Adaptive and Reliable Multi-Risk Assessment and Management Control Strategy for Autonomous Navigation in Dense Roundabouts *
自适应可靠的多风险评估和管理控制策略，用于密集环形交叉口的自主导航

Keywords: Adaptive control architecture, Risk Assessment and Management, Trajectory planning, Roundabout crossing
关键词：自适应控制架构，风险评估与管理，轨迹规划，环形交叉口

The roundabout is a very common road infrastructure that regulates road traffic and allows to greatly reduce the number of accidents compared to a conventional intersection. France is the country that contains the most roundabouts in the world with approximately 30000 roundabouts and builds between 500 and 800 roundabouts per year Dalloni (2021). This kind of intersection is very common because, unlike conventional intersections with traffic lights, roundabouts could a continuous traffic flow. This kind of intersection permits to reduce between 50 to the number of accidents Deluka Tibljaš et al. (2018) by decreasing the speed of vehicles wanting to pass through this intersection. Further, the vehicle arriving at this roundabout must adapt its speed according to the vehicles circulating in the roundabout, which have the priority, to always respect a safety distance between vehicles. In the literature, roundabouts are divided into several parts with a Decision zone where the EV does not have the priority and must evaluate the possibility of safe insertion.
环形交叉路口是一种非常常见的道路基础设施，它规范道路交通并能够大大减少与传统十字路口相比的事故数量。法国是世界上拥有最多环形交叉路口的国家，约有30000个环形交叉路口，并每年建造500至800个环形交叉路口（Dalloni，2021）。这种交叉路口非常常见，因为与带有交通信号灯的传统十字路口不同，环形交叉路口可以实现连续的交通流。这种交叉路口可以通过降低希望通过该交叉路口的车辆的速度，从而将事故数量减少50至 （Deluka Tibljaš等人，2018）。此外，到达这个环形交叉路口的车辆必须根据环形交叉路口内行驶的车辆调整速度，后者具有优先权，以始终保持车辆之间的安全距离。在文献中，环形交叉路口被分为几个部分，其中包括一个决策区，在这个区域，电动车没有优先权，必须评估安全插入的可能性。

A Transition zone that allows to reach the Ring zone and the last part is the Exit zone to go out the roundabout Masi et al. (2022), Rodrigues da Silva et al. (2022).
一个过渡区，允许到达环形交叉路口，并且最后部分是离开环形交叉路口的出口区域 Masi 等人（2022），Rodrigues da Silva 等人（2022）。

The curvature path is the first important information to maximize the speed window during the insertion, taking into account the comfort and the safety during the insertion. Before defining the speed to insert a roundabout containing obstacles, the EV must know the global path that allows it to pass through the roundabout, from the initial roundabout entrance to the desired exit section. The curvature of the path can give information about the speed limit, taking into account the lateral acceleration and the comfort. Some works have proposed to use Bezier curves to create a path to navigate in a roundabout Vinayak et al. (2021), Lattarulo et al. (2020), González et al. (2017), Rastelli et al. (2014). Nevertheless, all these approaches consider single-lane roundabouts. A two-lane roundabout is considered with paths based on clothoids Rodrigues da Silva et al. (2022), Silva and Grassi (2017) where the planned path is smooth with a continuous curvature but for the authors in Rastelli et al. (2014), the computation of this solution is more complex and expensive than using Bezier curves.
曲率路径是最大化插入速度窗口的第一个重要信息，考虑到插入过程中的舒适性和安全性。在定义插入圆环包含障碍物的速度之前，电动车必须了解全局路径，使其能够通过圆环，从初始圆环入口到期望的出口部分。路径的曲率可以提供关于速度限制的信息，考虑到横向加速度和舒适性。一些研究提出使用贝塞尔曲线创建在圆环中导航的路径 Vinayak 等人（2021 年），Lattarulo 等人（2020 年），González 等人（2017 年），Rastelli 等人（2014 年）。然而，所有这些方法都考虑单车道环岛。双车道环岛考虑基于布洛伊曲线的路径 Rodrigues da Silva 等人（2022 年），Silva 和 Grassi（2017 年），其中计划的路径平滑连续曲率，但对于 Rastelli 等人（2014 年）的作者来说，计算这个解决方案比使用贝塞尔曲线更复杂和昂贵。

Fig. 1. Overall proposed Multi-Risk Assessment and Management (MRAM) control architecture.
图 1. 总体提出的多风险评估和管理（MRAM）控制架构。

