Critical Lane Research Articles

On the Classification of Entire Solutions to the Critical Lane–Emden Equation

The positive solutions to the critical Lane–Emden equation in Rn have been classified completely by the moving plane method. Afterwards, with additional conditions such as limited energy or volume, there is proof that relies entirely on integration by parts and inequalities techniques. In this paper, the authors provide a new approach to obtain the same classification results without further assumptions.

Non-degeneracy of solution for critical Lane–Emden systems with linear perturbation

Non-degeneracy of solution for critical Lane–Emden systems with linear perturbation

Modeling driver’s evasive behavior during safety–critical lane changes: Two-dimensional time-to-collision and deep reinforcement learning

Lane changes are complex driving behaviors and frequently involve safety–critical situations. This study aims to develop a lane-change-related evasive behavior model, which can facilitate the development of safety-aware traffic simulations and predictive collision avoidance systems. Large-scale connected vehicle data from the Safety Pilot Model Deployment (SPMD) program were used for this study. A new surrogate safety measure, two-dimensional time-to-collision (2D-TTC), was proposed to identify the safety–critical situations during lane changes. The validity of 2D-TTC was confirmed by showing a high correlation between the detected conflict risks and the archived crashes. A deep deterministic policy gradient (DDPG) algorithm, which could learn the sequential decision-making process over continuous action spaces, was used to model the evasive behaviors in the identified safety–critical situations. The results showed the superiority of the proposed model in replicating both the longitudinal and lateral evasive behaviors.

Quantitative Analysis of the Impact of Baidu Apollo Parameterization on Trajectory Planning in a Critical Scenario

The increasing demand for reliable and safe high-driving automation algorithms in Autonomous Driving (AD) vehicles has driven significant advancements in the industry. This paper investigates the performance of a specific AD vehicle architecture in a critical lane change maneuver, extracted from the HighD Dataset, which consists of naturalistic vehicle trajectories recorded on German highways. The analysis focuses on different parameter configurations to understand their influence on the results. The selected AD algorithm is based on the Apollo Open Autonomous Driving Platform (AOADP). Simulation results demonstrate the significant impact of path planning algorithm parameters on lane change execution. The comparison between human driving behavior and AD systems plays a crucial role in determining sensing technology specifications. This approach provides a quantitative analysis of the impact on autonomous driving measurements, contributing to the safe specification of AD functions. These findings lay the foundation for future evaluations and improvements in the selected AD architecture.

What happens when drivers of automated vehicles take over control in critical lane change situations?

According to legislation, take-overs initiated by the driver must always be possible during automated driving. For example, when drivers mistrust the automation to handle a critical and hazardous lane change, they might intervene and take over control while the automation is performing the maneuver. In these situations, drivers may have little time to avoid an accident and can be exposed to high lateral forces. Due to lacking research, it is yet unknown if they recognize the criticality of the situation and how they behave and perform to manage it. In a driving simulator study, participants (N = 60) accomplished eight double lane changes to evade obstacles in their lane. Time-to-collision and traction usage were varied to establish different degrees of objective criticality. To manipulate these parameters as required, participants were triggered to take over control by an acoustic cue. This setting shows what might happen if drivers disable the automation and complete the maneuver themselves. The results of the experiment demonstrate that drivers rated objectively more critical driving situations as more critical and responded to the hazard very fast over all experimental conditions. However, their behavior was more extreme with respect to decelerating and steering than necessary. This impaired driving performance and increased the risk of lane departures and collisions. The results of the experiment can be used to develop an assistance system that supports driver-initiated take-overs.

Non-degeneracy for the critical Lane–Emden system

We prove the non-degeneracy for the critical Lane–Emden system − Δ U = V p , − Δ V = U q , U , V > 0 in R N \begin{equation*} -\Delta U = V^p,\quad -\Delta V = U^q,\quad U, V > 0 \quad \text {in } \mathbb {R}^N \end{equation*} for all N ≥ 3 N \ge 3 and p , q > 0 p,q > 0 such that 1 p + 1 + 1 q + 1 = N − 2 N \frac {1}{p+1} + \frac {1}{q+1} = \frac {N-2}{N} . We show that all solutions to the linearized system around a ground state must arise from the symmetries of the critical Lane–Emden system provided that they belong to the corresponding energy space or they tend to zero at infinity.

