Merging Trajectory Research Articles

Freeway merging trajectory prediction for automated vehicles using naturalistic driving data

Due to differences in speed and the complex interaction between merging and through-lane vehicles at freeway merging sections, crashes involving both human drivers and automated vehicles (AVs) persist. To assist AVs to predict the intentions of surrounding vehicles for further dynamic motion planning, researchers have focused on developing trajectory prediction algorithms. Few studies, however, have developed merging trajectory prediction models using naturalistic driving data in China, making it urgent to put it on the agenda for AVs’ safety and efficiency at freeway merging sections. Based on merging periods extracted from the Shanghai Naturalistic Driving Study (SH-NDS), this study compares merging behavior on freeways with through-lane speed limits of 80 km/h, 100 km/h, and 120 km/h using analysis of variance (ANOVA). Merging trajectory prediction algorithms for these three speed limit cases are trained and tested using backpropagation neural network (BPNN) and long short-term memory neural network (LSTM NN) approaches. Results show 1) significant differences among the three cases in all merging behavior variables except for longitudinal gap; and that 2) the BPNN algorithm for merging trajectory prediction demonstrates superior performance compared to the LSTM NN. Two major contributions to the safe operation of AVs are provided: 1) the developed algorithms can be integrated into AV systems to accurately predict real-time desired trajectories of nearby merging vehicles in uncongested traffic conditions, and assist ongoing motion planning strategies for AVs; and 2) the algorithms can be incorporated in simulation tests for AV safety evaluation involving freeway merging sections.

A Stackelberg game-based on-ramp merging controller for connected automated vehicles in mixed traffic flow

ABSTRACT This paper proposes a game theory-based on-ramp merging controller for connected automated vehicles (CAVs) in mixed traffic flow. First, a two-layer decision-making framework based on the Stackelberg game is designed to consider the fuel consumption and safety payoffs of mixed traffic flow under different driving behaviors. The upper layer of the framework determines the optimal merging decision (i.e. merging time and location) for on-ramp vehicles (RVs) based on the Stackelberg game. The lower layer optimizes the merging trajectory of CAVs to reduce energy consumption and safety risks during the ramp-merging process. Then, a driving behavior estimation algorithm is developed to describe the differences in mainline vehicles (MLVs) response to the merging behavior of RVs. Finally, the simulation experiments are adopted to verify the effectiveness and stability of the proposed framework. The results indicated that, the proposed framework promotes environmental protection, operational efficiency, and traffic flow stability in different traffic scenarios.

An enhanced motion planning approach by integrating driving heterogeneity and long-term trajectory prediction for automated driving systems: A highway merging case study

Navigating automated driving systems (ADSs) through complex driving environments is difficult. Predicting the driving behavior of surrounding human-driven vehicles (HDVs) is a critical component of an ADS. This paper proposes an enhanced motion-planning approach for an ADS in a highway-merging scenario. This method utilizes the results of two aspects: the driving behavior and long-term trajectory of surrounding HDVs, which are coupled using a hierarchical model that is used for the motion planning of an ADS to improve driving safety. An unsupervised clustering algorithm is utilized to classify HDV drivers into two categories: aggressive and normal, as part of predicting their driving behaviors. Subsequently, a logistic regression model is employed for driving style prediction. For trajectory prediction, a transformer-based model that concentrated parallelization computations on longer sequence predictions via a self-attention mechanism is developed. Based on the predicted driving styles and trajectories of the surrounding HDVs, an intelligent decision-making strategy is utilized for ADS motion planning. Finally, real-world traffic data collected from drones on a highway ramp in Xi’an is used as a case study to train and evaluate the proposed model. The results demonstrate that the proposed approach can predict HDVs merging trajectories with a mean squared error (MSE) smaller than 0.125 at 30 s away from the merging point, outperforming existing approaches in terms of predictable duration and accuracy. Furthermore, it exhibited safety improvements by adjusting the ADS motion state in advance with good predictive power for the surrounding HDVs’ motion. For both normal and aggressive driving styles, the ADS trajectories reached optimal safety at a prediction horizon of at least 10 s and over 6.67 s, respectively, when evaluating both time-to-collision (TTC) and deceleration rate to avoid a crash (DRAC) metrics. This indicates that our proposed procedures have improved safety for AVs with long-term predictive capabilities (i.e., over 6 s) for surrounding HDVs. Interestingly, the safety performance does not continue to improve with the increase in prediction horizon once the optimal safety performance (highest TTC and lowest DRAC) has been achieved for both normal and aggressive styles. This suggests that an excessively long prediction horizon (e.g., 30 s) is not always beneficial for safety performance of ADS in our case study. When ADS encounter aggressive HDVs, having a predicted surrounding HDV trajectory can extremely reduce crash risk and maintain a safe situation. This demonstrates that planning ADS trajectories with HDV predictions has significant effects on safety, especially for aggressive driving styles as compared to normal driving styles.