The desired speed to enter a roundabout, considering its diameter, is described in Rodegerdts (2010). For a roundabout with a diameter between 13 and , the entry speed should be between 25 and maximum. In Garcia Cuenca et al. (2019a) and García Cuenca et al. (2019b), a learning-based approach is used to define the predictive model of vehicle speeds and steering angles considering the size of the roundabout and other traffic participants. Another learning-based approach proposes to define whether it is safe to enter a roundabout and makes a decision learned from past examples Wang et al. (2018). In Masi et al. (2022), virtual projections are used to predict the dynamic situation in the roundabout. This solution uses communicating EVs and assumes that the intentions of the obstacles are considered known precisely. If we do not know the intentions of the obstacle-vehicle (in case of a human driver for instance), two virtual copies of the obstacle-vehicle are created at the ends of the possible paths to manage obstacles that can go out of the roundabout.
考虑到环岛的直径，进入环岛的理想速度在Rodegerdts（2010）中有描述。对于直径在13到 之间的环岛，进入速度应该在25到 之间。在Garcia Cuenca等人（2019a）和García Cuenca等人（2019b）中，采用基于学习的方法来定义预测车辆速度和转向角的模型，考虑到环岛的大小和其他交通参与者。另一种基于学习的方法提出了定义是否安全进入环岛的决策，并从过去的案例中学习决策，Wang等人（2018）。在Masi等人（2022）中，使用虚拟投影来预测环岛中的动态情况。该解决方案使用通信的电动车，并假设障碍物的意图被准确知晓。如果我们不知道障碍物车辆的意图（例如人类驾驶员的情况），则在可能路径的末端创建两个障碍物车辆的虚拟副本，以管理可能离开环岛的障碍物。

In this paper it is proposed a Multi-Risk Assessment and Management Control Strategy (MRAM-CS) allowing, on the one hand, to generate a flexible path for the entire roundabout navigation that respects the constraints of the static environment and the road traffic law, and on the other hand, an adaptive speed profile allowing a safe navigation through the roundabout while considering dense OVs flow. The dense roundabout treatment in the literature prioritizes the stop of the EV on the yield lane. It can be very penalizing because the waiting time can be long Medina-Lee et al. (2022). This paper is structured as following. Section 2 presents the overall proposed MRAM-CS. The first subpart of the MRAMCS is the Multi-Risk Assessment (cf. Section 3) with the Predictive Inter-Distance Profile (PIDP) metric. The Multi-Risk Management (cf. Section 4) with its main components such as an adaptive PD controller and a fuzzy fusion process to manage multiple obstacles. Simulation results are presented in Section 5 and a conclusion and some prospects are given finally in section 6 .
在本文中，提出了一种多风险评估和管理控制策略（MRAM-CS），一方面，可以为整个环形交叉路口导航生成灵活的路径，遵守静态环境和道路交通法规的约束，另一方面，提供一种自适应速度曲线，允许安全地通过环形交叉路口导航，同时考虑到密集的 OV 流量。文献中对密集环形交叉路口的处理优先考虑了 EV 在让行车道上停车。这可能会很惩罚性，因为等待时间可能会很长（Medina-Lee 等人，2022 年）。本文结构如下。第 2 节介绍了整体提出的 MRAM-CS。MRAMCS 的第一个子部分是多风险评估（参见第 3 节），具有预测性的互距轮廓（PIDP）度量。多风险管理（参见第 4 节）及其主要组成部分，如自适应 PD 控制器和模糊融合过程，以管理多个障碍物。模拟结果在第 5 节中呈现，最后在第 6 节中给出结论和展望。

The proposed control strategy for risk assessment and management is summarized in Figure 1. The perception and localization block is not discussed in this paper, but it is important to highlight the main inputs necessary for the proper functioning of the proposed overall strategy. It is assumed that a High Definition map is embedded in the where the static environment is described and allows to compute the path respecting the code and structure of the road (cf. Section 3.1). The embedded sensors allow to observe the dynamic environment with the ability to characterize and predict the behaviors of the encountered obstacles (e.g., calm, aggressive, ...) and allows to define their trajectories through an horizon time constant , corresponding to the inputs of the used monitoring metric, which is the Predicted Inter-Distance Profile (PIDP) (cf. Section 3.2). The block 2 given in Figure 1, corresponds to the architectural feature that allows to define the desired dynamic minimum safety temporal distance that should be maintained by the EV w.r.t. each detected OV, according to its behavior and also its velocity. In order to make the focus on the main contributions of the paper, this block will not be discussed in detail below. The minimum safety distance is assumed to be constant. It is important to notice that the proposed MRAM-CS works with the same strategy whether is variable or not. In this paper, obstacles behaviors are not treated but they can have different initial speeds. The proposed MultiRisk Assessment is based on the continuous monitoring metric PIDP (cf. Figure 1, block 3) allowing to define the groups of OVs that impose a same behavior on the EV (cf. Figure 1, block 4). The Multi-Risk Management (cf. Section 4 and Figure 1, block 5 and 6 ) allows to apply an adaptive speed profile based on an adaptive PD controller to find the right speed profile to maintain the safety distance with the considered obstacle and also based on a fuzzy fusion process to manage the groups of OVs. Once the proposed Multi-Risk Assessment and Management Strategy obtains the most suitable setpoints for the EV, it uses an appropriate Control law (defined by the block 7 in Figure 1). The nonlinear control law Vilca et al. (2015) allows to drive the EV towards a static or dynamic target
风险评估和管理的拟议控制策略总结如图1所示。感知和定位模块在本文中未讨论，但重要的是强调拟议整体策略正常运行所需的主要输入。假设高清晰度地图嵌入在 中，描述了静态环境并允许计算遵守道路代码和结构的路径（参见第3.1节）。嵌入式传感器允许观察动态环境，能够表征和预测遇到障碍物的行为（例如，平静、激进等），并允许通过时间常数 定义它们的轨迹，对应于所使用的监测度量的输入，即预测的车辆间距剖面（PIDP）（参见第3.2节）。图1中给出的第2模块对应于允许定义EV应该保持与每个检测到的OV之间的期望动态最小安全时间距离的架构特征，根据其行为和速度。 为了聚焦于论文的主要贡献，本部分将不在下文中进行详细讨论。假设最小安全距离是恒定的。需要注意的是，所提出的 MRAM-CS 无论 是否变化都采用相同的策略。在本文中，障碍物行为没有被处理，但它们可以具有不同的初始速度。所提出的多风险评估基于连续监测指标 PIDP（参见图 1，块 3），允许定义对 EV 施加相同行为的 OVs 组。多风险管理（参见第 4 节和图 1 的块 5 和 6）允许基于自适应 PD 控制器应用自适应速度曲线，以找到与所考虑的障碍物保持安全距离的正确速度曲线，并基于模糊融合过程来管理 OVs 组。一旦所提出的多风险评估和管理策略获得 EV 的最合适设定点，则使用适当的控制法则（由图 1 中的块 7 定义）。Vilca 等人的非线性控制法则（2015 年）允许将 EV 驱向静态或动态目标。（2015）允许将 EV 驱向静态或动态目标
and it is based on a Lyapunov function designed to ensure the convergence of the EV to the targeted setpoint.
并且它是基于设计的 Lyapunov 函数，以确保 EV 收敛到目标设定点。