IMU-Based Automated Vehicle Body Sideslip Angle and Attitude Estimation Aided by GNSS Using Parallel Adaptive Kalman Filters

The sideslip angle and attitude are crucial for automated driving especially for chassis integrated control and environmental perception. In this article an inertial measurement unit (IMU)-based automated vehicle body sideslip angle and attitude estimation method aided by low-sample-rate global navigation satellite system (GNSS) velocity and position measurements using parallel adaptive Kalman filters is proposed. This method can estimate the sideslip angle and attitude simultaneously and is robust against the vehicle parameters and road friction even as the vehicle enters critical maneuvers. First, based on the acceleration and angular rate from the six-dimensional inertial measurement unit, the attitude, velocity and position (AVP) are integrated with the navigation coordinates and the AVP error dynamics and observation equations of the integration results are developed. Second, parallel innovation adaptive estimation (IAE)-based Kalman filters is designed to estimate the AVP error of the integration method to address the issues of the GNSS low sampled rate and abnormal measurements. Then the AVP error is forwarded to the AVP integration to compensate the accumulated error. To improve the heading angle estimation accuracy, the heading error is estimated by a decoupled IAE-based Kalman filter aided by GNSS heading. In addition, time synchronization of the IMU and GNSS is realized through hardware based on the pulse per second signal of the GNSS receiver and the spatial synchronization is achieved by a direct compensation method. Lastly, the sideslip angle and attitude estimation method is validated by a comprehensive experimental test including critical double lane change and slalom maneuvers. The results show that the estimation error of the longitudinal velocity and lateral velocity is smaller than 0.1 m/s $({1\sigma })$ , and the estimation error of the sideslip angle is smaller than 0.15° $({1\sigma })$ .

Influence of Lane Width on Semi- Autonomous Vehicle Performance

In the medium-term, the number of semi-autonomous vehicles is expected to rise significantly. These changes in vehicle capabilities make it necessary to analyze their interaction with road infrastructure, which has been developed for human-driven vehicles. Current systems use artificial vision, recording the oncoming road and using the center and edgeline road markings to automatically facilitate keeping the vehicle within the lane. In addition to alignment and road markings, lane width has emerged as one of the geometric parameters that might cause disengagement and therefore must be assessed. The objective of this research was to study the impact of lane width on semi-autonomous vehicle performance. The automatic lateral control of this type of vehicle was tested along 81 lanes of an urban arterial comprising diverse widths. Results showed that the semi-autonomous system tended to fail on narrow lanes. There was a maximum width below which human control was always required—referred to as the human lane width—measuring 2.5 m. A minimum width above which automatic control was always possible—the automatic lane width—was established to be 2.75 m. Finally, a lane width of 2.72 m was found to have the same probability of automatic and human lateral control, namely the critical lane width. Following a similar methodology, these parameters could be determined for other vehicles, enhancing the interaction between autonomous vehicles and road infrastructure and thus supporting rapid deployment of autonomous technology without compromising safety.

A novel adaptive control approach for path tracking control of autonomous vehicles subject to uncertain dynamics

Autonomous ground vehicles are constantly exposed to matched/mismatched uncertainties and disturbances and different operating conditions. Consequently, robustness to resist the undesirable effect of changes in the nominal parameters of the vehicle is a significant provision for satisfactory path-tracking control of these vehicles. The accomplishment of lateral path-tracking control is an essential task expectable from autonomous ground vehicles, particularly during critical maneuvers, abrupt cornering, and lane changes at high speeds. This paper presents a new control approach based on immersion and invariance control theorem. The asymptotic stability of the proposed method is ensured and the adaptation laws for the parameters are derived based on the I&I stability theorem. The effectiveness of the proposed control method is confirmed for autonomous ground vehicles systems while making a double-lane-change at various forward speeds. The robustness of the proposed control method is evaluated under parametric uncertainties related to the autonomous ground vehicle and different road conditions. The obtained results suggest that the proposed control method holds the capacity to be applied effectively to the path-tracking task of autonomous ground vehicles under a broad range of operating conditions, parametric uncertainness, and external disturbances.