An improved scheme for merging trajectories in weighted ensemble simulations

An improved scheme for merging trajectories in weighted ensemble simulations

Research on Cooperative Control for On-Ramp Merging with Multiple Lanes in Connected and Automated Environments

This paper addresses the issue of on-ramp merging in multi-lane freeways and proposes a cooperative control method based on connected and automated vehicles. Focusing on a two-main-lane freeway scenario, the method consists of two key models: a merging sequence decision model and a motion planning model. The merging sequence decision model prioritizes collision avoidance by predicting the motion state and lane-changing trajectory of vehicles in the merging area. The motion planning model utilizes longitudinal and lateral cooperation to control the main lane vehicles to generate the merging gap through coordinated adjustments in the longitudinal speed or by performing lane changes. The optimal merging trajectory is determined using the entropy weight method, and a fast optimization method based on neural networks is employed. Through simulations considering different traffic density combinations, the proposed method is compared with traditional control schemes. Results demonstrate its superiority in improving traffic flow stability, rapidity, and overall efficiency.

A Game Lane Changing Model Considering Driver’s Risk Level in Ramp Merging Scenario

A ramp merging decision as an important part of the lane change model plays a crucial role in the efficiency and safety of the entire merging process. However, due to the inevitability of on-ramp merging, the limitations of the road environment, and the conflict between the merging vehicle and the following vehicle on the main road, it is difficult for human drivers to make optimal decisions in complex merging scenarios. First, based on the NGSIM dataset, a gain function is designed to represent the interaction between the ego vehicle (EV) and the surrounding vehicles, and the gain value is then used as one of the characteristic parameters. The K-means algorithm is employed to conduct a cluster analysis of the driving style under the condition of changing lanes. This paper models the interaction and conflict between the ego vehicle (vehicle merging) and the mainline lagging vehicle as a complete information non-cooperative game process. Further, various driving styles are coupled in the ramp decision model to mimic the different safety and travel efficiency preferences of human drivers. After EV decision-making, a quintic polynomial method with multi-constraints is proposed to implement merging trajectory planning. The proposed algorithm is tested and analyzed in an on-ramp scenario, and the results demonstrate that drivers with different driving styles can make correct decisions and complete the ramp merging. The changing trend of the speed and trajectory tests are also in line with the features of the driver’s driving style, offering a theoretical foundation for individualized on-ramp merging decisions.

Enhancing Cooperation of Vehicle Merging Control in Heavy Traffic Using Communication-Based Soft Actor-Critic Algorithm

A promising way to improve efficiency in highway on-ramp regions is to control connected and automated vehicles (CAVs) to pass the merging section sequentially. The primary objective of this paper is to incorporate the reinforcement learning (RL) technique into vehicle merging control to achieve global cooperation. A communication protocol among RL agents is integrated with the Soft Actor-Critic (CSAC) algorithm. The parallel SAC agents with a parameter-sharing structure cooperate to optimize the common reward function. It enables CAVs to know the actions of each other so that they proactively negotiate to adjust speeds. We designed a parsimonious state representation containing crucial merging information to speed up the RL training. The effects of the merging control strategy were investigated with the simulation model in scenarios with different CAV penetration rates and traffic flow compositions. Results showed that the CSAC-based merging strategy generated collision-free merging trajectories with a short travel time while guaranteeing traffic safety in various traffic conditions. Four baselines (including two rule-based and two RL-based merging strategies) were applied in the same scenarios for comparison. It was found that the proposed merging strategy took the safest merging behaviors (zero traffic conflicts) and reduced the most significant travel time (56.9%).