This section will make the focus on the main components characterizing the proposed Multi-Risk Assessment strategy, which relies, among others on the trajectory that should be taken by the EV (cf. Section 3.1) and the definition of two groups of dangerous obstacles (the one which require acceleration and the one which require deceleration to avoid them (cf. Section 3.2).
本节将重点介绍提出的多风险评估策略的主要组成部分，其中依赖于 EV 应采取的轨迹（参见第 3.1 节）以及定义两组危险障碍物（其中一组需要加速，另一组需要减速以避免它们（参见第 3.2 节）。

Fig. 2. Defined Limit-Cycle (LC) paths to manage the entire roundabout navigation according to defined entrance and exist that must be taken by the EV with maximum of 3 Limit-Cycles (entrance, ring zone with the lane change if necessary, and exit).
图 2. 定义的极限环(LC)路径，根据定义的入口和出口管理整个环形交叉路口导航，电动汽车必须经过最多 3 个极限环(入口、环形区域与必要时的车道变换、出口)。

The paths that allow to navigate with smooth and flexible way in the roundabout (phases of: entrance, ring zone and exit) are defined in this paper while using appropriate Elliptic Limit-Cycles (ELC) Adouane (2017), Adouane et al. (2011) (cf. Figure 1, block 1). These latter are defined according to elliptic periodic orbits, corresponding to ellipses of influences. In previous works Adouane (2017), Adouane et al. (2011), an ellipse of influence is generated around the obstacle and allows to circumvent this last one. In Iberraken and Adouane (2022), the generation of an ellipse of influence, around the obstacle-vehicle, allows to an EV to have smooth and adaptive overtaking in highway. In the proposed paper, it is not suggested to use the limit-cycles to achieve overtaking maneuver Iberraken et al. (2018) or to avoid obstacles Adouane (2017), but to achieve smooth and flexible navigation of the EV in a roundabout (thus: insertion, displacement/lane-change and exit; cf. Figure 2 to see the three mains used limitcycles).
本文定义了在环形交叉口中以平滑灵活方式导航的路径，同时使用适当的椭圆极限环(Elliptic Limit-Cycles, ELC) Adouane (2017)，Adouane 等人(2011) (参见图 1，块 1)。这些后者根据椭圆周期轨道进行定义，对应于影响椭圆。在之前的作品 Adouane (2017)，Adouane 等人(2011)中，围绕障碍物生成一个影响椭圆，允许绕过障碍物。在 Iberraken 和 Adouane (2022)中，围绕障碍物-车辆生成一个影响椭圆，使得电动车在高速公路上能够平稳自适应超车。在本文中，不建议使用极限环来实现超车操作 Iberraken 等人(2018)或避开障碍物 Adouane (2017)，而是实现电动车在环形交叉口中的平滑灵活导航(即：插入、位移/变道和退出；参见图 2 以查看使用的三个主要极限环)。