Operating Performance of Diverging Diamond Interchanges

As the result of changing traffic patterns, many conventional intersections and interchanges can no longer accommodate growing traffic volumes and heavy turning movements. In response, there are various innovative intersection and interchange designs proposed and implemented to better accommodate these changes, and the diverging diamond interchange (DDI) is one of these alternatives. While there is a significant amount of research on the relative performance of DDIs and conventional diamond interchanges (CDIs), a clear set of guidance on demand conditions under which a DDI is likely an operationally more efficient solution is not readily available. This effort conducts a sensitivity analysis of CDI and DDI operational performance under various interchange lane configurations, including the selected study area of the Jimmy Carter Boulevard and I-85 interchange in Norcross, Georgia, under varying traffic demands and turn-movement ratios. The sensitivity analysis explores the detailed conditions in which one interchange configuration provides superior performance over the other. The sensitivity analysis is structured into a two-step process with a critical lane volume (CLV) analysis as the first step, followed by a VISSIM microscopic simulation study as the second step. Overall, the study found that a CDI is likely to be the preferred option at locations with traffic volumes well below capacity and cross-street left-turn traffic proportions below 30% of the total cross-street demand, and a DDI is likely to be preferred at locations with traffic volumes near capacity and cross-street left-turn proportions exceeding 50% of the total cross-street demand.

Integrated longitudinal and lateral guidance of vehicles in critical high speed manoeuvres

One of the most important and conventional manoeuvres, that is not easy to even skilled drivers, is the high-speed critical lane change on the highways. The main contribution of this study is the development of an integrated longitudinal and lateral guidance algorithm for these manoeuvres. This algorithm consists of two parts: the trajectory planning and the integrated control. In the first part, taking into account the position of the target vehicle for different accelerations, several trajectories are produced. Next, considering the dynamic capabilities of the vehicle, the most appropriate trajectory is selected. Since the proposed trajectory planning approach works algebraically, its computational cost is negligible, which is very valuable for practical implementations. In the second step, using a robust-integrated longitudinal–lateral controller, the control inputs are calculated and transmitted to the brakes, throttle and steering actuators. It should be noted that the trajectory planning and the integrated controller are based on the seven degrees of freedom model of the vehicle, and the nonlinear dynamics of the tyre and the dynamics of the brakes/throttle actuators are also taken into account. To assess the efficiency of the integrated longitudinal–lateral guidance algorithm, the full vehicle model is used in the CarSim–Simulink software. In order to have conditions closer to real applications, it is assumed that the yaw rate and the longitudinal and lateral accelerations of the vehicle are noisy, and the longitudinal and lateral velocities are predicted using the same signals. Obtained results for the critical collision avoidance manoeuvres confirm the effectiveness of the proposed planned trajectory and the good performance of the combined control method. In addition, the results indicate that the integrated control is robust against the variation of friction coefficient and unmodelled dynamics while maintaining the vehicle stability.

Trajectory planning and combined control design for critical high-speed lane change manoeuvres

The purpose of this research is to develop an advanced driver assistance system for the integrated longitudinal and lateral guidance of vehicles in critical high-speed lane change manoeuvres. The system consists of two parts: trajectory planning and combined control. At the first, by considering the TV position and the available range of longitudinal acceleration, several trajectories with different accelerations are generated. Then, by taking into account the vehicle and tyre dynamics, the most appropriate trajectory is selected. Therefore, the chosen trajectory is collision free and dynamically feasible. Because the trajectory planning is carried out algebraically, it has low computational cost. This is especially valuable in the experimental implementations. At the second part of the study, using a robust combined longitudinal-lateral controller, the control inputs are determined and transmitted to the brake/throttle and steering actuators. Both in the trajectory planning and combined control design, the nonlinear tyre dynamics and the dynamics of throttle and brake actuators are considered. To evaluate the performance of the proposed guidance algorithm, a full CarSim dynamic model is utilized. The simulation results for critical high-speed lane change manoeuvres confirm that the proposed trajectory planning method works effectively. The tracking error is also very small and the yaw stability is guaranteed.