A Platoon-Based Hierarchical Merging Control for On-Ramp Vehicles Under Connected Environment

Connected autonomous vehicle technology is conductive to promoting the transition from traditional merging control (e.g., ramp metering) to automated merging control. This paper proposes a platoon-based hierarchical merging control algorithm for on-ramp vehicles to achieve automated merging control under connected traffic environment. The proposed algorithm optimizes merging maneuvers of on-ramp vehicles to smooth their merging trajectories without frequent decelerations or stops at the end of the ramp, and to minimize disruption to the mainline traffic in the merging zone. A tactical layer controller is designed to select pre-target merging gaps for on-ramp vehicles, in which the future motion (i.e., acceleration and deceleration) of mainline vehicles is considered through the grey prediction model. An operational layer controller is constructed based on model predictive control to adjust the speed of on-ramp vehicles in advance, and controls on-ramp vehicles to merge into the pre-target merging gaps under state constraints (i.e., safe headway, maximum speed and so on). Through numerical simulation, the effectiveness of the proposed algorithm is validated under different merging scenarios. It is shown that on-ramp vehicles smoothly merge into the mainline within the pre-target merging gap at the same speed as adjacent mainline vehicles. Compared with the baseline merging control algorithm, the proposed algorithm significantly reduces both fuel consumption and travel time of on-ramp vehicles, and improves passenger comfort.

Game Theoretic Merging Behavior Control for Autonomous Vehicle at Highway On-Ramp

In the most of previous studies, social interactions between vehicles are not considered explicitly when designing decision making and motion planning module. Nevertheless, the strong interaction exists in the most of driving scenarios, especially in highway junction. This paper presents a game theoretic merging behavior control system for autonomous vehicle at on-ramp junction considering the interaction between the merging vehicle and following vehicle in the main lane. In this work, a driving style estimation is proposed to deal with the heterogeneity of driving style. Then we adopt a model predictive control (MPC) method to plan the optimal merging trajectory based on the game theoretic decision making result. Finally, simulation and Human-in-the-loop (HIL) experiment result shows the effectiveness of our approach in on-ramp merging scenario.

A Cooperative Merging Strategy for Connected and Automated Vehicles Based on Game Theory With Transferable Utility

Traffic congestion is a serious social problem in modern society, while vehicle merging is one of the main causes of congestion since human driver has to decelerate to avoid collision when merging. Connected and automated vehicles (CAVs) can realize the coordinated merging which will improve the traffic efficiency, reduce the fuel consumption and improve the driving comfort. In this paper, a cooperative merging strategy for CAVs is proposed based on cooperative game theory with transferable utility (TU) and optimal control. By introducing the value of time (VOT), an economic payoff function including time benefit, fuel consumption and driving comfort is constructed. The cooperative game determines the merging sequence (MS) of vehicles and the side payment among them, and can achieve a win-win situation, while the coordinated merging trajectory of each vehicle is computed based on optimal control. The effectiveness and feasibility of the proposed framework are verified though simulation in different cases, and the comparison of simulation results indicates that the proposed framework can improve the economic benefit of vehicles and have the potential for practical application.

An integrated two‐dimensional merging trajectory optimization model for automated vehicles considering mixed traffic flow

Recently, automated vehicles have been recognized as a promising tool to address the problem of on-ramp merging. However, the complexity of the problem includes ignorance of the vehicle's lateral dynamics, the limitation of the fixed merging point, the mismatch problem caused by the sequential optimization scheme, and the fixed terminal states assumption. These factors make it intractable in practical driving scenarios. This paper proposed an integrated optimization model for on-ramp automated vehicles, which can guide the vehicle to complete the merging behaviour from the ramp lane to the main lane safely and efficiently. A merging path is first constructed in the two-dimensional plane with two critical parameters recommended by a neural network predictor, enabling it to incorporate both longitudinal and lateral dynamics. Then, an integrated Mixed Integer Quadratic Program (MIQP) model is built to determine the optimal velocity profiles and merging gap simultaneously while considering the safety and efficiency factors. Specifically, with the introduction of discretization and linearization techniques, linear collision avoidance constraints and smooth transition constraints can be built, which can address the challenging computational problem. The effectiveness of the proposed model is validated through the microscopic and macroscopic numerical results under different levels of mixed traffic.

Managing merging from a CAV lane to a human-driven vehicle lane considering the uncertainty of human driving

This paper proposes a control strategy for a freeway merging bottleneck consisting of a Connected and Automated Vehicle (CAV) exclusive lane and a human-driven vehicle (HDV) lane, aiming to achieve fuel economy and increase traffic efficiency. The trajectories of CAVs are optimized to enable them to smoothly merge into the gaps in the HDV lane. We utilize a stochastic car-following model to incorporate the uncertainty of HDVs and adopt the concept of α-percentile trajectory proposed in our earlier work (Xiong and Jiang, 2021) to estimate the trajectories of HDVs. Based on these, an optimization model is constructed to optimize the merging sequence and the merging trajectories of CAVs simultaneously. We use dynamic programming to solve the optimization model. Dividing RECTangles algorithm and Hamiltonian analysis are imbedded as a subroutine to obtain the energy efficient merging trajectory of each CAV. Simulation results show that the proposed control strategy is capable of reducing average fuel consumption and travel time under a wide range of inflow rates. The benefits depend on the inflow rate and the trajectory percentile α. When the total inflow rate is low, the impact of α is insignificant. If the total inflow rate increases to a high level, the impact of α becomes remarkable and the maximum benefits would be achieved at an intermediate range of α. Moreover, the computation efficiency of the proposed system is fast enough and can be implemented in real-time in the near future.