To have self-content paper, it is given in what follows the main features characterizing the used ELCs. They are defined according to the following equations:
为了有自洽的论文，以下给出了用于定义 ELC 的主要特征。它们根据以下方程式进行定义：

with according to the direction of avoidance (clockwise or counterclockwise). corresponds to the coordinate of the obtained path (limit-cycle (LC)) according to the center of the roundabout. and characterize the major and minor elliptic semi-axes respectively. In the case of a roundabout, . gives the orientation of the ellipse but not used in the case of a circular LC and a positive constant that enable us to modulate the speed of convergence of the LC trajectory toward the ellipse of influence (orbit). This last term allows to fit the curve entry and to minimize the curvature according to the roadsides (cf. Figure 2). Knowing the roundabout exit that the EV has to take, the internal or external lane must be used. The comfort for a roundabout insertion is approached in González et al. (2017) with Bezier curves and in Rodrigues da Silva et al. (2022) with clothoids. The choice of LC method to define trajectories on a roundabout is done because of the smooth and high flexibility of the trajectories that could be computed with these LC, for the different roundabout phases: entrance, ring zone and exit. The path planning phase is not the main focus of the proposed paper and is uncorrelated with the proposed method to determine the speed profile but it is important to know the evolution of the curvature to take into account the comfort of the passengers by limiting the speed according to the curvature of the trajectory. This part will be subject to future developments.
根据避让方向（顺时针或逆时针）使用 。 对应于根据环岛中心获得的路径（极限环(LC)）的坐标。 和 分别表示主要和次要椭圆半轴。在环岛的情况下， 。 给出了椭圆的方向，但在圆形LC的情况下不使用， 是一个正常数，使我们能够调节LC轨迹向影响椭圆（轨道）的收敛速度。这个术语允许拟合曲线入口并最小化根据路边的曲率（参见图2）。知道EV必须走的环岛出口后，必须使用内侧或外侧车道。González等人（2017）使用贝塞尔曲线和Rodrigues da Silva等人（2022）使用布料曲线来接近环岛插入的舒适度。 选择LC方法来定义环形交叉口上的轨迹是因为可以利用这些LC计算不同环形交叉口阶段的平滑和高灵活性的轨迹。路径规划阶段并非本文的主要焦点，与提出的确定速度曲线的方法无关，但了解曲率的演变对于考虑乘客舒适度并根据轨迹的曲率限制速度是重要的。这部分将在未来进行进一步发展。

Before safely entering a roundabout, the EV must take into-account dynamic obstacles which are already present in the roundabout. In this paper, as shown in Section 3.1, it is considered that the EV circulates on its already planned path, based on LC (cf. Figure 2). It is also assumed that each obstacle-vehicle navigates in its corridor and follows the center of the lane. To check if the EV's planned trajectory (defined path and adaptive velocity) induces collisions with the other dynamic obstacles, two buffer circles are defined for each vehicle (cf. Figure 3(a)). All obstacles are represented by two circles. This is justified by the fact that it is important to know whether the collision took place at the front or at the rear of each vehicle in order to adapt accordingly the behavior (acceleration/deceleration) of the EV.
在安全进入环岛之前，电动车必须考虑环岛中已经存在的动态障碍物。本文中，如第3.1节所示，假定电动车沿着已规划的路径行驶，基于LC（参见图2）。还假设每个障碍物车辆在其车道内导航并遵循车道中心。为了检查电动车的规划轨迹（定义的路径和自适应速度）是否会与其他动态障碍物发生碰撞，为每辆车定义了两个缓冲圆（参见图3(a)）。所有障碍物都用两个圆表示。这是因为重要的是要知道碰撞是发生在每辆车的前方还是后方，以便相应地调整电动车的行为（加速/减速）。

Before explaining the proposed strategy to know the EV's macro-behavior consisting of accelerating/decelerating to have a safe insertion, let us first define, the metric defined in previous works Iberraken et al. (2018), Bellingard et al. (2021) (cf. Figure 1, block 3). This metric, named Predicted Inter-Distance Profile (PIDP), represents the evolution of the distance between two vehicles (Ego and the considered obstacle) according to the time. Knowing the path and the dynamics of both vehicles, and if these ones remain unchanged in the desired time horizon , it is possible to predict the evolution of the inter-distance between them and thus assess the risk of collision. As mentioned before, it is assigned for each vehicle two circles (cf. Figure 3 (a)), four PIDP must be thus calculated (one for each pair of circles) in order to determine the macro-behavior that must be considered by the . If one of the PIDP crosses , the obstacle is considered as dangerous and the speed profile of the EV must be
在解释提出的策略以了解电动车的宏观行为，包括加速/减速以安全插入之前，让我们首先定义前作中定义的度量标准Iberraken等人（2018年），Bellingard等人（2021年）（参见图1，块3）。这个度量标准被命名为预测的车距轮廓（PIDP），表示两辆车（自车和考虑的障碍物）之间距离随时间的演变。了解两辆车的路径和动力学，如果它们在期望的时间范围内保持不变，就可以预测它们之间车距的演变，从而评估碰撞的风险。如前所述，为每辆车分配两个圆圈（参见图3（a）），因此必须计算四个PIDP（每对圆圈一个）以确定 必须考虑的宏观行为。如果其中一个PIDP穿过 ，则认为障碍物是危险的，电动车的速度曲线必须是

(a)