A comparative evaluation of in-vehicle side view displays layouts in critical lane changing situation

This study conducted a driving simulator experiment to comparatively evaluate three in-vehicle side view displays layouts for camera monitor systems (CMS) and the traditional side view mirror arrangement. The three layouts placed two electronic side view displays near the traditional mirrors positions, on the dashboard at each side of the steering wheel and on the centre fascia with the two displays joined side-by-side, respectively. Twenty-two participants performed a time- and safety-critical driving task that required rapidly gaining situation awareness through the side view displays/mirrors and making a lane change to avoid collision. The dependent variables were eye-off-the-road time, response time, and, ratings of perceived workload, preference and perceived safety. Overall, the layout placing the side view displays on the dashboard at each side of the steering wheel was found to be the best. The results indicated that reducing eye gaze travel distance and maintaining compatibility were both important for the design of CMS displays layout.Practitioner Summary: A driving simulator study was conducted to comparatively evaluate three in-vehicle side view displays layouts for camera monitor systems (CMS) and the traditional side view mirror arrangement in critical lane changing situation. Reducing eye movement and maintaining compatibility were found to be both important for the ergonomics design of CMS displays layout.

Saturation Flow Mathematical Model Based on Multiple Combinations of Lane Groups

The ideal value of the traffic stream that can pass through an intersection is known as the saturation flow rate per hour on vehicle green time. The saturation flow is important in the understanding of the traffic light cycle and from there the understanding the Level of Service. The paper wishes to evaluate through a series of applied mathematical methods the effect of different lane grouping and critical lane group concept on the saturation flow rate. The importance of this method is that it creates a base for a signalized intersections timing plan.

Situation assessment and decision making for lane change assistance using ensemble learning methods

Lane change maneuvers contribute to a significant number of road traffic accidents. Advanced driver assistance systems (ADAS) that can assess a traffic situation and warn drivers of unsafe lane changes can offer additional safety and convenience. In addition, ADAS can be extended for use in automatic lane changing in driverless vehicles. This paper investigated two ensemble learning methods, random forest, and AdaBoost, for developing a lane change assistance system. The focus on increasing the accuracy of safety critical lane change events has a significant impact on lowering the occurrence of crashes. This is the first study to explore ensemble learning methods for modeling lane changes using a comprehensive set of variables. Detailed vehicle trajectory data from the Next Generation Simulation (NGSIM) dataset in the US were used for model development and testing. The results showed that both ensemble learning methods produced higher classification accuracy and lower false positive rates than the Bayes/Decision tree classifier used in the literature. The impact of misclassification of lane changing events was also studied. A sensitivity analysis performed by varying the accuracy of lane changing showed that the lane keeping accuracy can be increased to as high as 99.1% for the AdaBoost system and 98.7% for the random forest system. The corresponding true positive rates were 96.3% and 94.6%. High accuracy of lane keeping and high true positive rates are desirable due to their safety implications.

Hybrid simulated annealing and genetic algorithm for optimizing arterial signal timings under oversaturated traffic conditions

SummaryThe implementation of system‐wide signal optimization models requires efficient solution algorithms that can quickly generate optimal or near‐optimal signal timings. This paper presents a hybrid algorithm based on simulated annealing (SA) and a genetic algorithm (GA) for arterial signal timing optimization. A decoding scheme is proposed that exploits our prior expectations about efficient solutions, namely, that the optimal green time distribution should reflect the proportion of the critical lane volumes of each phase. An SA algorithm, a GA algorithm and a hybrid SA‐GA algorithm are developed here using the proposed decoding scheme. These algorithms can be adapted to a wide range of signal optimization models and are especially suitable for those optimizing phase sequences with oversaturated intersections. To comparatively evaluate the performance of the proposed algorithms, we apply them to a signal optimization model for oversaturated arterial intersections based on an enhanced cell transmission model. The numerical results indicate that the SA‐GA algorithm outperforms both SA and GA in terms of solution quality and convergence rate. Copyright © 2014 John Wiley & Sons, Ltd.