A Trajectory Optimization Strategy for Connected and Automated Vehicles at Junction of Freeway and Urban Road

The phenomenon of stop-and-go traffic and its environmental impact has become a crucial issue that needs to be tackled, in terms of the junctions between freeway and urban road networks, which consist of freeway off-ramps, downstream intersections, and the junction section. The development of Connected and Automated Vehicles (CAVs) has provided promising solutions to tackle the difficulties that arise along intersections and freeway off-ramps separately. However, several problems still exist that need to be handled in terms of junction structure, including vehicle merging trajectory optimization, vehicle crossing trajectory optimization, and heterogeneous decision-making. In this paper, a two-stage CAV trajectory optimization strategy is presented to improve fuel economy and to reduce delays through a joint framework. The first stage considers an approach to determine travel time considering the different topological structures of each subarea to ensure maximum capacity. In the second stage, Pontryagin’s Minimum Principle (PMP) is employed to construct Hamiltonian equations to smooth vehicle trajectory under the requirements of vehicle dynamics and safety. Targeted methods are devised to avoid driving backwards and to ensure an optimal vehicle gap, which make up for the shortcomings of the PMP theory. Finally, simulation experiments are designed to verify the effectiveness of the proposed strategy. The evaluation results show that our strategy could effectively militate travel delays and fuel consumption.

Learning Game-Theoretic Models of Multiagent Trajectories Using Implicit Layers

For prediction of interacting agents' trajectories, we propose an end-to-end trainable architecture that hybridizes neural nets with game-theoretic reasoning, has interpretable intermediate representations, and transfers to downstream decision making. It uses a net that reveals preferences from the agents' past joint trajectory, and a differentiable implicit layer that maps these preferences to local Nash equilibria, forming the modes of the predicted future trajectory. Additionally, it learns an equilibrium refinement concept. For tractability, we introduce a new class of continuous potential games and an equilibrium-separating partition of the action space. We provide theoretical results for explicit gradients and soundness. In experiments, we evaluate our approach on two real-world data sets, where we predict highway drivers' merging trajectories, and on a simple decision-making transfer task.

Differentially private and utility-aware publication of trajectory data

Trajectory data is valuable for various applications, especially for intelligent transportation systems, which hunger for plenty of trajectories. However, publishing trajectory data while respecting users’ privacy has been a long-standing challenge. Currently, the prevailing releasing solutions usually merge trajectory locations based on k-means and add unbounded noise with Laplace distribution to the count of trajectory to achieve differential privacy protection. The trajectory merging methods based on k-means have a low efficiency and unbounded noise with Laplace distribution will leak user’ privacy and suffer from serious utility loss. To solve the above two problems, we devise two differentially private and utility-aware publication methods of trajectory data. More specifically, we first propose two trajectory merging schemes based on k-means || clustering. The first one is to use k-means || clustering algorithm to cluster the location area, and all the points in the cluster are replaced by the center of cluster. The other is to utilize Staircase mechanism to perturb the cluster centers in order to improve the level of privacy protection. Afterwards, we propose a bounded Staircase noise generation algorithm to perturb the true count of generalized trajectories. We prove our proposed methods preserve differential privacy theoretically. Experimental comparison show that our proposed publication methods significantly outperform existing approaches in terms of data utility and efficiency.

Emergency vehicle lane pre-clearing: From microscopic cooperation to routing decision making

Emergency vehicles (EVs) play a crucial role in providing timely help for the general public in saving lives and avoiding property loss. However, very few efforts have been made for EV prioritization on normal road segments, such as the road section between intersections or highways between ramps. In this paper, we propose an EV lane pre-clearing strategy to prioritize EVs on such roads through cooperative driving with surrounding connected vehicles (CVs). The cooperative driving problem is formulated as a mixed-integer nonlinear programming (MINP) problem aiming at (i) guaranteeing the desired speed of EVs, and (ii) minimizing the disturbances on CVs. To tackle this NP-hard MINP problem, we formulate the model in a bi-level optimization manner to address these two objectives, respectively. In the lower-level problem, CVs in front of the emergency vehicle will be divided into several blocks. For each block, we developed an EV sorting algorithm to design optimal merging trajectories for CVs. With resultant sorting trajectories, a constrained optimization problem is solved in the upper-level to determine the initiation time/distance to conduct the sorting trajectories. Case studies show that with the proposed algorithm, emergency vehicles are able to drive at a desired speed while minimizing disturbances on normal traffic flows. We further reveal a linear relationship between the optimal solution and road density, which could help to improve EV routing decision makings when high-resolution data is not available.