(b)
Fig. 3. Circles used as buffers to characterize the different possible collisions between the EV and the ObstacleVehicle. The macro-behavior (acceleration or deceleration) that can be taken by the EV according to the projected situation is resumed in the above Table. For the insertion, deceleration is always prioritized because EV does not have priority. For example, in its line 5, Ef (Ego's front) and Or (Obstacle's rear) , the designed macro-behavior is to decelerate.
图 3。圆圈用作缓冲区，以表征 EV 与障碍车之间可能发生的不同碰撞。根据预测的情况，EV 可以采取的宏观行为（加速或减速）总结在上表中。对于插入，始终优先考虑减速，因为 EV 没有优先权。例如，在其第 5 行，Ef（自车前方） 和 Or（障碍车后方） ，设计的 宏观行为是减速。

adapted. To know the behavior, all times (i.e., at each time step) where the Safety is Non Respected (cf. Figure 4, which represents the first crossing point (if it exists obviously) between and PIDP, are computed. For one obstacle, the considered PIDP is the one that cross first. If there is no crossing point, the EV can keep his dynamic without any risk of collision. The behavior that must be adopted by the EV can be checked in the table given in Figure 3 (b).
调整。要了解行为，需要计算所有时间（即每个时间步）在其中安全性未受到尊重 的时刻（参见图 4，表示第一个交点（如果存在的话）在 和 PIDP 之间，对于一个障碍物，考虑的 PIDP 是首先交叉的那个。如果没有交点，EV 可以保持其动态而不会发生碰撞风险。EV 必须采取的行为可以在图 3（b）中给出的表中进行检查。

Fig. 4. Example of PIDP plotting progress that the EV can meet during an insertion or a lane change in a roundabout where are detected and these 3 risky OVs corresponding PIDP are computed. The two closest obstacles impose a deceleration of the EV and can be grouped. The third one imposes an acceleration while taking into account the table given in Figure 3 (b).
图4. 在环形交叉口进行插入或变道时，EV可以满足的PIDP绘图进展示例，其中检测到 ，并计算这3个风险OV对应的PIDP。最近的两个障碍物会使EV减速并可以分组。第三个障碍物在考虑图3（b）中给出的表格的情况下会强制加速。

Once the set of PIDP are computed for each OV, through a time horizon, and the behavior that each obstacle imposes on the EV are known (cf. Figure 4), the proposed control strategy suggests to bring together all the obstacles that impose the same macro-behavior (acceleration or deceleration (AccOrDec)) (cf. Figure 1, input block 4). As shown in Figure 4, three obstacles are considered with their respective PIDP. If the collision takes place at the front of the EV (PIDP solid lines for the Obstacles 1 and 2 in Figure 4), the EV has to decelerate considering the most dangerous obstacle, i.e., the one that crosses first , otherwise the EV must accelerate (PIDP dashed line for the obstacle 3). For a number of obstacles with rear (or front respectively) consecutive collisions, the obstacle considered for each group is defined by the following:
一旦为每个障碍物车辆计算了PIDP集合，通过一个时间范围， 和每个障碍物对电动车施加的行为是已知的（参见图4），所提出的控制策略建议将施加相同宏观行为（加速或减速（AccOrDec））的所有障碍物聚集在一起（参见图1，输入块4）。如图4所示，考虑了三个障碍物及其各自的PIDP。如果碰撞发生在EV的前方（图4中障碍物1和2的PIDP实线），EV必须考虑最危险的障碍物减速，即最先穿越的那个 ，否则EV必须加速（障碍物3的PIDP虚线）。对于具有后（或前）连续碰撞的一组障碍物，每组考虑的障碍物由以下定义：

with for each possible existing group of induced macro-behavior (acceleration/deceleration). The min is selected since it is the closest time of collision, considering the defined obstacles' group. Due to the proposed control strategy and the traffic rules, there is no alternation of more than two groups in the given time horizon. There will be a maximum of 2 groups, one requiring a deceleration with a collision rather at the front of the EV and another at the rear with an acceleration demand. This situation, when two groups are identified in the given time horizon , means an insertion between two vehicles, one requesting an appropriate average deceleration (during the overall considered time horizon) and the other an appropriate acceleration to avoid the collision. All the challenge is therefore to define the most suitable velocity adaptation profile to guarantee the EV insertion between these two OVs because it is in this situation that vehicles can be stopped for an indefinite period, depending on the traffic Medina-Lee et al. (2022). The proposed online and reliable approach is given below.
对于每个可能存在的诱导宏观行为组，选择最小值，因为它是考虑到定义的障碍物组的最接近碰撞时间。由于提出的控制策略和交通规则，在给定的时间范围内不会有超过两组的交替。最多会有2组，一个需要减速以在EV前方发生碰撞，另一个在后方需要加速。当在给定的时间范围内识别出两组时，意味着在两辆车之间插入，一辆要求适当的平均减速（在整个考虑的时间范围内），另一辆要求适当的加速以避免碰撞。因此，所有挑战在于定义最适合的速度调整曲线，以确保EV在这两个OV之间插入，因为在这种情况下，车辆可能会因交通而停止一段不确定的时间，取决于交通Medina-Lee等人（2022年）。下面给出了提出的在线和可靠方法。