Diverging Diamond Interchange Analysis: Planning Tool

Many traffic simulation software tools have emerged over the last decade and are widely used for analyzing capacity, delay, and level of service at intersections, ramps, and along arterial/freeway segments. Although these tools have shown great promise, they are expensive and the data collection and input setup is time consuming and resource intensive. Traffic engineers predominantly use one of those tools to analyze a diverging diamond interchange (DDI), also known as double crossover diamond interchange. Developing a simulation model and performing required analysis takes considerable time. Because it is not necessary to obtain a detailed traffic operational analysis of a DDI while interchange alternatives are being developed, a quick and easy evaluation procedure is warranted. In this paper, a critical lane volume (CLV)-based DDI analysis methodology is developed, which could be an appropriate tool to bridge the gap. In this methodology, two intersections or nodes of a DDI, where through-traffic movements along the arterial cross each other, are considered crucial. Understanding of the crossover movements, ramp movements, and coordination of traffic movements between the two nodes and lane configuration are used in developing the methodology. Critical movements are analyzed, compared, and logically added to obtain the CLV of the two nodes. The obtained CLV is used in deriving the level of service of the two intersections in a DDI. The paper describes the mathematical formulation and analysis procedure to evaluate a DDI. Two real-world DDIs are analyzed by using the developed method and compared with simulation results for reliability and accuracy.

Revisiting the Cycle Length

During oversaturation, a popular objective in traffic signal operations is to maximize throughput to keep traffic moving. As cycle lengths are increased, the proportion of lost time used to transition between signal phases is reduced. This factor is often a rationale for programming long cycle lengths into signal timing plans. An investigation of the impact of cycle length revisited the concept of the use of critical lane analysis to calculate throughput and applied the technique to data collected at an oversaturated intersection in Indianapolis, Indiana. Traffic volumes were measured for 10 weeks while various cycle lengths, ranging from 80 to 135 s, were tested at the intersection. During saturated conditions, no clear increase in the sum of critical lane throughput was observed, even when the cycle length increased by more than 50%. At 135 s, there was a slight reduction in the total critical lane sum volume. These findings concur with a recent study by Denney et al. The decrease in throughput during the longer cycle lengths is attributed to the reduction of saturation flow during long green times. Possible results of use of a time-dependent saturation flow rate are discussed. Additionally, critical lane analysis may have applications to evaluation and ranking of intersections within corridors as under, near, or over saturation.

Should the Diverging Diamond Interchange Always be Considered a Diamond Interchange Form?

The diverging diamond interchange (DDI) has proved to be an ideal interchange solution because of its safety features, low costs, and operational benefits in different scenarios of turning movement volume. Pre vious studies have compared the DDI with other interchange forms by using the same number of through lanes for each interchange design. Those studies used microsimulation software for the analysis and had a limited number of turning movement combinations to sample. This study considered a large sample of turning movement combinations and compared more interchange configurations to determine whether the DDI might have more applications than previous studies have indicated. A basic form of the critical lane volume method was used to evaluate the different interchange configurations. Although this method is not the most perfect method, there is reason to believe that the results are accurate enough to indicate that the DDI may be a viable option in many more scenarios than previously thought. This study concludes that it is worthwhile for practitioners to consider the DDI for any interchange improvement when comparing it with other diamond interchange forms.

Improving Intersection Design Practices

This study aims to use operational characteristics to help determine the size and the design of intersections on the basis of a targeted level of operation. This approach will allow for a preliminary evaluation of a broader range of possible designs, by screening out those designs considered less desirable or inappropriate on the basis of operational performance. This approach will also allow for a more objective comparison of all alternatives because all options target the same operational service level. The use of the critical lane analysis method was considered an appropriate approach for developing such size estimates for intersections. Similar methods for stop-controlled and yield-controlled intersections were also identified because it was necessary to expand these methods to include unsignalized designs as well. The Intersection Design Alternative Tool developed through this effort is capable of evaluating 13 intersection alternatives and identifying preferred lane configurations from more than 12,000 available configurations.