Merging trajectory generation method using real-time optimization with enhanced robustness against sensor noise

To reduce drivers’ mental load and traffic congestion caused by merging maneuver, a merging trajectory generation method aiming for practical automatic driving was proposed in the past research by the authors. In this paper, the robustness of the method against sensor noises is enhanced. The robustness is improved by the dummy optimization variables that relax the equality constraints and the barrier functions. The stage costs composed by these introduced dummy variables are designed to generate safe and smooth merging maneuver. The effectiveness of the proposed method for a typical case is observed in the simulation results. To check if the proposed method works well under different initial conditions, 116 initial conditions are generated randomly. The proposed method solves all the cases of merging problem, while the conventional method fails in 80% of the cases.

Segmentation of crowd flow by trajectory clustering in active contours

Crowd analysis has become an important topic of research for visual surveillance community. This paper proposes an active contour-based trajectory clustering approach for crowd flow segmentation. To this end, the active contour method is applied to segment the foreground crowd region with an aim to optimize further tracking. From the segmented foreground region, spatiotemporal interest points are detected and tracked to extract crowd trajectories. The trajectories are then parameterized by their shape, location information, flow direction, and neighborhood density. A clustering algorithm is designed to cluster these trajectories, and further flow patterns are segmented by merging trajectory clusters on the basis of their spatial overlapping and distinction in location and in flow direction. Once the flow patterns are segmented, trajectory density of each segment is estimated to analyze crowd flow. Experiments are conducted on three publicly available UCF Web, Collective Motion, and Violent Flows crowd datasets. The proposed work is compared with various state-of-the-art methods and achieves remarkable accuracy while maintaining the lower computational complexity.

Single-Lane Roundabout Manager under Fully Automated Vehicle Environment

In the advent of new automation and communication technologies, the introduction of connected and autonomous vehicles (CAVs) can make efficient use of the space on our road networks. Since roundabouts suffer from lower efficiencies when traffic flows are unbalanced and unfamiliar drivers are present, CAVs have the potential to improve traffic operations, reducing lost time and inefficiency in gap-usage. The aim of this research is to take advantage of those recently available technologies to design a traffic management system for roundabouts. Such a system can provide CAVs with optimal trajectories to negotiate the roundabout, maximizing throughput and minimizing control delay. The rule-based Roundabout Manager algorithm developed considers the roundabout as a whole system, assessing the priority of incoming vehicles on a first-come-first-served scheduling to solve conflicts. The management system takes into consideration the geometry of the roundabout, including the flared entries and exits and the location of conflict sections based on merging trajectories of vehicles in negotiating the roundabout. To illustrate the operation of the algorithm, a total of 15 undersaturated demand scenarios with 10 replications per scenario were simulated. From the results, it can be concluded that the system can reduce control delay for medium demand scenarios, maximizing the throughput for all demand scenarios. The Roundabout Manager can work in real time providing optimized trajectories in less than 0.02 s at any traffic flow rate simulated.

Experimental investigations on co-rotating vortex pair merger in convergent/divergent channel flow with single-side-wall deflection

The co-rotating vortex pair merger in the convergent and divergent channel flow was investigated in both equal and unequal cases. The crossflow flow phenomenon of vortex pair merger was acquired by applying particle image velocimetry in a series of streamwise locations. The main finding is that the resultant single-side-wall deflection convergent and divergent channel flow can vary the merging rate and merging trajectories of the equal vortex pair. In the unequal vortex merger, distortion and absorption of the weaker vortex by the stronger vortex were observed, which is different from the mutual induction phenomenon in the equal strength vortex pair case. Furthermore, it was found that the flow converging and diverging have common effects on the merging process in both equal and unequal vortex merger. In the convergent channel flow, vortex pair separation experienced early reduction at upper stream locations, and the merger was accelerated. As the vortex pair developed further downstream, the difference in the merger progress among different channel flow environments becomes less significant, which is believed to be due to the combined effect of pressure gradient and developing time variations.