The time that will be between the two defined critic obstacles, is expressed by (cf. Figure 4):
两个定义的临界障碍物之间的时间 ，由以下方式表示（参见图 4）：

If this parameter, , is below the set limit where insertion is allowed to guarantee safe insertion (by keeping safe distances between the two designed obstacles), then the insertion can be performed. Otherwise, the two identified groups are grouped together to form a single group that will impose a single dynamic (acceleration or deceleration) to the EV, while considering the most dangerous obstacle. All this strategy is resumed in the upper part of the flowchart presented in Figure 5.
如果此参数 低于允许插入的设定限制（通过保持两个设计障碍物之间的安全距离来保证安全插入），则可以执行插入。否则，两个识别的组将被组合在一起形成一个单一组，将对电动汽车施加单一动态（加速或减速），同时考虑最危险的障碍物。所有这些策略都总结在图 5 中呈现的流程图的上部。

The aim of the proposed control strategy is to adapt the speed profile based on an adaptive PD controller (cf. Section 4.1) and a fuzzy fusion process (cf. Section 4.2). The continuous monitoring metric, PIDP allows the EV to maintain safety distances even with a dense traffic flow. During an insertion in a roundabout, the EV has the possibility to stop (before to enter the roundabout) and to give priority to the OVs navigating in the roundabout. This is not the case during a lane changing in the roundabout. If there is no speed profile that allows to respect the safe distances, the component parameters which define the differential equations of the LC (1) allow to redefine a path, online, but this part is not the focus of this paper (cf. Section 3.1). When one of the detected OV will not allows to respect the safety distances (i.e., with the minimum of PIDP (cf. Figure 4)), the EV has to update its speed profile in order to respect the defined safety distance . The error , represents the difference between and .
所提出的控制策略的目标是基于自适应PD控制器（参见第4.1节）和模糊融合过程（参见第4.2节）调整速度曲线。连续监测指标PIDP允许电动车即使在交通拥挤时保持安全距离。在环形交叉口插入时，电动车有可能停下（在进入环形交叉口之前）并让行驶在环形交叉口内的其他车辆优先通行。但在环形交叉口变道时情况不同。如果没有速度曲线可以保持安全距离，定义LC的微分方程的组件参数（1）可以在线重新定义路径，但这部分不是本文的重点（参见第3.1节）。当检测到的其他车辆之一不允许保持安全距离时（即， 与PIDP的最小值（参见图4）），电动车必须更新其速度曲线以保持定义的安全距离 。误差 表示 和 之间的差异。

Fig. 5. Flowchart of the main steps describing the sequentiality of the proposed Multi-Risk Assessment and Management parts of the overall MRAM Control Architecture
提议的多风险评估和管理部分的顺序性的主要步骤流程图

with for each group. The sign of , computed at each time step, depends on the behavior imposed by the concerned group and that must be adopted by the EV (acceleration or deceleration). This error is managed by an adaptive PD controller which applies an appropriate correction based on the proportional and derivative of this error according to the following (5):
对于每个组，使用 。在每个时间步骤计算的 的符号取决于受影响组施加的行为，并且 EV 必须采用该行为（加速或减速）。这个误差由自适应 PD 控制器管理，该控制器根据以下关系（5）应用适当的校正，该校正是基于该误差的比例和导数的：

where and are the proportional and derivative coefficients, respectively, and the command is the speed that the EV must add to its current velocity in order to converge the towards the limit (cf. Figure 4). This means that the EV updates online its velocity to always maintain a minimum distance .
其中 和 分别为比例和导数系数，命令 是 EV 必须在其当前速度上添加的速度，以便将 收敛到 极限（参见图 4）。这意味着 EV 在线更新其速度，以始终保持最小距离 。

In order to reach the safety distance, according to the situations (positions represented by the PIDP derivative and speeds of the obstacles), it is proposed to update the parameters of and (cf. Figure 1, block 5), according to the optimization of a multi-criteria given in (6). For different scenarios involving several initial speeds of obstacles and EV, several proportional values of are used. A cost function , that must be minimized, is used in order to find the right proportional gain value for this situation which
为了达到安全距离，根据情况（由 PIDP 导数和障碍物的速度表示的位置），建议根据多标准优化（6 中给出）更新 和 的参数（参见图 1，块 5）。对涉及多个障碍物和 EV 的不同场景，使用几个 的比例值。使用必须最小化的成本函数 ，以找到适合此情况的比例增益值

