0\) in the first case, or \(2p_{x,t_{0}}a_{x,d}+a_{x,t_{0}}^{2}+2p_{m}a_{x,d}-2p_{x,1,t_{y,f}}a_{x,d}>0\) in the second case, or \(C_{2}>0\) in the third and fourth cases, we have \(t_{x,1}<0\), which means the ego vehicle cannot prevent collisions even when it keeps decelerating with \(a_{x,d}\) from \(t=0\), which means that the safe evasion trajectory does not exist.

Let \(\tau_{1}\) denote the time that the ego vehicle decelerates to the same velocity with the leading vehicle, and let \(\tau_{2}\) denote the time that the ego vehicle longitudinally decelerates to a velocity of zero. We present \(\tau
Assuming that the following vehicle accelerates with \(a_{x,f}\in[-a_{x,d},a_{x,a}]\), its position at \(t\) is

(9) \[p_{x,f,t}=\begin{cases}p_{x,f}+v_{x,f}t+\frac{a_{x,f}t^{2}}{2}\\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \
is \(N=5\). The horizontal axes show the sudden deceleration of non-connected leading vehicle \(L_{N+1}\). It is considered to be successful if the ego vehicle finally crosses the border of two lanes within the simulation horizon without any collision. Because safety is ensured by the trajectory adjustment function and there is indeed no collision in all simulations, we only present the results of lane changing success rate.

As we expected, lane changing success rate decreases when the deceleration \(a_{x,N+1,d}\) gets larger. Under these planners, 'CV_all', 'CV_follow' and 'CV_none' correspond to full, partial and none utilization of connectivity, respectively. 'No_agg_assess' represents that when even aggressiveness assessment function is disabled, which leverages less information and is more conservative. It shows that 'CV_all' performs slightly better than 'CV_follow', and these two planners result in considerably larger success rate, when compared to 'CV_none' and 'No_agg_assess'. **This clearly shows the effectiveness of our approach in improving system performance.** It means that understanding the following vehicle's intention can greatly help the lane changing maneuver of the ego vehicle, and connectivity of leading vehicles can further improve that.

Table 1 shows the average lane changing success rate when \(N\) and \(a_{x,N+1,d}\) change. It consistently presents that the more utilization of connectivity, system performance is better. Moreover, when \(N\) gets larger, it results in larger success rate because more connected leading vehicles can cooperate to leave larger space for the ego vehicle.

Figure 5 demonstrates the performance of our planner design with a specific example, in which \(N=5\) and \(a_{x,N+1,d}=5\) meters per second squared. It shows the lateral position and longitudinal velocity of the ego vehicle under different planners. Under 'CV_all' planner, the ego vehicle completes lane changing in about three seconds. Under other three planners, the ego vehicle first move laterally to the target lane, and then turn back to the original lane when \(t=3\) seconds. 'CV_follow' results in longer time of staying in the target lane, compared with 'CV_none' and 'No_agg_assess'. In this example, 'CV_none' and 'No_agg_assess' lead to the same trajectory of the ego vehicle.

### Impact of Unexpected Promise Violation

According to the _promise_ assumption introduced in Section 3, connected leading vehicle \(L_{i}\) will keep its acceleration in the range

\begin{table}
\begin{tabular}{c c|c c c c} \hline \(N\) & \(a_{x,N+1,d}\) & CV\_all & CV\_follow & CV\_none & No\_agg\_assess \\ \hline \multirow{5}{*}{1} & 2 & 1 & 1 & 0.995 & 0.995 \\  & 3 & 1 & 1 & 0.875 & 0.83 \\  & 4 & 0.356 & 0.337 & 0.23 & 0.195 \\  & 5 & 0.001 & 0 & 0 & 0 \\  & 6 & 0 & 0 & 0 & 0 \\ \hline \multirow{5}{*}{3} & 2 & 1 & 1 & 1 & 1 \\  & 3 & 1 & 1 & 0.928 & 0.894 \\  & 4 & 0.998 & 0.982 & 0.712 & 0.672 \\  & 5 & 0.534 & 0.489 & 0.288 & 0.256 \\  & 6 & 0.01 & 0.008 & 0.024 & 0.022 \\ \hline \multirow{5}{*}{10} & 2 & 1 & 1 & 1 & 1 \\  & 3 & 1 & 1 & 1 & 1 \\ \cline{1-1}  & 4 & 1 & 1 & 0.993 & 0.998 \\ \cline{1-1}  & 5 & 1 & 1 & 0.969 & 0.956 \\ \cline{1-1}  & 6 & 1 & 1 & 0.95 & 0.928 \\ \hline \end{tabular}
\end{table}
Table 1. Lane changing success rate of different planners.

Figure 4. Lane changing success rate under different planners are compared when the number of connected leading vehicles is \(N=5\). The horizontal axes show the sudden deceleration of non-connected leading vehicle \(L_{N+1}\).

Figure 5. Lateral position and longitudinal velocity of the ego vehicle in an example scenario are plotted under different planners, when the number of connected leading vehicles is \(N=5\) and the deceleration of non-connected leading vehicle \(L_{N+1}\) is \(a_{x,N+1,d}=5\) meters per second squared.
\([-q_{i}^{m,d},a_{i}^{m,d}]\) as long as that does not hurt its own safety. Let us define the promise violation rate \(p_{o}\), which denotes the probability that the promise is violated unexpectedly in every control period. We assume that promise violation is independent among all connected vehicles, and the vehicle can take any deceleration following the uniform distribution \([z_{x,i,d},a_{x,N+1,d}]\) when violating the promise.

Figure 6 presents the collision rate and lane changing success rate under varied promise violation rate \(p_{o}\) when the first non-connected leading vehicle \(L_{N+1}\) takes different sudden deceleration \(a_{x,N+1,d}\). Generally speaking, a larger promise violation rate and deceleration result in smaller lane changing success rate and higher collision risk. However, when promise violation rate is within 20% and the sudden deceleration is less than 5 meters per second squared, collision rate is 0% and success rate remains to be relatively high.

## 5. Conclusion

In this work, we present a connectivity-enhanced planning framework for neural network based lane changing in mixed traffic. The framework can significantly improve lane changing performance by coordinating with surrounding connected vehicles in dynamic environment. Extensive experiments demonstrate the strength of our planner design in improving efficiency while ensuring safety. Our experiments suggest that (1) connectivity of the immediate following vehicle plays a more important role for ego vehicle's lane changing than the connectivity of leading vehicles, and (2) when there are more connected leading vehicles, the system performance can be further improved because more vehicles can coordinate to leave larger space for the ego vehicle. We also demonstrate the system robustness under different extent of promise violation rate of surrounding connected vehicles.

Figure 6. Collision rate and lane changing success rate under different promise violation rates are presented when the number of connected leading vehicles is \(N=10\). Promise violation rate \(p_{o}\) is the probability that the promise is violated unexpectedly every control period. We assume that promise violation is independent among all connected vehicles, and the vehicle can take any deceleration following the uniform distribution \([z_{x,i,d},a_{x,N+1,d}]\) when violating the promise. The horizontal axes show the sudden deceleration of non-connected leading vehicle \(L_{N+1}\).