Fig. 6. Polynomial regression to describe the variables and with different initial speed of the Ego-vehicle and the obstacle-vehicle.
图 6。多项式回归来描述不同初始速度的自车和障碍车的变量 和 。

allows smooth insertion without oscillations of the speed while respecting the safety distances with a response time that respects the maximum acceleration/deceleration that can be provided by the . The cost function used is defined as follow:
允许平滑插入，无需速度振荡，同时在尊重 提供的最大加速度/减速度的情况下尊重安全距离，响应时间。使用的成本函数 定义如下：

where: 其中：

and are positive constants permitting to give the right balance between the different subcriteria. All sub-criteria are normalized by using the weighted sum method Triantaphyllou (2000). Once the right proportional is found for each scenario, the same process is used to find using the best found from the cost function . When and satisfying the constraints are found for each scenario, a polynomial regression is performed to describe the appropriate selected and , according to the obtained results as shown in Figure 6).
和 是正常数，允许在不同子标准之间找到正确的平衡。所有子标准都通过使用 Triantaphyllou（2000）的加权和方法进行归一化。一旦为每种情景找到了正确的比例 ，则使用相同的过程来找到 ，使用从成本函数 找到的最佳 。当为每种情景找到满足约束条件的 和 时，将执行多项式回归来描述适当选择的 和 ，根据所得结果如图 6 所示。

In order to take into account the possible conflicting behaviors given by two identified groups of vehicles and to manage the two computed speed profiles, if , defined by the equation (3), respects the chosen limit time to allow an insertion, a fuzzy fusion process is carried out to determine the speed that must be applied to maintain the safety distance with the two groups simultaneously (cf. Figure 1, Block 6). Priority must be given to the group with the highest level of risk of collision:
为了考虑由两个识别的车辆组给出的可能的冲突行为，并管理两个计算得到的速度曲线，如果 ，由方程（3）定义，遵守选择的限制时间以允许插入，将进行模糊融合过程以确定必须应用的速度，以同时保持与两个组的安全距离（参见图 1，块 6）。必须优先考虑具有最高碰撞风险水平的组：

with , the speed at each time step that must be applied to respect the safety distances with all the obstacles' groups and , determined by a fuzzy logic controller (cf. Figure 7 ) while considering the gap and the error
使用 ，必须在每个时间步骤应用的速度，以尊重与所有障碍物组的安全距离和 ，由模糊逻辑控制器确定（参见图 7），同时考虑间隙 和误差
of each group. If the gap is high, this means that the collision with the most dangerous vehicle of the first group is imminent and the EV must consider this first group as a priority. Otherwise, if is close to the limit where the insertion is aborted, the priority given to each group is equivalent but are also used to determine the right balance and it is useful in this particular case. The priority will be given to the one with the highest error . This allows to find the right balance between the action to be performed, for each group, in order to safely deal between all the observed OVs.
每个组的 。如果间隙很大，这意味着与第一组中最危险车辆的碰撞即将发生，EV 必须将这第一组视为优先考虑。否则，如果 接近插入中止的极限，给予每个组的优先级是等效的，但 也用于确定正确的平衡，在这种特殊情况下很有用。优先级将给予具有最高误差 的那个。这样可以找到要执行的正确平衡，以便为每个组之间安全处理所有观察到的 OV 之间的行动。

Fig. 7. Fuzzy membership functions used to find the right balance between speed profiles computed for the two groups with 3 inputs and 1 output .
图 7. 用于找到为两组计算的速度曲线之间的正确平衡的模糊隶属函数，具有 3 个输入和 1 个输出 。

The simulation results have been performed in Matlab/Simulink. To highlight the proposed strategy, a two lane roundabout with a size of has been built on RoadRunner to reproduce a real roundabout and to generate an HD map described in OpenDrive format. Each performed scenario includes 8 obstacles with random initial velocities (inside an interval of coherent velocity in the roundabout) and positions, and on the external and internal lane (cf. Figure 2 and 9). The initial speed of each vehicle is set at the beginning of the scenario and it is kept constant throughout the simulation. The acceptable time between two obstacles is considered equal to . For all tested scenarios, the safety distance is set to , for all the obstacles. At the beginning of the decision zone, the detects online the visible obstacles (according to its sensors) represented by a number of dynamic obstacles (or not if they are on the other side of the roundabout). Let us consider some constraints that the EV must take into account:
仿真结果已在Matlab/Simulink中进行。为了突出提出的策略，已在RoadRunner上建立了一个大小为 的双车道环形交叉口，以重现真实的环形交叉口，并生成一个以OpenDrive 格式描述的高清地图。每个场景包括8个障碍物，随机初始速度（在环形交叉口内的一致速度区间内）和位置，分布在外部和内部车道（参见图2和9）。每辆车的初始速度在场景开始时设定，并在整个模拟过程中保持恒定。两个障碍物之间的可接受时间 被认为等于 。对于所有测试场景，安全距离 被设置为 ，适用于所有障碍物。在决策区域的开始， 在线检测可见障碍物（根据其传感器），由一定数量的动态障碍物表示（如果它们在环形交叉口的另一侧，则不表示）。让我们考虑一些电动车必须考虑的约束条件：

In order to find the best parameters and that minimize the cost function simulations have been performed with one group of vehicles. Different initial
为了找到最小化成本函数 的最佳参数 和 ，已经对一组车辆进行了模拟。考虑了障碍车辆和电动车的不同初始速度，范围在 6 和 之间，并考虑了 PIDP 的不同初始坡度（由于 OVs 在不同的初始距离被检测和考虑，因此不同），由 PIDP 导数表示为实际距离和其最小 mPIDP 之间的差异。

speeds for the obstacle-vehicle and the EV have been considered between 6 and and for different initial slopes of PIDP (different by the fact that OVs are detected and considered at different initial distances) represented by the PIDP derivative between the actual distance and its minimum mPIDP.

The obtained and (cf. Figure 6) are used for 50 random scenarios. During these 50 scenarios, the EV has to insert and cross the roundabout while considering all the detected dynamics obstacles. All these scenarios represent a critical aspect to test the actual ability of the overall control architecture, where the future possible collisions are detected at the beginning of the scenario (cf. Figure 8 with MPIDP close to ) and will appear if the EV does not adapt its speed. In some scenarios, the EV detects obstacles from afar before entering the roundabout, this is why the actual inter-distance, at the beginning of the scenario, starts at (cf. Figure 8, right figure). Some other scenarios present a late detection, close to the insertion, to test the reactivity of the proposed strategy. The mean time of convergence of mPIDP is with a maximum of and a minimum of in these scenarios. The safety distance of is always respected during these 50 scenarios. One case is presented in Figure 9, and in the video given though this link: https://urlz.fr/lfuH to illustrate an insertion between vehicles. The video highlight also several other scenarios.
获得的 和 （参见图6）用于50个随机场景。在这50个场景中，电动汽车必须插入和穿过环形交叉路口，同时考虑所有检测到的动态障碍物。所有这些场景代表了测试整体控制架构实际能力的关键方面，未来可能的碰撞在场景开始时被检测到（参见图8，MPIDP接近 ），如果电动汽车不调整速度，碰撞将发生。在一些场景中，电动汽车在进入环形交叉路口之前就从远处检测到障碍物，这就是为什么在场景开始时，实际的车辆间距从 开始（参见图8，右图）。一些其他场景呈现出晚期检测，接近插入点，以测试所提出策略的反应性。mPIDP的平均收敛时间为 ，在这些场景中最大为 ，最小为 。在这50个场景中， 的安全距离始终得到尊重。图9中呈现了一个案例，视频通过此链接提供：https://urlz.为了说明车辆之间的插入。视频还突出显示了其他几种情况。

Fig. 8. Simulation of 50 scenarios of a roundabout crossing.
图 8. 模拟 50 种环岛交叉情景。

Fig. 9. One example where the EV, in blue, has to insert in a roundabout. Red vehicles are the detected obstacles and the white ones are not detected (not dangerous here). PIDP at the given time step is also represented on the right figure for all detected obstacles. We can see that an acceleration is needed to avoid one OV (green PIDP) and a deceleration needed for another (violet PIDP).
图 9. 一个例子，其中蓝色的电动车必须插入一个环岛。红色车辆是被检测到的障碍物，白色车辆是未被检测到的（在这里不构成危险）。给定时间步骤的 PIDP 也在右图中表示所有检测到的障碍物。我们可以看到需要加速以避开一个 OV（绿色 PIDP），需要减速以避开另一个（紫色 PIDP）。

This paper proposed a Multi-Risk Assessment and Management (MRAM) global strategy allowing to an EV to navigate safely in a roundabout (entrance, ring zone and
本文提出了一种多风险评估和管理（MRAM）全球战略，使电动汽车能够安全地在环形交叉路口（入口、环形区域和
exit) even in dense dynamic traffic. A flexible path definition based on Limit-Cycles has been presented and allows to define a global path that respects the road structure and the traffic rules for each phase of the roundabout, knowing the entrance and the exit. An entire strategy to apply an adaptive speed profile allowing the EV to insert and navigate in the roundabout, while considering a dense continuous traffic flow has been presented. This strategy aims to analyze traffic to identify groups of Obstaclesvehicles in order to perform a safe insertion and allows the crossing of the roundabout despite of the density of traffic. It is based on the continuous monitoring metric PIDP and its minimum mPIDP, controlled by an adaptive PD controller. The proposed control is also based on a fuzzy fusion process to respect the imposed constraints of the identified groups of obstacles. Several simulations have been performed to demonstrate the reliability and the safety of the proposed approach that allows a flexible and reliable crossing of dense roundabout. As a short-term perspective, it is planned to implement the proposed approach on the autonomous vehicles available in the laboratory.
即使在密集的动态交通中也可以安全退出。基于极限环的灵活路径定义已经提出，允许定义一个全局路径，以尊重每个环岛阶段的道路结构和交通规则，了解入口和出口。提出了一整套策略，应用自适应速度曲线，使电动车能够插入和穿越环岛，同时考虑到密集的连续交通流。该策略旨在分析交通情况，识别障碍车辆群，以便安全插入并允许穿越环岛，尽管交通密度很大。它基于连续监控度量PIDP及其最小mPIDP，由自适应PD控制器控制。所提出的控制还基于模糊融合过程，以尊重已识别的障碍车辆群的强制约束。进行了多次模拟，以证明所提方法的可靠性和安全性，使得在密集环岛中可以灵活且可靠地穿越。作为短期展望，计划在实验室可用的自动驾驶车辆上实施所提出的方法。

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